%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV156^5 : 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 : n025.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 09:40:25 AM UTC 2026
% Result : Theorem 1.46s 1.49s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 23
% Syntax : Number of formulae : 414 ( 32 unt; 0 typ; 22 def)
% Number of atoms : 4865 ( 388 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 16441 ( 579 ~; 937 |; 879 &;10447 @)
% ( 22 <=>;1304 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 1290 (1290 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 54 con; 0-2 aty)
% (2273 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2616 (2355 ^; 261 !; 0 ?;2616 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a > a > $o ).
thf(func_def_22,type,
sK3: a ).
thf(func_def_23,type,
sK4: a > a > $o ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a > a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a ).
thf(func_def_30,type,
sK11: a > a > $o ).
thf(func_def_31,type,
sK12: ( a > a > $o ) > a ).
thf(func_def_32,type,
sK13: a ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a > a > $o ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a ).
thf(func_def_50,type,
sK31: a ).
thf(func_def_51,type,
sK32: a ).
thf(func_def_52,type,
sK33: a ).
thf(func_def_53,type,
sK34: a ).
thf(func_def_54,type,
sK35: a ).
thf(func_def_55,type,
sK36: a ).
thf(f2752,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f29,f264,f285,f463,f488,f500,f775,f845,f877,f912,f1105,f1247,f1288,f1565,f1657,f1664,f1671,f1863,f2000,f2070,f2570,f2588,f2751]) ).
thf(f2751,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f2750]) ).
thf(f2750,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f2749]) ).
thf(f2749,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_25 ),
inference(backward_demodulation,[status(thm)],[f2616,f2748]) ).
thf(f2748,plain,
( ( $false
= ( sK11 @ sK29 @ sK28 ) )
| ~ spl0_9
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f2747]) ).
thf(f2747,plain,
( ( $false
= ( $true
=> ( sK11 @ sK29 @ sK28 ) ) )
| ~ spl0_9
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f2746]) ).
thf(f2746,plain,
( ( ( ( ( sK2 @ sK29 @ sK28 )
| $true )
=> ( sK11 @ sK29 @ sK28 ) )
= $false )
| ~ spl0_9
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f2745,f1287]) ).
thf(f1287,plain,
( ( $true
= ( sK4 @ sK29 @ sK28 ) )
| ~ spl0_25 ),
inference(avatar_component_clause,[status(thm)],[f1286]) ).
thf(f1286,definition,
( spl0_25
<=> ( $true
= ( sK4 @ sK29 @ sK28 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition]) ).
thf(f2745,plain,
( ( ( ( ( sK2 @ sK29 @ sK28 )
| ( sK4 @ sK29 @ sK28 ) )
=> ( sK11 @ sK29 @ sK28 ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f2744]) ).
thf(f2744,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK28 )
| ( sK4 @ Y0 @ sK28 ) )
=> ( sK11 @ Y0 @ sK28 ) )
@ sK29 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f2732]) ).
thf(f2732,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK28 )
| ( sK4 @ Y0 @ sK28 ) )
=> ( sK11 @ Y0 @ sK28 ) ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f2725]) ).
thf(f2725,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ sK28 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f462]) ).
thf(f462,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f461]) ).
thf(f461,definition,
( spl0_9
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f2616,plain,
( ( $true
= ( sK11 @ sK29 @ sK28 ) )
| ~ spl0_2
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f2615]) ).
thf(f2615,plain,
( ( $true
= ( $true
=> ( sK11 @ sK29 @ sK28 ) ) )
| ~ spl0_2
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f2611]) ).
thf(f2611,plain,
( ( $true
= ( ( $true
| ( sK2 @ sK29 @ sK28 ) )
=> ( sK11 @ sK29 @ sK28 ) ) )
| ~ spl0_2
| ~ spl0_25 ),
inference(superposition,[status(thm)],[f2451,f1287]) ).
thf(f2451,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK4 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) )
=> ( sK11 @ X2 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2450]) ).
thf(f2450,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f2440]) ).
thf(f2440,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2439]) ).
thf(f2439,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f2274]) ).
thf(f2274,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f2203]) ).
thf(f2203,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f2197]) ).
thf(f2197,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK11 @ sK8 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2196]) ).
thf(f2196,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK11 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f2118]) ).
thf(f2118,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f2101]) ).
thf(f2101,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK9 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2100]) ).
thf(f2100,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f2094]) ).
thf(f2094,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2093]) ).
thf(f2093,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f2080]) ).
thf(f2080,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2079]) ).
thf(f2079,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl0_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f2588,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f2587]) ).
thf(f2587,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f2586]) ).
thf(f2586,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f2585]) ).
thf(f2585,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f2584]) ).
thf(f2584,plain,
( ( $true
= ( ~ ( ( sK4 @ sK21 @ sK22 )
| $true ) ) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f2578,f911]) ).
thf(f911,plain,
( ( $true
= ( sK2 @ sK21 @ sK22 ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f910]) ).
thf(f910,definition,
( spl0_17
<=> ( $true
= ( sK2 @ sK21 @ sK22 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f2578,plain,
( ( $true
= ( ~ ( ( sK4 @ sK21 @ sK22 )
| ( sK2 @ sK21 @ sK22 ) ) ) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f2574]) ).
thf(f2574,plain,
( ( $true
= ( ( ( sK4 @ sK21 @ sK22 )
| ( sK2 @ sK21 @ sK22 ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f2451,f2573]) ).
thf(f2573,plain,
( ( ( sK11 @ sK21 @ sK22 )
= $false )
| ~ spl0_7
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f2572]) ).
thf(f2572,plain,
( ( ( $true
=> ( sK11 @ sK21 @ sK22 ) )
= $false )
| ~ spl0_7
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f2571]) ).
thf(f2571,plain,
( ( $false
= ( ( $true
| ( sK4 @ sK21 @ sK22 ) )
=> ( sK11 @ sK21 @ sK22 ) ) )
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f2564,f911]) ).
thf(f2564,plain,
( ( ( ( ( sK2 @ sK21 @ sK22 )
| ( sK4 @ sK21 @ sK22 ) )
=> ( sK11 @ sK21 @ sK22 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f2563]) ).
thf(f2563,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK21 @ Y0 )
| ( sK4 @ sK21 @ Y0 ) )
=> ( sK11 @ sK21 @ Y0 ) )
@ sK22 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f2555]) ).
thf(f2555,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK21 @ Y0 )
| ( sK4 @ sK21 @ Y0 ) )
=> ( sK11 @ sK21 @ Y0 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f2552]) ).
thf(f2552,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK21 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f284]) ).
thf(f284,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f283]) ).
thf(f283,definition,
( spl0_7
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f2570,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[status(thm)],[f2569]) ).
thf(f2569,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f2568]) ).
thf(f2568,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f2485,f2567]) ).
thf(f2567,plain,
( ( ( sK11 @ sK21 @ sK22 )
= $false )
| ~ spl0_7
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f2566]) ).
thf(f2566,plain,
( ( ( $true
=> ( sK11 @ sK21 @ sK22 ) )
= $false )
| ~ spl0_7
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f2565]) ).
thf(f2565,plain,
( ( ( ( ( sK2 @ sK21 @ sK22 )
| $true )
=> ( sK11 @ sK21 @ sK22 ) )
= $false )
| ~ spl0_7
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f2564,f908]) ).
thf(f908,plain,
( ( ( sK4 @ sK21 @ sK22 )
= $true )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f907]) ).
thf(f907,definition,
( spl0_16
<=> ( ( sK4 @ sK21 @ sK22 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f2485,plain,
( ( ( sK11 @ sK21 @ sK22 )
= $true )
| ~ spl0_2
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f2484]) ).
thf(f2484,plain,
( ( ( $true
=> ( sK11 @ sK21 @ sK22 ) )
= $true )
| ~ spl0_2
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f2469]) ).
thf(f2469,plain,
( ( $true
= ( ( $true
| ( sK2 @ sK21 @ sK22 ) )
=> ( sK11 @ sK21 @ sK22 ) ) )
| ~ spl0_2
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f2451,f908]) ).
thf(f2070,plain,
( ~ spl0_10
| ~ spl0_12
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f2069]) ).
thf(f2069,plain,
( $false
| ~ spl0_10
| ~ spl0_12
| ~ spl0_20 ),
inference(trivial_inequality_removal,[status(thm)],[f2068]) ).
thf(f2068,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_20 ),
inference(boolean_simplification,[status(thm)],[f2067]) ).
thf(f2067,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_20 ),
inference(boolean_simplification,[status(thm)],[f2066]) ).
thf(f2066,plain,
( ( $true
= ( ~ ( $true
| ( sK4 @ sK35 @ sK36 ) ) ) )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_20 ),
inference(forward_demodulation,[status(thm)],[f2060,f2053]) ).
thf(f2053,plain,
( ( ( sK2 @ sK35 @ sK36 )
= $true )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[status(thm)],[f2051]) ).
thf(f2051,plain,
( ( ( ( sK2 @ sK35 @ sK36 )
=> ( sK20 @ sK35 @ sK36 ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[status(thm)],[f2050]) ).
thf(f2050,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK35 @ Y0 )
=> ( sK20 @ sK35 @ Y0 ) )
@ sK36 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[status(thm)],[f2046]) ).
thf(f2046,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK35 @ Y0 )
=> ( sK20 @ sK35 @ Y0 ) ) ) )
| ~ spl0_20 ),
inference(beta_eta_normalization,[status(thm)],[f2042]) ).
thf(f2042,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) )
@ sK35 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[status(thm)],[f1101]) ).
thf(f1101,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f1100]) ).
thf(f1100,definition,
( spl0_20
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition]) ).
thf(f2060,plain,
( ( ( ~ ( ( sK2 @ sK35 @ sK36 )
| ( sK4 @ sK35 @ sK36 ) ) )
= $true )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_20 ),
inference(boolean_simplification,[status(thm)],[f2056]) ).
thf(f2056,plain,
( ( ( ( ( sK2 @ sK35 @ sK36 )
| ( sK4 @ sK35 @ sK36 ) )
=> $false )
= $true )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_20 ),
inference(superposition,[status(thm)],[f1986,f2055]) ).
thf(f2055,plain,
( ( ( sK20 @ sK35 @ sK36 )
= $false )
| ~ spl0_20 ),
inference(boolean_simplification,[status(thm)],[f2054]) ).
thf(f2054,plain,
( ( $false
= ( $true
=> ( sK20 @ sK35 @ sK36 ) ) )
| ~ spl0_20 ),
inference(backward_demodulation,[status(thm)],[f2051,f2053]) ).
thf(f1986,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) )
=> ( sK20 @ X2 @ X1 ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1985]) ).
thf(f1985,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK20 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_10
| ~ spl0_12 ),
inference(pi_clausification,[status(thm)],[f1981]) ).
thf(f1981,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK20 @ Y0 @ X1 ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1980]) ).
thf(f1980,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(pi_clausification,[status(thm)],[f1903]) ).
thf(f1903,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_10
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f1872]) ).
thf(f1872,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_10
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f1868]) ).
thf(f1868,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
=> ( sK20 @ sK19 @ sK18 ) )
= $false )
| ~ spl0_10
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1867]) ).
thf(f1867,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) )
@ sK20 ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f1866]) ).
thf(f1866,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f1865]) ).
thf(f1865,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f1864]) ).
thf(f1864,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f1714,f841]) ).
thf(f841,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f840]) ).
thf(f840,definition,
( spl0_12
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f1714,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f1713]) ).
thf(f1713,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) )
@ sK19 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f1692]) ).
thf(f1692,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f1691]) ).
thf(f1691,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f496]) ).
thf(f496,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f495]) ).
thf(f495,definition,
( spl0_10
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f2000,plain,
( ~ spl0_10
| ~ spl0_12
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f1999]) ).
thf(f1999,plain,
( $false
| ~ spl0_10
| ~ spl0_12
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f1998]) ).
thf(f1998,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f1992,f1917]) ).
thf(f1917,plain,
( ( $false
= ( sK20 @ sK33 @ sK34 ) )
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f1916]) ).
thf(f1916,plain,
( ( $false
= ( $true
=> ( sK20 @ sK33 @ sK34 ) ) )
| ~ spl0_21 ),
inference(backward_demodulation,[status(thm)],[f1911,f1915]) ).
thf(f1915,plain,
( ( $true
= ( ( sK20 @ sK33 @ sK32 )
& ( sK20 @ sK32 @ sK34 ) ) )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[status(thm)],[f1911]) ).
thf(f1911,plain,
( ( ( ( ( sK20 @ sK33 @ sK32 )
& ( sK20 @ sK32 @ sK34 ) )
=> ( sK20 @ sK33 @ sK34 ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[status(thm)],[f1910]) ).
thf(f1910,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK20 @ sK33 @ sK32 )
& ( sK20 @ sK32 @ Y0 ) )
=> ( sK20 @ sK33 @ Y0 ) )
@ sK34 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[status(thm)],[f1907]) ).
thf(f1907,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK20 @ sK33 @ sK32 )
& ( sK20 @ sK32 @ Y0 ) )
=> ( sK20 @ sK33 @ Y0 ) ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[status(thm)],[f1906]) ).
thf(f1906,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ Y0 @ sK32 )
& ( sK20 @ sK32 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) )
@ sK33 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[status(thm)],[f1870]) ).
thf(f1870,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ Y0 @ sK32 )
& ( sK20 @ sK32 @ Y1 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[status(thm)],[f1869]) ).
thf(f1869,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) )
@ sK32 )
= $false )
| ~ spl0_21 ),
inference(sigma_clausification,[status(thm)],[f1104]) ).
thf(f1104,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f1103]) ).
thf(f1103,definition,
( spl0_21
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f1992,plain,
( ( $true
= ( sK20 @ sK33 @ sK34 ) )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f1990]) ).
thf(f1990,plain,
( ( $true
= ( $true
=> ( sK20 @ sK33 @ sK34 ) ) )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f1948,f1937]) ).
thf(f1937,plain,
( ( $true
= ( sK20 @ sK32 @ sK34 ) )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[status(thm)],[f1915]) ).
thf(f1948,plain,
( ! [X0: a] :
( ( ( sK20 @ sK32 @ X0 )
=> ( sK20 @ sK33 @ X0 ) )
= $true )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f1944]) ).
thf(f1944,plain,
( ! [X0: a] :
( $true
= ( ( ( sK20 @ sK32 @ X0 )
& $true )
=> ( sK20 @ sK33 @ X0 ) ) )
| ~ spl0_10
| ~ spl0_12
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f1919,f1940]) ).
thf(f1940,plain,
( ( $true
= ( sK20 @ sK33 @ sK32 ) )
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f1939]) ).
thf(f1939,plain,
( ( $true
= ( ( sK20 @ sK33 @ sK32 )
& $true ) )
| ~ spl0_21 ),
inference(backward_demodulation,[status(thm)],[f1915,f1937]) ).
thf(f1919,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK20 @ X3 @ X2 )
& ( sK20 @ X1 @ X3 ) )
=> ( sK20 @ X1 @ X2 ) )
= $true )
| ~ spl0_10
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1918]) ).
thf(f1918,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK20 @ Y0 @ X2 )
& ( sK20 @ X1 @ Y0 ) )
=> ( sK20 @ X1 @ X2 ) )
@ X3 ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(pi_clausification,[status(thm)],[f1913]) ).
thf(f1913,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK20 @ Y0 @ X2 )
& ( sK20 @ X1 @ Y0 ) )
=> ( sK20 @ X1 @ X2 ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1912]) ).
thf(f1912,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ X1 @ Y1 ) )
=> ( sK20 @ X1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(pi_clausification,[status(thm)],[f1909]) ).
thf(f1909,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ X1 @ Y1 ) )
=> ( sK20 @ X1 @ Y0 ) ) ) )
= $true )
| ~ spl0_10
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1908]) ).
thf(f1908,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(pi_clausification,[status(thm)],[f1905]) ).
thf(f1905,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f1904]) ).
thf(f1904,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f1872,f1903]) ).
thf(f1863,plain,
( ~ spl0_10
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f1862]) ).
thf(f1862,plain,
( $false
| ~ spl0_10
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1861]) ).
thf(f1861,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1860]) ).
thf(f1860,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_10
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1859]) ).
thf(f1859,plain,
( ( $true
= ( ~ ( ( sK2 @ sK23 @ sK24 )
| $true ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f1858,f1846]) ).
thf(f1846,plain,
( ( $true
= ( sK4 @ sK23 @ sK24 ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f1844]) ).
thf(f1844,plain,
( ( $false
= ( ( sK4 @ sK23 @ sK24 )
=> ( sK20 @ sK23 @ sK24 ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f1843]) ).
thf(f1843,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK4 @ sK23 @ Y0 )
=> ( sK20 @ sK23 @ Y0 ) )
@ sK24 ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(sigma_clausification,[status(thm)],[f1840]) ).
thf(f1840,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK23 @ Y0 )
=> ( sK20 @ sK23 @ Y0 ) ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f1838]) ).
thf(f1838,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) )
@ sK23 ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(sigma_clausification,[status(thm)],[f1835]) ).
thf(f1835,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(not_proxy_clausification,[status(thm)],[f1807]) ).
thf(f1807,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1806]) ).
thf(f1806,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
& $true ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f1805,f1744]) ).
thf(f1744,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f1739]) ).
thf(f1739,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_10
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f1734]) ).
thf(f1734,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
=> ( sK20 @ sK19 @ sK18 ) )
= $false )
| ~ spl0_10
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f1733]) ).
thf(f1733,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) )
@ sK20 ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(sigma_clausification,[status(thm)],[f1717]) ).
thf(f1717,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1716]) ).
thf(f1716,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1715]) ).
thf(f1715,plain,
( ( ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
= $false )
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f1714,f844]) ).
thf(f844,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f843]) ).
thf(f843,definition,
( spl0_13
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f1805,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1804]) ).
thf(f1804,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f1799,f1738]) ).
thf(f1738,plain,
( ( ( sK20 @ sK19 @ sK18 )
= $false )
| ~ spl0_10
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f1734]) ).
thf(f1799,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK19 @ sK18 ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f1798]) ).
thf(f1798,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) )
@ X1 )
= $true )
| ~ spl0_13 ),
inference(pi_clausification,[status(thm)],[f844]) ).
thf(f1858,plain,
( ( $true
= ( ~ ( ( sK2 @ sK23 @ sK24 )
| ( sK4 @ sK23 @ sK24 ) ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1857]) ).
thf(f1857,plain,
( ( $true
= ( ( ( sK2 @ sK23 @ sK24 )
| ( sK4 @ sK23 @ sK24 ) )
=> $false ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f1761,f1845]) ).
thf(f1845,plain,
( ( ( sK20 @ sK23 @ sK24 )
= $false )
| ~ spl0_10
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f1844]) ).
thf(f1761,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) )
=> ( sK20 @ X2 @ X1 ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f1760]) ).
thf(f1760,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK20 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_10
| ~ spl0_13 ),
inference(pi_clausification,[status(thm)],[f1755]) ).
thf(f1755,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK20 @ Y0 @ X1 ) ) ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f1754]) ).
thf(f1754,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(pi_clausification,[status(thm)],[f1747]) ).
thf(f1747,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_10
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f1746]) ).
thf(f1746,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_10
| ~ spl0_13 ),
inference(backward_demodulation,[status(thm)],[f1739,f1744]) ).
thf(f1671,plain,
( ~ spl0_15
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f1670]) ).
thf(f1670,plain,
( $false
| ~ spl0_15
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f1669]) ).
thf(f1669,plain,
( ( $true = $false )
| ~ spl0_15
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1668]) ).
thf(f1668,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_15
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1665]) ).
thf(f1665,plain,
( ( $true
= ( ~ ( ( sK4 @ sK30 @ sK31 )
| $true ) ) )
| ~ spl0_15
| ~ spl0_29 ),
inference(backward_demodulation,[status(thm)],[f1647,f1656]) ).
thf(f1656,plain,
( ( $true
= ( sK2 @ sK30 @ sK31 ) )
| ~ spl0_29 ),
inference(avatar_component_clause,[status(thm)],[f1655]) ).
thf(f1655,definition,
( spl0_29
<=> ( $true
= ( sK2 @ sK30 @ sK31 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition]) ).
thf(f1647,plain,
( ( $true
= ( ~ ( ( sK4 @ sK30 @ sK31 )
| ( sK2 @ sK30 @ sK31 ) ) ) )
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f1643]) ).
thf(f1643,plain,
( ( $true
= ( ( ( sK4 @ sK30 @ sK31 )
| ( sK2 @ sK30 @ sK31 ) )
=> $false ) )
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f61,f1634]) ).
thf(f1634,plain,
( ( $false
= ( sK6 @ sK30 @ sK31 ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f1633]) ).
thf(f1633,plain,
( ( ( ( ( sK2 @ sK30 @ sK31 )
| ( sK4 @ sK30 @ sK31 ) )
=> ( sK6 @ sK30 @ sK31 ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f1632]) ).
thf(f1632,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK30 @ Y0 )
| ( sK4 @ sK30 @ Y0 ) )
=> ( sK6 @ sK30 @ Y0 ) )
@ sK31 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f1613]) ).
thf(f1613,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK30 @ Y0 )
| ( sK4 @ sK30 @ Y0 ) )
=> ( sK6 @ sK30 @ Y0 ) ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f1612]) ).
thf(f1612,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK30 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f876]) ).
thf(f876,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f875]) ).
thf(f875,definition,
( spl0_15
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f61,plain,
! [X2: a,X1: a] :
( ( ( ( sK4 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
=> ( sK6 @ sK3 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) )
@ sK6 ) ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( Y0 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( Y0 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a,X3: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X7 @ X5 ) )
=> ( X4 @ X7 @ X6 ) )
& ! [X8: a,X9: a] :
( ( ( X3 @ X9 @ X8 )
| ( X1 @ X9 @ X8 ) )
=> ( X4 @ X9 @ X8 ) ) )
=> ( X4 @ X2 @ X0 ) )
| ( ! [X10: a,X11: a,X12: a] :
( ( ! [X13: a > a > $o] :
( ( ! [X14: a,X15: a,X16: a] :
( ( ( X13 @ X15 @ X16 )
& ( X13 @ X16 @ X14 ) )
=> ( X13 @ X15 @ X14 ) )
& ! [X17: a,X18: a] :
( ( ( X1 @ X18 @ X17 )
| ( X3 @ X18 @ X17 ) )
=> ( X13 @ X18 @ X17 ) ) )
=> ( X13 @ X11 @ X10 ) )
& ! [X19: a > a > $o] :
( ( ! [X20: a,X21: a,X22: a] :
( ( ( X19 @ X20 @ X22 )
& ( X19 @ X22 @ X21 ) )
=> ( X19 @ X20 @ X21 ) )
& ! [X23: a,X24: a] :
( ( ( X1 @ X23 @ X24 )
| ( X3 @ X23 @ X24 ) )
=> ( X19 @ X23 @ X24 ) ) )
=> ( X19 @ X10 @ X12 ) ) )
=> ! [X25: a > a > $o] :
( ( ! [X26: a,X27: a,X28: a] :
( ( ( X25 @ X27 @ X26 )
& ( X25 @ X26 @ X28 ) )
=> ( X25 @ X27 @ X28 ) )
& ! [X29: a,X30: a] :
( ( ( X3 @ X29 @ X30 )
| ( X1 @ X29 @ X30 ) )
=> ( X25 @ X29 @ X30 ) ) )
=> ( X25 @ X11 @ X12 ) ) )
& ! [X31: a,X32: a] :
( ( ! [X33: a > a > $o] :
( ( ! [X34: a,X35: a,X36: a] :
( ( ( X33 @ X36 @ X34 )
& ( X33 @ X35 @ X36 ) )
=> ( X33 @ X35 @ X34 ) )
& ! [X37: a,X38: a] :
( ( X3 @ X38 @ X37 )
=> ( X33 @ X38 @ X37 ) ) )
=> ( X33 @ X31 @ X32 ) )
| ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a,X42: a] :
( ( ( X39 @ X42 @ X40 )
& ( X39 @ X40 @ X41 ) )
=> ( X39 @ X42 @ X41 ) )
& ! [X43: a,X44: a] :
( ( X1 @ X44 @ X43 )
=> ( X39 @ X44 @ X43 ) ) )
=> ( X39 @ X31 @ X32 ) ) )
=> ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a,X48: a] :
( ( ( X45 @ X48 @ X46 )
& ( X45 @ X46 @ X47 ) )
=> ( X45 @ X48 @ X47 ) )
& ! [X49: a,X50: a] :
( ( ( X1 @ X49 @ X50 )
| ( X3 @ X49 @ X50 ) )
=> ( X45 @ X49 @ X50 ) ) )
=> ( X45 @ X31 @ X32 ) ) )
& ~ ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a,X54: a] :
( ( ( X51 @ X52 @ X54 )
& ( X51 @ X53 @ X52 ) )
=> ( X51 @ X53 @ X54 ) )
& ! [X55: a,X56: a] :
( ( ( X1 @ X56 @ X55 )
| ( X3 @ X56 @ X55 ) )
=> ( X51 @ X56 @ X55 ) ) )
=> ( X51 @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X1: a > a > $o,X2: a,X0: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X6: a,X7: a,X5: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
| ( ! [X6: a,X5: a,X7: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X10: a,X8: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X4: a > a > $o] :
( ( ! [X8: a,X10: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X6 @ X7 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X7 ) ) )
& ! [X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ~ ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X3: a,X1: a > a > $o,X2: a,X0: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X6: a,X7: a,X5: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
| ( ! [X6: a,X5: a,X7: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X10: a,X8: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X4: a > a > $o] :
( ( ! [X8: a,X10: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X6 @ X7 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X7 ) ) )
& ! [X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ~ ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6Vfhle69yx/DTF2THF_27930.p',cTHM250H_pme) ).
thf(f1664,plain,
( ~ spl0_15
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f1663]) ).
thf(f1663,plain,
( $false
| ~ spl0_15
| ~ spl0_28 ),
inference(trivial_inequality_removal,[status(thm)],[f1662]) ).
thf(f1662,plain,
( ( $true = $false )
| ~ spl0_15
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1661]) ).
thf(f1661,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_15
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1658]) ).
thf(f1658,plain,
( ( ( ~ ( $true
| ( sK2 @ sK30 @ sK31 ) ) )
= $true )
| ~ spl0_15
| ~ spl0_28 ),
inference(backward_demodulation,[status(thm)],[f1647,f1653]) ).
thf(f1653,plain,
( ( $true
= ( sK4 @ sK30 @ sK31 ) )
| ~ spl0_28 ),
inference(avatar_component_clause,[status(thm)],[f1652]) ).
thf(f1652,definition,
( spl0_28
<=> ( $true
= ( sK4 @ sK30 @ sK31 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition]) ).
thf(f1657,plain,
( spl0_28
| spl0_29
| ~ spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f1650,f875,f1655,f1652]) ).
thf(f1650,plain,
( ( $true
= ( sK2 @ sK30 @ sK31 ) )
| ( $true
= ( sK4 @ sK30 @ sK31 ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f1635]) ).
thf(f1635,plain,
( ( $true
= ( ( sK2 @ sK30 @ sK31 )
| ( sK4 @ sK30 @ sK31 ) ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f1633]) ).
thf(f1565,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[status(thm)],[f1564]) ).
thf(f1564,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_24 ),
inference(trivial_inequality_removal,[status(thm)],[f1563]) ).
thf(f1563,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_24 ),
inference(forward_demodulation,[status(thm)],[f1551,f1270]) ).
thf(f1270,plain,
( ( $false
= ( sK11 @ sK29 @ sK28 ) )
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1269]) ).
thf(f1269,plain,
( ( $false
= ( $true
=> ( sK11 @ sK29 @ sK28 ) ) )
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f1260,f1268]) ).
thf(f1268,plain,
( ( $true
= ( ( sK2 @ sK29 @ sK28 )
| ( sK4 @ sK29 @ sK28 ) ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f1260]) ).
thf(f1260,plain,
( ( ( ( ( sK2 @ sK29 @ sK28 )
| ( sK4 @ sK29 @ sK28 ) )
=> ( sK11 @ sK29 @ sK28 ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f1259]) ).
thf(f1259,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK28 )
| ( sK4 @ Y0 @ sK28 ) )
=> ( sK11 @ Y0 @ sK28 ) )
@ sK29 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f1256]) ).
thf(f1256,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK28 )
| ( sK4 @ Y0 @ sK28 ) )
=> ( sK11 @ Y0 @ sK28 ) ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f1255]) ).
thf(f1255,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ sK28 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f462]) ).
thf(f1551,plain,
( ( $true
= ( sK11 @ sK29 @ sK28 ) )
| ~ spl0_2
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f1550]) ).
thf(f1550,plain,
( ( $true
= ( $true
=> ( sK11 @ sK29 @ sK28 ) ) )
| ~ spl0_2
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f1543]) ).
thf(f1543,plain,
( ( ( ( ( sK4 @ sK29 @ sK28 )
| $true )
=> ( sK11 @ sK29 @ sK28 ) )
= $true )
| ~ spl0_2
| ~ spl0_24 ),
inference(superposition,[status(thm)],[f1526,f1284]) ).
thf(f1284,plain,
( ( $true
= ( sK2 @ sK29 @ sK28 ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[status(thm)],[f1283]) ).
thf(f1283,definition,
( spl0_24
<=> ( $true
= ( sK2 @ sK29 @ sK28 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition]) ).
thf(f1526,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK4 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) )
=> ( sK11 @ X2 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1525]) ).
thf(f1525,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f1513]) ).
thf(f1513,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1512]) ).
thf(f1512,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f1330]) ).
thf(f1330,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1274]) ).
thf(f1274,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1272]) ).
thf(f1272,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK11 @ sK8 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1271]) ).
thf(f1271,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK11 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f1264]) ).
thf(f1264,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f1263]) ).
thf(f1263,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f1258,f1262]) ).
thf(f1262,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK9 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1258]) ).
thf(f1258,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK9 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1257]) ).
thf(f1257,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f1254]) ).
thf(f1254,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1253]) ).
thf(f1253,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f1252]) ).
thf(f1252,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1251]) ).
thf(f1251,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f1288,plain,
( spl0_24
| spl0_25
| ~ spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f1281,f461,f1286,f1283]) ).
thf(f1281,plain,
( ( $true
= ( sK2 @ sK29 @ sK28 ) )
| ( $true
= ( sK4 @ sK29 @ sK28 ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f1268]) ).
thf(f1247,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[status(thm)],[f1246]) ).
thf(f1246,plain,
( $false
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1243]) ).
thf(f1243,plain,
( ( $true = $false )
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f106,f1222]) ).
thf(f1222,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK26 @ Y0 )
& ( sK6 @ Y0 @ sK25 ) )
=> ( sK6 @ sK26 @ sK25 ) ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f1221]) ).
thf(f1221,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ sK25 ) )
=> ( sK6 @ Y0 @ sK25 ) ) )
@ sK26 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[status(thm)],[f1218]) ).
thf(f1218,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ sK25 ) )
=> ( sK6 @ Y0 @ sK25 ) ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f1217]) ).
thf(f1217,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ sK25 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[status(thm)],[f873]) ).
thf(f873,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f872]) ).
thf(f872,definition,
( spl0_14
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f106,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y0 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f37,f45]) ).
thf(f1105,plain,
( spl0_20
| spl0_21
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f1096,f840,f495,f1103,f1100]) ).
thf(f1096,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_10
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f1087]) ).
thf(f1087,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(not_proxy_clausification,[status(thm)],[f1061]) ).
thf(f1061,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_10
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f1060]) ).
thf(f1060,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK20 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y1 @ Y0 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y1 @ Y2 ) ) ) ) ) )
=> $false ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f1047,f1011]) ).
thf(f1011,plain,
( ( ( sK20 @ sK19 @ sK18 )
= $false )
| ~ spl0_10
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f1010]) ).
thf(f1010,plain,
( ( $false
= ( $true
=> ( sK20 @ sK19 @ sK18 ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f1005,f1009]) ).
thf(f1009,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_10
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f1005]) ).
thf(f1005,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK20 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK20 @ Y2 @ Y1 )
& ( sK20 @ Y0 @ Y2 ) )
=> ( sK20 @ Y0 @ Y1 ) ) ) ) ) )
=> ( sK20 @ sK19 @ sK18 ) )
= $false )
| ~ spl0_10
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1004]) ).
thf(f1004,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) )
@ sK20 ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f1001]) ).
thf(f1001,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f1000]) ).
thf(f1000,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f999]) ).
thf(f999,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) ) )
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f998,f841]) ).
thf(f998,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f997]) ).
thf(f997,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) )
@ sK19 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f994]) ).
thf(f994,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f993]) ).
thf(f993,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f496]) ).
thf(f1047,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y0 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK19 @ sK18 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1046]) ).
thf(f1046,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) )
@ X1 ) )
| ~ spl0_12 ),
inference(pi_clausification,[status(thm)],[f841]) ).
thf(f912,plain,
( spl0_16
| spl0_17
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f905,f283,f910,f907]) ).
thf(f905,plain,
( ( $true
= ( sK2 @ sK21 @ sK22 ) )
| ( ( sK4 @ sK21 @ sK22 )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f894]) ).
thf(f894,plain,
( ( ( ( sK2 @ sK21 @ sK22 )
| ( sK4 @ sK21 @ sK22 ) )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f890]) ).
thf(f890,plain,
( ( ( ( ( sK2 @ sK21 @ sK22 )
| ( sK4 @ sK21 @ sK22 ) )
=> ( sK11 @ sK21 @ sK22 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f889]) ).
thf(f889,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK21 @ Y0 )
| ( sK4 @ sK21 @ Y0 ) )
=> ( sK11 @ sK21 @ Y0 ) )
@ sK22 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f886]) ).
thf(f886,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK21 @ Y0 )
| ( sK4 @ sK21 @ Y0 ) )
=> ( sK11 @ sK21 @ Y0 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f885]) ).
thf(f885,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK21 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f284]) ).
thf(f877,plain,
( spl0_14
| spl0_15
| ~ spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f868,f498,f875,f872]) ).
thf(f498,definition,
( spl0_11
<=> ( $false
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f868,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f865]) ).
thf(f865,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_11 ),
inference(not_proxy_clausification,[status(thm)],[f864]) ).
thf(f864,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f858]) ).
thf(f858,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
=> $false ) )
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f855,f39]) ).
thf(f39,plain,
( $false
= ( sK6 @ sK3 @ sK5 ) ),
inference(boolean_simplification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $true
=> ( sK6 @ sK3 @ sK5 ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f33,f37]) ).
thf(f855,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK3 @ sK5 ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f854]) ).
thf(f854,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) )
@ X1 ) )
| ~ spl0_11 ),
inference(pi_clausification,[status(thm)],[f851]) ).
thf(f851,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) )
| ~ spl0_11 ),
inference(not_proxy_clausification,[status(thm)],[f499]) ).
thf(f499,plain,
( ( $false
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f498]) ).
thf(f845,plain,
( spl0_12
| spl0_13
| ~ spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f838,f495,f843,f840]) ).
thf(f838,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f786]) ).
thf(f786,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f784]) ).
thf(f784,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK19 @ sK18 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f783]) ).
thf(f783,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) )
@ sK19 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f782]) ).
thf(f782,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK18 ) ) ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f781]) ).
thf(f781,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK18 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f496]) ).
thf(f775,plain,
( ~ spl0_2
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f774]) ).
thf(f774,plain,
( $false
| ~ spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f773]) ).
thf(f773,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f772]) ).
thf(f772,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f766,f533]) ).
thf(f533,plain,
( ( ( sK11 @ sK15 @ sK16 )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f524]) ).
thf(f524,plain,
( ( $true
= ( ( sK11 @ sK15 @ sK16 )
& ( sK11 @ sK17 @ sK15 ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f514]) ).
thf(f514,plain,
( ( $false
= ( ( ( sK11 @ sK15 @ sK16 )
& ( sK11 @ sK17 @ sK15 ) )
=> ( sK11 @ sK17 @ sK16 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f513]) ).
thf(f513,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK11 @ sK15 @ sK16 )
& ( sK11 @ Y0 @ sK15 ) )
=> ( sK11 @ Y0 @ sK16 ) )
@ sK17 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f510]) ).
thf(f510,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ sK15 @ sK16 )
& ( sK11 @ Y0 @ sK15 ) )
=> ( sK11 @ Y0 @ sK16 ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f509]) ).
thf(f509,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ sK15 @ Y0 )
& ( sK11 @ Y1 @ sK15 ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ sK16 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f506]) ).
thf(f506,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ sK15 @ Y0 )
& ( sK11 @ Y1 @ sK15 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f505]) ).
thf(f505,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) )
@ sK15 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f459]) ).
thf(f459,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f458]) ).
thf(f458,definition,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f766,plain,
( ( ( ~ ( sK11 @ sK15 @ sK16 ) )
= $true )
| ~ spl0_2
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f764]) ).
thf(f764,plain,
( ( ( ( sK11 @ sK15 @ sK16 )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f681,f526]) ).
thf(f526,plain,
( ( ( sK11 @ sK17 @ sK16 )
= $false )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f525]) ).
thf(f525,plain,
( ( $false
= ( $true
=> ( sK11 @ sK17 @ sK16 ) ) )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f514,f524]) ).
thf(f681,plain,
( ! [X0: a] :
( $true
= ( ( sK11 @ sK15 @ X0 )
=> ( sK11 @ sK17 @ X0 ) ) )
| ~ spl0_2
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f663]) ).
thf(f663,plain,
( ! [X0: a] :
( $true
= ( ( ( sK11 @ sK15 @ X0 )
& $true )
=> ( sK11 @ sK17 @ X0 ) ) )
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f644,f535]) ).
thf(f535,plain,
( ( ( sK11 @ sK17 @ sK15 )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f534]) ).
thf(f534,plain,
( ( ( $true
& ( sK11 @ sK17 @ sK15 ) )
= $true )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f524,f533]) ).
thf(f644,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK11 @ X3 @ X1 )
& ( sK11 @ X2 @ X3 ) )
=> ( sK11 @ X2 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f643]) ).
thf(f643,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK11 @ Y0 @ X1 )
& ( sK11 @ X2 @ Y0 ) )
=> ( sK11 @ X2 @ X1 ) )
@ X3 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f639]) ).
thf(f639,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 @ X1 )
& ( sK11 @ X2 @ Y0 ) )
=> ( sK11 @ X2 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f638]) ).
thf(f638,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ X1 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ X1 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f629]) ).
thf(f629,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ X1 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ X1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f628]) ).
thf(f628,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f553]) ).
thf(f553,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f546]) ).
thf(f546,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f544]) ).
thf(f544,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK11 @ sK8 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f543]) ).
thf(f543,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK11 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f515]) ).
thf(f515,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f512]) ).
thf(f512,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK9 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f511]) ).
thf(f511,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f508]) ).
thf(f508,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f507]) ).
thf(f507,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f504]) ).
thf(f504,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f503]) ).
thf(f503,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f500,plain,
( spl0_10
| spl0_11
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f493,f24,f498,f495]) ).
thf(f24,definition,
( spl0_1
<=> ( $false
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f493,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $false
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f488,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f487]) ).
thf(f487,plain,
( $false
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f483]) ).
thf(f483,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f480,f195]) ).
thf(f195,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK11 @ X3 @ X1 )
& ( sK11 @ X2 @ X3 ) )
=> ( sK11 @ X2 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f194]) ).
thf(f194,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK11 @ Y0 @ X1 )
& ( sK11 @ X2 @ Y0 ) )
=> ( sK11 @ X2 @ X1 ) )
@ X3 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f193]) ).
thf(f193,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 @ X1 )
& ( sK11 @ X2 @ Y0 ) )
=> ( sK11 @ X2 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f192]) ).
thf(f192,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ X1 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ X1 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ X1 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ X1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f182]) ).
thf(f182,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK11 @ sK8 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK11 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK9 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f480,plain,
( ( $false
= ( ( ( sK11 @ ( sK12 @ sK11 ) @ sK14 )
& ( sK11 @ sK13 @ ( sK12 @ sK11 ) ) )
=> ( sK11 @ sK13 @ sK14 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f479]) ).
thf(f479,plain,
( ( ( ^ [Y0: a] :
( ( ( sK11 @ ( sK12 @ sK11 ) @ Y0 )
& ( sK11 @ sK13 @ ( sK12 @ sK11 ) ) )
=> ( sK11 @ sK13 @ Y0 ) )
@ sK14 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f478]) ).
thf(f478,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ ( sK12 @ sK11 ) @ Y0 )
& ( sK11 @ sK13 @ ( sK12 @ sK11 ) ) )
=> ( sK11 @ sK13 @ Y0 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f477]) ).
thf(f477,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ ( sK12 @ sK11 ) @ Y1 )
& ( sK11 @ Y0 @ ( sK12 @ sK11 ) ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK13 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f476]) ).
thf(f476,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ ( sK12 @ sK11 ) @ Y1 )
& ( sK11 @ Y0 @ ( sK12 @ sK11 ) ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f467]) ).
thf(f467,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) )
@ ( sK12 @ sK11 ) )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f281]) ).
thf(f281,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f280]) ).
thf(f280,definition,
( spl0_6
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f463,plain,
( spl0_8
| spl0_9
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f452,f262,f27,f461,f458]) ).
thf(f262,definition,
( spl0_4
<=> ( $false
= ( sK11 @ sK10 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f452,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f439]) ).
thf(f439,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f292]) ).
thf(f292,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f291]) ).
thf(f291,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f101,f263]) ).
thf(f263,plain,
( ( $false
= ( sK11 @ sK10 @ sK7 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f262]) ).
thf(f101,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK10 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
@ sK10 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> $false ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f41,f48]) ).
thf(f285,plain,
( spl0_6
| spl0_7
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f274,f259,f283,f280]) ).
thf(f259,definition,
( spl0_3
<=> ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f274,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f269]) ).
thf(f269,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f260]) ).
thf(f260,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f259]) ).
thf(f264,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f253,f27,f262,f259]) ).
thf(f253,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( $false
= ( sK11 @ sK10 @ sK7 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f247]) ).
thf(f247,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) )
=> $false ) )
| ( $false
= ( sK11 @ sK10 @ sK7 ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f76,f214]) ).
thf(f214,plain,
( ! [X0: a] :
( ( ( sK11 @ sK8 @ X0 )
= $false )
| ( ( sK11 @ X0 @ sK7 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f205]) ).
thf(f205,plain,
( ! [X0: a] :
( $false
= ( ( sK11 @ X0 @ sK7 )
& ( sK11 @ sK8 @ X0 ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f204]) ).
thf(f204,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK11 @ X0 @ sK7 )
& ( sK11 @ sK8 @ X0 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f197]) ).
thf(f197,plain,
( ! [X0: a] :
( $true
= ( ( ( sK11 @ X0 @ sK7 )
& ( sK11 @ sK8 @ X0 ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f195,f94]) ).
thf(f94,plain,
( ( $false
= ( sK11 @ sK8 @ sK7 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f76,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK8 @ sK10 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true
= ( $true
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f62,f69]) ).
thf(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f22,f27,f24]) ).
thf(f22,plain,
( ( $false
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $false
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| $false ) ),
inference(backward_demodulation,[status(thm)],[f17,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV156^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n025.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:41:12 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SEV156^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.42 % Domain : Set Theory (Relations)
% 0.15/0.42 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bro09]
% 0.15/0.42 % Names : tps_1233 [Bro09]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.42 v8.2.0, 0.27 v8.1.0, 0.42 v7.5.0, 0.58 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 1.00 v4.0.0
% 0.15/0.42 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.15/0.42 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 0 ( 0 avg)
% 0.15/0.42 % Number of connectives : 162 ( 1 ~; 8 |; 19 &; 108 @)
% 0.15/0.42 % ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 23 ( 23 avg)
% 0.15/0.42 % Number of types : 2 ( 1 usr)
% 0.15/0.42 % Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.15/0.42 % Number of variables : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% 0.15/0.42 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(a_type,type,
% 0.15/0.42 a: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(cTHM250H_pme,conjecture,
% 0.15/0.42 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.15/0.42 ( ! [Xp1: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx0: a,Xy0: a] :
% 0.15/0.42 ( ( ( R @ Xx0 @ Xy0 )
% 0.15/0.42 | ( S @ Xx0 @ Xy0 ) )
% 0.15/0.42 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.15/0.42 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.15/0.42 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.15/0.42 & ( Xp1 @ Xy0 @ Xz ) )
% 0.15/0.42 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.15/0.42 => ( Xp1 @ Xx @ Xy ) )
% 0.15/0.42 | ( ~ ! [Xp1: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx0: a,Xy0: a] :
% 0.15/0.42 ( ( ( R @ Xx0 @ Xy0 )
% 0.15/0.42 | ( S @ Xx0 @ Xy0 ) )
% 0.15/0.42 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.15/0.42 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.15/0.42 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.15/0.42 & ( Xp1 @ Xy0 @ Xz ) )
% 0.15/0.42 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.15/0.42 => ( Xp1 @ Xx @ Xy ) )
% 0.15/0.42 & ! [Xx0: a,Xy0: a] :
% 0.15/0.42 ( ( ! [Xp1: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx1: a,Xy1: a] :
% 0.15/0.42 ( ( R @ Xx1 @ Xy1 )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.15/0.42 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.15/0.42 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.15/0.42 & ( Xp1 @ Xy1 @ Xz ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.15/0.42 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.15/0.42 | ! [Xp1: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx1: a,Xy1: a] :
% 0.15/0.42 ( ( S @ Xx1 @ Xy1 )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.15/0.42 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.15/0.42 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.15/0.42 & ( Xp1 @ Xy1 @ Xz ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.15/0.42 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 0.15/0.42 => ! [Xp1: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx1: a,Xy1: a] :
% 0.15/0.42 ( ( ( R @ Xx1 @ Xy1 )
% 0.15/0.42 | ( S @ Xx1 @ Xy1 ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.15/0.42 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.15/0.42 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.15/0.42 & ( Xp1 @ Xy1 @ Xz ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.15/0.42 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 0.15/0.42 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.15/0.42 ( ( ! [Xp1: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx1: a,Xy1: a] :
% 0.15/0.42 ( ( ( R @ Xx1 @ Xy1 )
% 0.15/0.42 | ( S @ Xx1 @ Xy1 ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.15/0.42 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.15/0.42 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.15/0.42 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.15/0.42 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.15/0.42 & ! [Xp1: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx1: a,Xy1: a] :
% 0.15/0.42 ( ( ( R @ Xx1 @ Xy1 )
% 0.15/0.42 | ( S @ Xx1 @ Xy1 ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.15/0.42 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.15/0.42 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.15/0.42 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.15/0.42 => ( Xp1 @ Xy0 @ Xz ) ) )
% 0.15/0.42 => ! [Xp1: a > a > $o] :
% 0.15/0.42 ( ( ! [Xx1: a,Xy1: a] :
% 0.15/0.42 ( ( ( R @ Xx1 @ Xy1 )
% 0.15/0.42 | ( S @ Xx1 @ Xy1 ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.15/0.42 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.15/0.42 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.15/0.42 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.15/0.42 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.15/0.42 => ( Xp1 @ Xx0 @ Xz ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.34/1.17 ---- Embedded in THF ---
% 1.34/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.34/1.17 %%% Generated on Tue Feb 24 12:41:13 EST 2026
% 1.34/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.34/1.17 %%% Logic specification used:
% 1.34/1.17 %%% thf(spec, logic, $$dhol).
% 1.34/1.17
% 1.34/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6Vfhle69yx/DTF2DTF27930.p
% See solution above
% 1.34/1.17 ------------------------
% 1.34/1.18 ---- Cleaned THF ---
% 1.34/1.18 thf(a_type,type,
% 1.34/1.18 a: $tType ).
% 1.34/1.18
% 1.34/1.18 thf(cTHM250H_pme,conjecture,
% 1.34/1.18 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.34/1.18 ( ! [Xp1: a > a > $o] :
% 1.34/1.18 ( ( ! [Xx0: a,Xy0: a] :
% 1.34/1.18 ( ( ( R @ Xx0 @ Xy0 )
% 1.34/1.18 | ( S @ Xx0 @ Xy0 ) )
% 1.34/1.18 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.34/1.18 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.34/1.18 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 1.34/1.18 & ( Xp1 @ Xy0 @ Xz ) )
% 1.34/1.18 => ( Xp1 @ Xx0 @ Xz ) ) )
% 1.34/1.18 => ( Xp1 @ Xx @ Xy ) )
% 1.34/1.18 | ( ~ ! [Xp1: a > a > $o] :
% 1.34/1.18 ( ( ! [Xx0: a,Xy0: a] :
% 1.34/1.18 ( ( ( R @ Xx0 @ Xy0 )
% 1.34/1.18 | ( S @ Xx0 @ Xy0 ) )
% 1.34/1.18 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.34/1.18 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.34/1.18 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 1.34/1.18 & ( Xp1 @ Xy0 @ Xz ) )
% 1.34/1.18 => ( Xp1 @ Xx0 @ Xz ) ) )
% 1.34/1.18 => ( Xp1 @ Xx @ Xy ) )
% 1.34/1.18 & ! [Xx0: a,Xy0: a] :
% 1.34/1.18 ( ( ! [Xp1: a > a > $o] :
% 1.34/1.18 ( ( ! [Xx1: a,Xy1: a] :
% 1.34/1.18 ( ( R @ Xx1 @ Xy1 )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.34/1.18 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.34/1.18 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.34/1.18 & ( Xp1 @ Xy1 @ Xz ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xz ) ) )
% 1.34/1.18 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.34/1.18 | ! [Xp1: a > a > $o] :
% 1.34/1.18 ( ( ! [Xx1: a,Xy1: a] :
% 1.34/1.18 ( ( S @ Xx1 @ Xy1 )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.34/1.18 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.34/1.18 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.34/1.18 & ( Xp1 @ Xy1 @ Xz ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xz ) ) )
% 1.34/1.18 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 1.34/1.18 => ! [Xp1: a > a > $o] :
% 1.34/1.18 ( ( ! [Xx1: a,Xy1: a] :
% 1.34/1.18 ( ( ( R @ Xx1 @ Xy1 )
% 1.34/1.18 | ( S @ Xx1 @ Xy1 ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.34/1.18 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.34/1.18 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.34/1.18 & ( Xp1 @ Xy1 @ Xz ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xz ) ) )
% 1.34/1.18 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 1.34/1.18 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.34/1.18 ( ( ! [Xp1: a > a > $o] :
% 1.34/1.18 ( ( ! [Xx1: a,Xy1: a] :
% 1.34/1.18 ( ( ( R @ Xx1 @ Xy1 )
% 1.34/1.18 | ( S @ Xx1 @ Xy1 ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.34/1.18 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 1.34/1.18 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.34/1.18 & ( Xp1 @ Xy1 @ Xz0 ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 1.34/1.18 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.34/1.18 & ! [Xp1: a > a > $o] :
% 1.34/1.18 ( ( ! [Xx1: a,Xy1: a] :
% 1.34/1.18 ( ( ( R @ Xx1 @ Xy1 )
% 1.34/1.18 | ( S @ Xx1 @ Xy1 ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.34/1.18 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 1.34/1.18 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.34/1.18 & ( Xp1 @ Xy1 @ Xz0 ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 1.34/1.18 => ( Xp1 @ Xy0 @ Xz ) ) )
% 1.34/1.18 => ! [Xp1: a > a > $o] :
% 1.34/1.18 ( ( ! [Xx1: a,Xy1: a] :
% 1.34/1.18 ( ( ( R @ Xx1 @ Xy1 )
% 1.34/1.18 | ( S @ Xx1 @ Xy1 ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.34/1.18 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 1.34/1.18 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.34/1.18 & ( Xp1 @ Xy1 @ Xz0 ) )
% 1.34/1.18 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 1.34/1.18 => ( Xp1 @ Xx0 @ Xz ) ) ) ) ) ).
% 1.34/1.18 ------------------------
% 1.34/1.19 % (28027)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/183Mi)
% 1.46/1.20 % (28028)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_27930 for (2999ds/4Mi)
% 1.46/1.20 % (28029)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_27930 for (2999ds/27Mi)
% 1.46/1.20 % (28031)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_27930 for (2999ds/2Mi)
% 1.46/1.20 % (28030)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/2Mi)
% 1.46/1.20 % (28032)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_27930 for (2999ds/275Mi)
% 1.46/1.20 % (28033)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/18Mi)
% 1.46/1.20 % (28031)Instruction limit reached!
% 1.46/1.20 % (28031)------------------------------
% 1.46/1.20 % (28031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.20 % (28031)Termination reason: Unknown
% 1.46/1.20 % (28031)Termination phase: shuffling
% 1.46/1.20
% 1.46/1.20 % (28031)Memory used [KB]: 1023
% 1.46/1.20 % (28031)Time elapsed: 0.002 s
% 1.46/1.20 % (28031)Instructions burned: 2 (million)
% 1.46/1.20 % (28031)------------------------------
% 1.46/1.20 % (28031)------------------------------
% 1.46/1.20 % (28028)Instruction limit reached!
% 1.46/1.20 % (28028)------------------------------
% 1.46/1.20 % (28028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.20 % (28028)Termination reason: Unknown
% 1.46/1.20 % (28028)Termination phase: Naming
% 1.46/1.20
% 1.46/1.20 % (28028)Memory used [KB]: 1023
% 1.46/1.20 % (28028)Time elapsed: 0.003 s
% 1.46/1.20 % (28028)Instructions burned: 4 (million)
% 1.46/1.20 % (28028)------------------------------
% 1.46/1.20 % (28028)------------------------------
% 1.46/1.20 % (28030)Instruction limit reached!
% 1.46/1.20 % (28030)------------------------------
% 1.46/1.20 % (28030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.20 % (28030)Termination reason: Unknown
% 1.46/1.20 % (28030)Termination phase: Naming
% 1.46/1.20
% 1.46/1.20 % (28030)Memory used [KB]: 1023
% 1.46/1.20 % (28030)Time elapsed: 0.003 s
% 1.46/1.20 % (28030)Instructions burned: 3 (million)
% 1.46/1.20 % (28030)------------------------------
% 1.46/1.20 % (28030)------------------------------
% 1.46/1.21 % (28033)Instruction limit reached!
% 1.46/1.21 % (28033)------------------------------
% 1.46/1.21 % (28033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.21 % (28033)Termination reason: Unknown
% 1.46/1.21 % (28033)Termination phase: Saturation
% 1.46/1.21
% 1.46/1.21 % (28033)Memory used [KB]: 5628
% 1.46/1.21 % (28033)Time elapsed: 0.010 s
% 1.46/1.21 % (28033)Instructions burned: 19 (million)
% 1.46/1.21 % (28033)------------------------------
% 1.46/1.21 % (28033)------------------------------
% 1.46/1.21 % (28029)Instruction limit reached!
% 1.46/1.21 % (28029)------------------------------
% 1.46/1.21 % (28029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.21 % (28029)Termination reason: Unknown
% 1.46/1.21 % (28029)Termination phase: Saturation
% 1.46/1.21
% 1.46/1.21 % (28029)Memory used [KB]: 5756
% 1.46/1.21 % (28029)Time elapsed: 0.014 s
% 1.46/1.21 % (28029)Instructions burned: 27 (million)
% 1.46/1.21 % (28029)------------------------------
% 1.46/1.21 % (28029)------------------------------
% 1.46/1.21 % (28034)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/3Mi)
% 1.46/1.21 % (28034)Instruction limit reached!
% 1.46/1.21 % (28034)------------------------------
% 1.46/1.21 % (28034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.21 % (28034)Termination reason: Unknown
% 1.46/1.21 % (28035)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_27930 for (2999ds/37Mi)
% 1.46/1.21 % (28034)Termination phase: Preprocessing 3
% 1.46/1.21
% 1.46/1.21 % (28034)Memory used [KB]: 1023
% 1.46/1.21 % (28036)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_27930 for (2999ds/15Mi)
% 1.46/1.21 % (28034)Time elapsed: 0.003 s
% 1.46/1.21 % (28034)Instructions burned: 4 (million)
% 1.46/1.21 % (28034)------------------------------
% 1.46/1.21 % (28034)------------------------------
% 1.46/1.22 % (28037)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_27930 for (2999ds/3Mi)
% 1.46/1.22 % (28036)Instruction limit reached!
% 1.46/1.22 % (28036)------------------------------
% 1.46/1.22 % (28036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.22 % (28036)Termination reason: Unknown
% 1.46/1.22 % (28036)Termination phase: Saturation
% 1.46/1.22
% 1.46/1.22 % (28036)Memory used [KB]: 5756
% 1.46/1.22 % (28036)Time elapsed: 0.009 s
% 1.46/1.22 % (28036)Instructions burned: 16 (million)
% 1.46/1.22 % (28036)------------------------------
% 1.46/1.22 % (28036)------------------------------
% 1.46/1.22 % (28037)Instruction limit reached!
% 1.46/1.22 % (28037)------------------------------
% 1.46/1.22 % (28037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.22 % (28037)Termination reason: Unknown
% 1.46/1.22 % (28037)Termination phase: Naming
% 1.46/1.22
% 1.46/1.22 % (28037)Memory used [KB]: 1023
% 1.46/1.22 % (28037)Time elapsed: 0.003 s
% 1.46/1.22 % (28037)Instructions burned: 4 (million)
% 1.46/1.22 % (28037)------------------------------
% 1.46/1.22 % (28037)------------------------------
% 1.46/1.22 % (28035)Instruction limit reached!
% 1.46/1.22 % (28035)------------------------------
% 1.46/1.22 % (28035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.22 % (28035)Termination reason: Unknown
% 1.46/1.22 % (28035)Termination phase: Saturation
% 1.46/1.22
% 1.46/1.22 % (28035)Memory used [KB]: 5628
% 1.46/1.22 % (28035)Time elapsed: 0.012 s
% 1.46/1.22 % (28035)Instructions burned: 37 (million)
% 1.46/1.22 % (28035)------------------------------
% 1.46/1.22 % (28035)------------------------------
% 1.46/1.23 % (28039)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_27930 for (2999ds/1041Mi)
% 1.46/1.23 % (28040)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/7Mi)
% 1.46/1.23 % (28040)Instruction limit reached!
% 1.46/1.23 % (28040)------------------------------
% 1.46/1.23 % (28040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.23 % (28040)Termination reason: Unknown
% 1.46/1.23 % (28040)Termination phase: Property scanning
% 1.46/1.23
% 1.46/1.23 % (28040)Memory used [KB]: 1151
% 1.46/1.23 % (28040)Time elapsed: 0.005 s
% 1.46/1.23 % (28040)Instructions burned: 8 (million)
% 1.46/1.23 % (28040)------------------------------
% 1.46/1.23 % (28040)------------------------------
% 1.46/1.23 % (28042)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_27930 for (2999ds/3Mi)
% 1.46/1.24 % (28042)Instruction limit reached!
% 1.46/1.24 % (28042)------------------------------
% 1.46/1.24 % (28042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.24 % (28042)Termination reason: Unknown
% 1.46/1.24 % (28042)Termination phase: Naming
% 1.46/1.24
% 1.46/1.24 % (28042)Memory used [KB]: 1023
% 1.46/1.24 % (28042)Time elapsed: 0.002 s
% 1.46/1.24 % (28042)Instructions burned: 4 (million)
% 1.46/1.24 % (28042)------------------------------
% 1.46/1.24 % (28042)------------------------------
% 1.46/1.24 % (28041)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/16Mi)
% 1.46/1.24 % (28043)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_27930 for (2999ds/3Mi)
% 1.46/1.24 % (28043)Instruction limit reached!
% 1.46/1.24 % (28043)------------------------------
% 1.46/1.24 % (28043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.24 % (28043)Termination reason: Unknown
% 1.46/1.24 % (28043)Termination phase: Preprocessing 3
% 1.46/1.24
% 1.46/1.24 % (28043)Memory used [KB]: 1023
% 1.46/1.24 % (28043)Time elapsed: 0.003 s
% 1.46/1.24 % (28043)Instructions burned: 4 (million)
% 1.46/1.24 % (28043)------------------------------
% 1.46/1.24 % (28043)------------------------------
% 1.46/1.24 % (28044)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/7Mi)
% 1.46/1.25 % (28041)Instruction limit reached!
% 1.46/1.25 % (28041)------------------------------
% 1.46/1.25 % (28041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (28041)Termination reason: Unknown
% 1.46/1.25 % (28041)Termination phase: Property scanning
% 1.46/1.25
% 1.46/1.25 % (28041)Memory used [KB]: 1151
% 1.46/1.25 % (28041)Time elapsed: 0.009 s
% 1.46/1.25 % (28041)Instructions burned: 18 (million)
% 1.46/1.25 % (28041)------------------------------
% 1.46/1.25 % (28041)------------------------------
% 1.46/1.25 % (28044)Instruction limit reached!
% 1.46/1.25 % (28044)------------------------------
% 1.46/1.25 % (28044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (28044)Termination reason: Unknown
% 1.46/1.25 % (28044)Termination phase: Property scanning
% 1.46/1.25
% 1.46/1.25 % (28044)Memory used [KB]: 1151
% 1.46/1.25 % (28044)Time elapsed: 0.003 s
% 1.46/1.25 % (28044)Instructions burned: 8 (million)
% 1.46/1.25 % (28044)------------------------------
% 1.46/1.25 % (28044)------------------------------
% 1.46/1.25 % (28045)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/3Mi)
% 1.46/1.25 % (28045)Instruction limit reached!
% 1.46/1.25 % (28045)------------------------------
% 1.46/1.25 % (28045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (28045)Termination reason: Unknown
% 1.46/1.25 % (28045)Termination phase: Property scanning
% 1.46/1.25
% 1.46/1.25 % (28045)Memory used [KB]: 1023
% 1.46/1.25 % (28045)Time elapsed: 0.003 s
% 1.46/1.25 % (28045)Instructions burned: 4 (million)
% 1.46/1.25 % (28045)------------------------------
% 1.46/1.25 % (28045)------------------------------
% 1.46/1.26 % (28048)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/710Mi)
% 1.46/1.26 % (28027)Instruction limit reached!
% 1.46/1.26 % (28027)------------------------------
% 1.46/1.26 % (28027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (28027)Termination reason: Unknown
% 1.46/1.26 % (28027)Termination phase: Saturation
% 1.46/1.26
% 1.46/1.26 % (28027)Memory used [KB]: 6140
% 1.46/1.26 % (28027)Time elapsed: 0.069 s
% 1.46/1.26 % (28027)Instructions burned: 183 (million)
% 1.46/1.26 % (28027)------------------------------
% 1.46/1.26 % (28027)------------------------------
% 1.46/1.26 % (28046)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/4Mi)
% 1.46/1.26 % (28047)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/18Mi)
% 1.46/1.26 % (28046)Instruction limit reached!
% 1.46/1.26 % (28046)------------------------------
% 1.46/1.26 % (28046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (28046)Termination reason: Unknown
% 1.46/1.26 % (28046)Termination phase: Preprocessing 3
% 1.46/1.26
% 1.46/1.26 % (28046)Memory used [KB]: 1023
% 1.46/1.26 % (28046)Time elapsed: 0.003 s
% 1.46/1.26 % (28046)Instructions burned: 4 (million)
% 1.46/1.26 % (28046)------------------------------
% 1.46/1.26 % (28046)------------------------------
% 1.46/1.27 % (28047)Instruction limit reached!
% 1.46/1.27 % (28047)------------------------------
% 1.46/1.27 % (28047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (28047)Termination reason: Unknown
% 1.46/1.27 % (28047)Termination phase: Saturation
% 1.46/1.27
% 1.46/1.27 % (28047)Memory used [KB]: 5628
% 1.46/1.27 % (28047)Time elapsed: 0.010 s
% 1.46/1.27 % (28047)Instructions burned: 18 (million)
% 1.46/1.27 % (28047)------------------------------
% 1.46/1.27 % (28047)------------------------------
% 1.46/1.27 % (28050)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_27930 for (2999ds/902Mi)
% 1.46/1.28 % (28049)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/6Mi)
% 1.46/1.28 % (28051)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_27930 for (2999ds/21Mi)
% 1.46/1.28 % (28049)Instruction limit reached!
% 1.46/1.28 % (28049)------------------------------
% 1.46/1.28 % (28049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (28049)Termination reason: Unknown
% 1.46/1.28 % (28049)Termination phase: Preprocessing 3
% 1.46/1.28
% 1.46/1.28 % (28049)Memory used [KB]: 1151
% 1.46/1.28 % (28049)Time elapsed: 0.004 s
% 1.46/1.28 % (28049)Instructions burned: 6 (million)
% 1.46/1.28 % (28049)------------------------------
% 1.46/1.28 % (28049)------------------------------
% 1.46/1.29 % (28052)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/5Mi)
% 1.46/1.29 % (28051)Instruction limit reached!
% 1.46/1.29 % (28051)------------------------------
% 1.46/1.29 % (28051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (28051)Termination reason: Unknown
% 1.46/1.29 % (28051)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (28051)Memory used [KB]: 5756
% 1.46/1.29 % (28051)Time elapsed: 0.011 s
% 1.46/1.29 % (28051)Instructions burned: 21 (million)
% 1.46/1.29 % (28051)------------------------------
% 1.46/1.29 % (28051)------------------------------
% 1.46/1.29 % (28052)Instruction limit reached!
% 1.46/1.29 % (28052)------------------------------
% 1.46/1.29 % (28052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (28052)Termination reason: Unknown
% 1.46/1.29 % (28052)Termination phase: Property scanning
% 1.46/1.29
% 1.46/1.29 % (28052)Memory used [KB]: 1023
% 1.46/1.29 % (28052)Time elapsed: 0.004 s
% 1.46/1.29 % (28052)Instructions burned: 6 (million)
% 1.46/1.29 % (28052)------------------------------
% 1.46/1.29 % (28052)------------------------------
% 1.46/1.30 % (28053)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_27930 for (2999ds/6Mi)
% 1.46/1.30 % (28053)Instruction limit reached!
% 1.46/1.30 % (28053)------------------------------
% 1.46/1.30 % (28053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.30 % (28053)Termination reason: Unknown
% 1.46/1.30 % (28053)Termination phase: Unused predicate definition removal
% 1.46/1.30
% 1.46/1.30 % (28053)Memory used [KB]: 1023
% 1.46/1.30 % (28053)Time elapsed: 0.004 s
% 1.46/1.30 % (28053)Instructions burned: 6 (million)
% 1.46/1.30 % (28053)------------------------------
% 1.46/1.30 % (28053)------------------------------
% 1.46/1.31 % (28054)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27930 for (2999ds/377Mi)
% 1.46/1.31 % (28055)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_27930 for (2999ds/779Mi)
% 1.46/1.32 % (28056)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_27930 for (2998ds/19Mi)
% 1.46/1.32 % (28056)Instruction limit reached!
% 1.46/1.32 % (28056)------------------------------
% 1.46/1.32 % (28056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.32 % (28056)Termination reason: Unknown
% 1.46/1.32 % (28056)Termination phase: Saturation
% 1.46/1.32
% 1.46/1.32 % (28056)Memory used [KB]: 5500
% 1.46/1.32 % (28056)Time elapsed: 0.009 s
% 1.46/1.32 % (28056)Instructions burned: 19 (million)
% 1.46/1.32 % (28056)------------------------------
% 1.46/1.32 % (28056)------------------------------
% 1.46/1.33 % (28032)Instruction limit reached!
% 1.46/1.33 % (28032)------------------------------
% 1.46/1.33 % (28032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.33 % (28032)Termination reason: Unknown
% 1.46/1.33 % (28032)Termination phase: Saturation
% 1.46/1.33
% 1.46/1.33 % (28032)Memory used [KB]: 6268
% 1.46/1.33 % (28032)Time elapsed: 0.132 s
% 1.46/1.33 % (28032)Instructions burned: 275 (million)
% 1.46/1.33 % (28032)------------------------------
% 1.46/1.33 % (28032)------------------------------
% 1.46/1.34 % (28057)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27930 for (2998ds/879Mi)
% 1.46/1.34 % (28058)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27930 for (2998ds/17Mi)
% 1.46/1.35 % (28058)Instruction limit reached!
% 1.46/1.35 % (28058)------------------------------
% 1.46/1.35 % (28058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.35 % (28058)Termination reason: Unknown
% 1.46/1.35 % (28058)Termination phase: Saturation
% 1.46/1.35
% 1.46/1.35 % (28058)Memory used [KB]: 5756
% 1.46/1.35 % (28058)Time elapsed: 0.010 s
% 1.46/1.35 % (28058)Instructions burned: 17 (million)
% 1.46/1.35 % (28058)------------------------------
% 1.46/1.35 % (28058)------------------------------
% 1.46/1.38 % (28059)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27930 for (2998ds/3Mi)
% 1.46/1.38 % (28059)Instruction limit reached!
% 1.46/1.38 % (28059)------------------------------
% 1.46/1.38 % (28059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.38 % (28059)Termination reason: Unknown
% 1.46/1.38 % (28059)Termination phase: Property scanning
% 1.46/1.38
% 1.46/1.38 % (28059)Memory used [KB]: 1023
% 1.46/1.38 % (28059)Time elapsed: 0.002 s
% 1.46/1.38 % (28059)Instructions burned: 3 (million)
% 1.46/1.38 % (28059)------------------------------
% 1.46/1.38 % (28059)------------------------------
% 1.46/1.39 % (28060)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27930 for (2998ds/30Mi)
% 1.46/1.40 % (28060)Instruction limit reached!
% 1.46/1.40 % (28060)------------------------------
% 1.46/1.40 % (28060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.40 % (28060)Termination reason: Unknown
% 1.46/1.40 % (28060)Termination phase: Saturation
% 1.46/1.40
% 1.46/1.40 % (28060)Memory used [KB]: 5756
% 1.46/1.40 % (28060)Time elapsed: 0.016 s
% 1.46/1.40 % (28060)Instructions burned: 31 (million)
% 1.46/1.40 % (28060)------------------------------
% 1.46/1.40 % (28060)------------------------------
% 1.46/1.42 % (28061)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27930 for (2997ds/127Mi)
% 1.46/1.47 % (28039)First to succeed.
% 1.46/1.47 % (28061)Instruction limit reached!
% 1.46/1.47 % (28061)------------------------------
% 1.46/1.47 % (28061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.47 % (28061)Termination reason: Unknown
% 1.46/1.47 % (28061)Termination phase: Saturation
% 1.46/1.47
% 1.46/1.47 % (28061)Memory used [KB]: 6268
% 1.46/1.47 % (28061)Time elapsed: 0.079 s
% 1.46/1.47 % (28061)Instructions burned: 129 (million)
% 1.46/1.47 % (28061)------------------------------
% 1.46/1.47 % (28061)------------------------------
% 1.46/1.48 % (28054)Instruction limit reached!
% 1.46/1.48 % (28054)------------------------------
% 1.46/1.48 % (28054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.48 % (28054)Termination reason: Unknown
% 1.46/1.48 % (28054)Termination phase: Saturation
% 1.46/1.48
% 1.46/1.48 % (28054)Memory used [KB]: 6012
% 1.46/1.48 % (28054)Time elapsed: 0.173 s
% 1.46/1.48 % (28054)Instructions burned: 377 (million)
% 1.46/1.48 % (28054)------------------------------
% 1.46/1.48 % (28054)------------------------------
% 1.46/1.48 % (28062)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27930 for (2997ds/100Mi)
% 1.46/1.49 % (28039)Refutation found. Thanks to Tanya!
% 1.46/1.49 % SZS status Theorem for DTF2THF_27930
% 1.46/1.49 % SZS output start Proof for DTF2THF_27930
% 1.46/1.49 thf(type_def_5, type, a: $tType).
% 1.46/1.49 thf(func_def_0, type, a: $tType).
% 1.46/1.49 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.46/1.49 thf(func_def_21, type, sK2: a > a > $o).
% 1.46/1.49 thf(func_def_22, type, sK3: a).
% 1.46/1.49 thf(func_def_23, type, sK4: a > a > $o).
% 1.46/1.49 thf(func_def_24, type, sK5: a).
% 1.46/1.49 thf(func_def_25, type, sK6: a > a > $o).
% 1.46/1.49 thf(func_def_26, type, sK7: a).
% 1.46/1.49 thf(func_def_27, type, sK8: a).
% 1.46/1.49 thf(func_def_28, type, sK9: a).
% 1.46/1.49 thf(func_def_29, type, sK10: a).
% 1.46/1.49 thf(func_def_30, type, sK11: a > a > $o).
% 1.46/1.49 thf(func_def_31, type, sK12: (a > a > $o) > a).
% 1.46/1.49 thf(func_def_32, type, sK13: a).
% 1.46/1.49 thf(func_def_33, type, sK14: a).
% 1.46/1.49 thf(func_def_34, type, sK15: a).
% 1.46/1.49 thf(func_def_35, type, sK16: a).
% 1.46/1.49 thf(func_def_36, type, sK17: a).
% 1.46/1.49 thf(func_def_37, type, sK18: a).
% 1.46/1.49 thf(func_def_38, type, sK19: a).
% 1.46/1.49 thf(func_def_39, type, sK20: a > a > $o).
% 1.46/1.49 thf(func_def_40, type, sK21: a).
% 1.46/1.49 thf(func_def_41, type, sK22: a).
% 1.46/1.49 thf(func_def_42, type, sK23: a).
% 1.46/1.49 thf(func_def_43, type, sK24: a).
% 1.46/1.49 thf(func_def_44, type, sK25: a).
% 1.46/1.49 thf(func_def_45, type, sK26: a).
% 1.46/1.49 thf(func_def_46, type, sK27: a).
% 1.46/1.49 thf(func_def_47, type, sK28: a).
% 1.46/1.49 thf(func_def_48, type, sK29: a).
% 1.46/1.49 thf(func_def_49, type, sK30: a).
% 1.46/1.49 thf(func_def_50, type, sK31: a).
% 1.46/1.49 thf(func_def_51, type, sK32: a).
% 1.46/1.49 thf(func_def_52, type, sK33: a).
% 1.46/1.49 thf(func_def_53, type, sK34: a).
% 1.46/1.49 thf(func_def_54, type, sK35: a).
% 1.46/1.49 thf(func_def_55, type, sK36: a).
% 1.46/1.49 thf(f2752,plain,(
% 1.46/1.49 $false),
% 1.46/1.49 inference(avatar_sat_refutation,[status(thm)],[f29,f264,f285,f463,f488,f500,f775,f845,f877,f912,f1105,f1247,f1288,f1565,f1657,f1664,f1671,f1863,f2000,f2070,f2570,f2588,f2751])).
% 1.46/1.49 thf(f2751,plain,(
% 1.46/1.49 ~spl0_2 | ~spl0_9 | ~spl0_25),
% 1.46/1.49 inference(avatar_contradiction_clause,[status(thm)],[f2750])).
% 1.46/1.49 thf(f2750,plain,(
% 1.46/1.49 $false | (~spl0_2 | ~spl0_9 | ~spl0_25)),
% 1.46/1.49 inference(trivial_inequality_removal,[status(thm)],[f2749])).
% 1.46/1.49 thf(f2749,plain,(
% 1.46/1.49 ($true = $false) | (~spl0_2 | ~spl0_9 | ~spl0_25)),
% 1.46/1.49 inference(backward_demodulation,[status(thm)],[f2616,f2748])).
% 1.46/1.49 thf(f2748,plain,(
% 1.46/1.50 ($false = (sK11 @ sK29 @ sK28)) | (~spl0_9 | ~spl0_25)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2747])).
% 1.46/1.50 thf(f2747,plain,(
% 1.46/1.50 ($false = ($true => (sK11 @ sK29 @ sK28))) | (~spl0_9 | ~spl0_25)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2746])).
% 1.46/1.50 thf(f2746,plain,(
% 1.46/1.50 ((((sK2 @ sK29 @ sK28) | $true) => (sK11 @ sK29 @ sK28)) = $false) | (~spl0_9 | ~spl0_25)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f2745,f1287])).
% 1.46/1.50 thf(f1287,plain,(
% 1.46/1.50 ($true = (sK4 @ sK29 @ sK28)) | ~spl0_25),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f1286])).
% 1.46/1.50 thf(f1286,definition,(
% 1.46/1.50 spl0_25 <=> ($true = (sK4 @ sK29 @ sK28))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition])).
% 1.46/1.50 thf(f2745,plain,(
% 1.46/1.50 ((((sK2 @ sK29 @ sK28) | (sK4 @ sK29 @ sK28)) => (sK11 @ sK29 @ sK28)) = $false) | ~spl0_9),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2744])).
% 1.46/1.50 thf(f2744,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (((sK2 @ Y0 @ sK28) | (sK4 @ Y0 @ sK28)) => (sK11 @ Y0 @ sK28))) @ sK29)) | ~spl0_9),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f2732])).
% 1.46/1.50 thf(f2732,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK28) | (sK4 @ Y0 @ sK28)) => (sK11 @ Y0 @ sK28))))) | ~spl0_9),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2725])).
% 1.46/1.50 thf(f2725,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0))))) @ sK28)) | ~spl0_9),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f462])).
% 1.46/1.50 thf(f462,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) = $false) | ~spl0_9),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f461])).
% 1.46/1.50 thf(f461,definition,(
% 1.46/1.50 spl0_9 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) = $false)),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.46/1.50 thf(f2616,plain,(
% 1.46/1.50 ($true = (sK11 @ sK29 @ sK28)) | (~spl0_2 | ~spl0_25)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2615])).
% 1.46/1.50 thf(f2615,plain,(
% 1.46/1.50 ($true = ($true => (sK11 @ sK29 @ sK28))) | (~spl0_2 | ~spl0_25)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2611])).
% 1.46/1.50 thf(f2611,plain,(
% 1.46/1.50 ($true = (($true | (sK2 @ sK29 @ sK28)) => (sK11 @ sK29 @ sK28))) | (~spl0_2 | ~spl0_25)),
% 1.46/1.50 inference(superposition,[status(thm)],[f2451,f1287])).
% 1.46/1.50 thf(f2451,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = (((sK4 @ X2 @ X1) | (sK2 @ X2 @ X1)) => (sK11 @ X2 @ X1)))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2450])).
% 1.46/1.50 thf(f2450,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK4 @ Y0 @ X1) | (sK2 @ Y0 @ X1)) => (sK11 @ Y0 @ X1))) @ X2))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f2440])).
% 1.46/1.50 thf(f2440,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ Y0 @ X1) | (sK2 @ Y0 @ X1)) => (sK11 @ Y0 @ X1)))))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2439])).
% 1.46/1.50 thf(f2439,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0))))) @ X1))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f2274])).
% 1.46/1.50 thf(f2274,plain,(
% 1.46/1.50 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0))))))) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f2203])).
% 1.46/1.50 thf(f2203,plain,(
% 1.46/1.50 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0)))))))))) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f2197])).
% 1.46/1.50 thf(f2197,plain,(
% 1.46/1.50 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0))))))))) => (sK11 @ sK8 @ sK7))) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2196])).
% 1.46/1.50 thf(f2196,plain,(
% 1.46/1.50 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))) @ sK11) = $false) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f2118])).
% 1.46/1.50 thf(f2118,plain,(
% 1.46/1.50 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) = $false) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f2101])).
% 1.46/1.50 thf(f2101,plain,(
% 1.46/1.50 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK9 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK9))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2100])).
% 1.46/1.50 thf(f2100,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK8 @ sK7)))))) @ sK9)) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f2094])).
% 1.46/1.50 thf(f2094,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK8 @ sK7))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2093])).
% 1.46/1.50 thf(f2093,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ sK7)))))))) @ sK8)) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f2080])).
% 1.46/1.50 thf(f2080,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ sK7))))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2079])).
% 1.46/1.50 thf(f2079,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))))))))) @ sK7) = $false) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f28])).
% 1.46/1.50 thf(f28,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.46/1.50 thf(f27,definition,(
% 1.46/1.50 spl0_2 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))))))))) = $false)),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.46/1.50 thf(f2588,plain,(
% 1.46/1.50 ~spl0_2 | ~spl0_7 | ~spl0_17),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f2587])).
% 1.46/1.50 thf(f2587,plain,(
% 1.46/1.50 $false | (~spl0_2 | ~spl0_7 | ~spl0_17)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f2586])).
% 1.46/1.50 thf(f2586,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_2 | ~spl0_7 | ~spl0_17)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2585])).
% 1.46/1.50 thf(f2585,plain,(
% 1.46/1.50 ((~ $true) = $true) | (~spl0_2 | ~spl0_7 | ~spl0_17)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2584])).
% 1.46/1.50 thf(f2584,plain,(
% 1.46/1.50 ($true = (~ ((sK4 @ sK21 @ sK22) | $true))) | (~spl0_2 | ~spl0_7 | ~spl0_17)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f2578,f911])).
% 1.46/1.50 thf(f911,plain,(
% 1.46/1.50 ($true = (sK2 @ sK21 @ sK22)) | ~spl0_17),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f910])).
% 1.46/1.50 thf(f910,definition,(
% 1.46/1.50 spl0_17 <=> ($true = (sK2 @ sK21 @ sK22))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.46/1.50 thf(f2578,plain,(
% 1.46/1.50 ($true = (~ ((sK4 @ sK21 @ sK22) | (sK2 @ sK21 @ sK22)))) | (~spl0_2 | ~spl0_7 | ~spl0_17)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2574])).
% 1.46/1.50 thf(f2574,plain,(
% 1.46/1.50 ($true = (((sK4 @ sK21 @ sK22) | (sK2 @ sK21 @ sK22)) => $false)) | (~spl0_2 | ~spl0_7 | ~spl0_17)),
% 1.46/1.50 inference(superposition,[status(thm)],[f2451,f2573])).
% 1.46/1.50 thf(f2573,plain,(
% 1.46/1.50 ((sK11 @ sK21 @ sK22) = $false) | (~spl0_7 | ~spl0_17)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2572])).
% 1.46/1.50 thf(f2572,plain,(
% 1.46/1.50 (($true => (sK11 @ sK21 @ sK22)) = $false) | (~spl0_7 | ~spl0_17)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2571])).
% 1.46/1.50 thf(f2571,plain,(
% 1.46/1.50 ($false = (($true | (sK4 @ sK21 @ sK22)) => (sK11 @ sK21 @ sK22))) | (~spl0_7 | ~spl0_17)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f2564,f911])).
% 1.46/1.50 thf(f2564,plain,(
% 1.46/1.50 ((((sK2 @ sK21 @ sK22) | (sK4 @ sK21 @ sK22)) => (sK11 @ sK21 @ sK22)) = $false) | ~spl0_7),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2563])).
% 1.46/1.50 thf(f2563,plain,(
% 1.46/1.50 (((^[Y0 : a]: (((sK2 @ sK21 @ Y0) | (sK4 @ sK21 @ Y0)) => (sK11 @ sK21 @ Y0))) @ sK22) = $false) | ~spl0_7),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f2555])).
% 1.46/1.50 thf(f2555,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK21 @ Y0) | (sK4 @ sK21 @ Y0)) => (sK11 @ sK21 @ Y0)))) = $false) | ~spl0_7),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2552])).
% 1.46/1.50 thf(f2552,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1))))) @ sK21) = $false) | ~spl0_7),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f284])).
% 1.46/1.50 thf(f284,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1))))))) | ~spl0_7),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f283])).
% 1.46/1.50 thf(f283,definition,(
% 1.46/1.50 spl0_7 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1)))))))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.46/1.50 thf(f2570,plain,(
% 1.46/1.50 ~spl0_2 | ~spl0_7 | ~spl0_16),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f2569])).
% 1.46/1.50 thf(f2569,plain,(
% 1.46/1.50 $false | (~spl0_2 | ~spl0_7 | ~spl0_16)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f2568])).
% 1.46/1.50 thf(f2568,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_2 | ~spl0_7 | ~spl0_16)),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f2485,f2567])).
% 1.46/1.50 thf(f2567,plain,(
% 1.46/1.50 ((sK11 @ sK21 @ sK22) = $false) | (~spl0_7 | ~spl0_16)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2566])).
% 1.46/1.50 thf(f2566,plain,(
% 1.46/1.50 (($true => (sK11 @ sK21 @ sK22)) = $false) | (~spl0_7 | ~spl0_16)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2565])).
% 1.46/1.50 thf(f2565,plain,(
% 1.46/1.50 ((((sK2 @ sK21 @ sK22) | $true) => (sK11 @ sK21 @ sK22)) = $false) | (~spl0_7 | ~spl0_16)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f2564,f908])).
% 1.46/1.50 thf(f908,plain,(
% 1.46/1.50 ((sK4 @ sK21 @ sK22) = $true) | ~spl0_16),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f907])).
% 1.46/1.50 thf(f907,definition,(
% 1.46/1.50 spl0_16 <=> ((sK4 @ sK21 @ sK22) = $true)),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.46/1.50 thf(f2485,plain,(
% 1.46/1.50 ((sK11 @ sK21 @ sK22) = $true) | (~spl0_2 | ~spl0_16)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2484])).
% 1.46/1.50 thf(f2484,plain,(
% 1.46/1.50 (($true => (sK11 @ sK21 @ sK22)) = $true) | (~spl0_2 | ~spl0_16)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2469])).
% 1.46/1.50 thf(f2469,plain,(
% 1.46/1.50 ($true = (($true | (sK2 @ sK21 @ sK22)) => (sK11 @ sK21 @ sK22))) | (~spl0_2 | ~spl0_16)),
% 1.46/1.50 inference(superposition,[status(thm)],[f2451,f908])).
% 1.46/1.50 thf(f2070,plain,(
% 1.46/1.50 ~spl0_10 | ~spl0_12 | ~spl0_20),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f2069])).
% 1.46/1.50 thf(f2069,plain,(
% 1.46/1.50 $false | (~spl0_10 | ~spl0_12 | ~spl0_20)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f2068])).
% 1.46/1.50 thf(f2068,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_10 | ~spl0_12 | ~spl0_20)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2067])).
% 1.46/1.50 thf(f2067,plain,(
% 1.46/1.50 ((~ $true) = $true) | (~spl0_10 | ~spl0_12 | ~spl0_20)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2066])).
% 1.46/1.50 thf(f2066,plain,(
% 1.46/1.50 ($true = (~ ($true | (sK4 @ sK35 @ sK36)))) | (~spl0_10 | ~spl0_12 | ~spl0_20)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f2060,f2053])).
% 1.46/1.50 thf(f2053,plain,(
% 1.46/1.50 ((sK2 @ sK35 @ sK36) = $true) | ~spl0_20),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f2051])).
% 1.46/1.50 thf(f2051,plain,(
% 1.46/1.50 (((sK2 @ sK35 @ sK36) => (sK20 @ sK35 @ sK36)) = $false) | ~spl0_20),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2050])).
% 1.46/1.50 thf(f2050,plain,(
% 1.46/1.50 (((^[Y0 : a]: ((sK2 @ sK35 @ Y0) => (sK20 @ sK35 @ Y0))) @ sK36) = $false) | ~spl0_20),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f2046])).
% 1.46/1.50 thf(f2046,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK35 @ Y0) => (sK20 @ sK35 @ Y0))))) | ~spl0_20),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f2042])).
% 1.46/1.50 thf(f2042,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1))))) @ sK35) = $false) | ~spl0_20),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1101])).
% 1.46/1.50 thf(f1101,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))) = $false) | ~spl0_20),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f1100])).
% 1.46/1.50 thf(f1100,definition,(
% 1.46/1.50 spl0_20 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))) = $false)),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])).
% 1.46/1.50 thf(f2060,plain,(
% 1.46/1.50 ((~ ((sK2 @ sK35 @ sK36) | (sK4 @ sK35 @ sK36))) = $true) | (~spl0_10 | ~spl0_12 | ~spl0_20)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2056])).
% 1.46/1.50 thf(f2056,plain,(
% 1.46/1.50 ((((sK2 @ sK35 @ sK36) | (sK4 @ sK35 @ sK36)) => $false) = $true) | (~spl0_10 | ~spl0_12 | ~spl0_20)),
% 1.46/1.50 inference(superposition,[status(thm)],[f1986,f2055])).
% 1.46/1.50 thf(f2055,plain,(
% 1.46/1.50 ((sK20 @ sK35 @ sK36) = $false) | ~spl0_20),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f2054])).
% 1.46/1.50 thf(f2054,plain,(
% 1.46/1.50 ($false = ($true => (sK20 @ sK35 @ sK36))) | ~spl0_20),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f2051,f2053])).
% 1.46/1.50 thf(f1986,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = (((sK2 @ X2 @ X1) | (sK4 @ X2 @ X1)) => (sK20 @ X2 @ X1)))) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1985])).
% 1.46/1.50 thf(f1985,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK4 @ Y0 @ X1)) => (sK20 @ Y0 @ X1))) @ X2) = $true)) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f1981])).
% 1.46/1.50 thf(f1981,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK4 @ Y0 @ X1)) => (sK20 @ Y0 @ X1)))))) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1980])).
% 1.46/1.50 thf(f1980,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0))))) @ X1))) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f1903])).
% 1.46/1.50 thf(f1903,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0)))))) = $true) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1872])).
% 1.46/1.50 thf(f1872,plain,(
% 1.46/1.50 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))) = $true) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1868])).
% 1.46/1.50 thf(f1868,plain,(
% 1.46/1.50 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))) => (sK20 @ sK19 @ sK18)) = $false) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1867])).
% 1.46/1.50 thf(f1867,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))) @ sK20)) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1866])).
% 1.46/1.50 thf(f1866,plain,(
% 1.46/1.50 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1865])).
% 1.46/1.50 thf(f1865,plain,(
% 1.46/1.50 ($false = ($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1864])).
% 1.46/1.50 thf(f1864,plain,(
% 1.46/1.50 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))) | $true) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1714,f841])).
% 1.46/1.50 thf(f841,plain,(
% 1.46/1.50 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK19 @ sK18))))) | ~spl0_12),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f840])).
% 1.46/1.50 thf(f840,definition,(
% 1.46/1.50 spl0_12 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK19 @ sK18)))))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.46/1.50 thf(f1714,plain,(
% 1.46/1.50 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK19 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))))) = $false) | ~spl0_10),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1713])).
% 1.46/1.50 thf(f1713,plain,(
% 1.46/1.50 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))))) @ sK19) = $false) | ~spl0_10),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1692])).
% 1.46/1.50 thf(f1692,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))))))) | ~spl0_10),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1691])).
% 1.46/1.50 thf(f1691,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK18) = $false) | ~spl0_10),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f496])).
% 1.46/1.50 thf(f496,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false) | ~spl0_10),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f495])).
% 1.46/1.50 thf(f495,definition,(
% 1.46/1.50 spl0_10 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false)),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.46/1.50 thf(f2000,plain,(
% 1.46/1.50 ~spl0_10 | ~spl0_12 | ~spl0_21),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f1999])).
% 1.46/1.50 thf(f1999,plain,(
% 1.46/1.50 $false | (~spl0_10 | ~spl0_12 | ~spl0_21)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f1998])).
% 1.46/1.50 thf(f1998,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_10 | ~spl0_12 | ~spl0_21)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f1992,f1917])).
% 1.46/1.50 thf(f1917,plain,(
% 1.46/1.50 ($false = (sK20 @ sK33 @ sK34)) | ~spl0_21),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1916])).
% 1.46/1.50 thf(f1916,plain,(
% 1.46/1.50 ($false = ($true => (sK20 @ sK33 @ sK34))) | ~spl0_21),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1911,f1915])).
% 1.46/1.50 thf(f1915,plain,(
% 1.46/1.50 ($true = ((sK20 @ sK33 @ sK32) & (sK20 @ sK32 @ sK34))) | ~spl0_21),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1911])).
% 1.46/1.50 thf(f1911,plain,(
% 1.46/1.50 ((((sK20 @ sK33 @ sK32) & (sK20 @ sK32 @ sK34)) => (sK20 @ sK33 @ sK34)) = $false) | ~spl0_21),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1910])).
% 1.46/1.50 thf(f1910,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (((sK20 @ sK33 @ sK32) & (sK20 @ sK32 @ Y0)) => (sK20 @ sK33 @ Y0))) @ sK34)) | ~spl0_21),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1907])).
% 1.46/1.50 thf(f1907,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((sK20 @ sK33 @ sK32) & (sK20 @ sK32 @ Y0)) => (sK20 @ sK33 @ Y0)))) = $false) | ~spl0_21),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1906])).
% 1.46/1.50 thf(f1906,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK20 @ Y0 @ sK32) & (sK20 @ sK32 @ Y1)) => (sK20 @ Y0 @ Y1))))) @ sK33)) | ~spl0_21),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1870])).
% 1.46/1.50 thf(f1870,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK20 @ Y0 @ sK32) & (sK20 @ sK32 @ Y1)) => (sK20 @ Y0 @ Y1)))))) = $false) | ~spl0_21),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1869])).
% 1.46/1.50 thf(f1869,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y1 @ Y0) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y1 @ Y2))))))) @ sK32) = $false) | ~spl0_21),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1104])).
% 1.46/1.50 thf(f1104,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y1 @ Y0) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y1 @ Y2))))))))) | ~spl0_21),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f1103])).
% 1.46/1.50 thf(f1103,definition,(
% 1.46/1.50 spl0_21 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y1 @ Y0) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y1 @ Y2)))))))))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 1.46/1.50 thf(f1992,plain,(
% 1.46/1.50 ($true = (sK20 @ sK33 @ sK34)) | (~spl0_10 | ~spl0_12 | ~spl0_21)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1990])).
% 1.46/1.50 thf(f1990,plain,(
% 1.46/1.50 ($true = ($true => (sK20 @ sK33 @ sK34))) | (~spl0_10 | ~spl0_12 | ~spl0_21)),
% 1.46/1.50 inference(superposition,[status(thm)],[f1948,f1937])).
% 1.46/1.50 thf(f1937,plain,(
% 1.46/1.50 ($true = (sK20 @ sK32 @ sK34)) | ~spl0_21),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1915])).
% 1.46/1.50 thf(f1948,plain,(
% 1.46/1.50 ( ! [X0 : a] : ((((sK20 @ sK32 @ X0) => (sK20 @ sK33 @ X0)) = $true)) ) | (~spl0_10 | ~spl0_12 | ~spl0_21)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1944])).
% 1.46/1.50 thf(f1944,plain,(
% 1.46/1.50 ( ! [X0 : a] : (($true = (((sK20 @ sK32 @ X0) & $true) => (sK20 @ sK33 @ X0)))) ) | (~spl0_10 | ~spl0_12 | ~spl0_21)),
% 1.46/1.50 inference(superposition,[status(thm)],[f1919,f1940])).
% 1.46/1.50 thf(f1940,plain,(
% 1.46/1.50 ($true = (sK20 @ sK33 @ sK32)) | ~spl0_21),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1939])).
% 1.46/1.50 thf(f1939,plain,(
% 1.46/1.50 ($true = ((sK20 @ sK33 @ sK32) & $true)) | ~spl0_21),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1915,f1937])).
% 1.46/1.50 thf(f1919,plain,(
% 1.46/1.50 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK20 @ X3 @ X2) & (sK20 @ X1 @ X3)) => (sK20 @ X1 @ X2)) = $true)) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1918])).
% 1.46/1.50 thf(f1918,plain,(
% 1.46/1.50 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK20 @ Y0 @ X2) & (sK20 @ X1 @ Y0)) => (sK20 @ X1 @ X2))) @ X3))) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f1913])).
% 1.46/1.50 thf(f1913,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK20 @ Y0 @ X2) & (sK20 @ X1 @ Y0)) => (sK20 @ X1 @ X2)))))) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1912])).
% 1.46/1.50 thf(f1912,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK20 @ Y1 @ Y0) & (sK20 @ X1 @ Y1)) => (sK20 @ X1 @ Y0))))) @ X2))) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f1909])).
% 1.46/1.50 thf(f1909,plain,(
% 1.46/1.50 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK20 @ Y1 @ Y0) & (sK20 @ X1 @ Y1)) => (sK20 @ X1 @ Y0)))))) = $true)) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1908])).
% 1.46/1.50 thf(f1908,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))) @ X1))) ) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f1905])).
% 1.46/1.50 thf(f1905,plain,(
% 1.46/1.50 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1904])).
% 1.46/1.50 thf(f1904,plain,(
% 1.46/1.50 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1)))))))))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1872,f1903])).
% 1.46/1.50 thf(f1863,plain,(
% 1.46/1.50 ~spl0_10 | ~spl0_13),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f1862])).
% 1.46/1.50 thf(f1862,plain,(
% 1.46/1.50 $false | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f1861])).
% 1.46/1.50 thf(f1861,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1860])).
% 1.46/1.50 thf(f1860,plain,(
% 1.46/1.50 ((~ $true) = $true) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1859])).
% 1.46/1.50 thf(f1859,plain,(
% 1.46/1.50 ($true = (~ ((sK2 @ sK23 @ sK24) | $true))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f1858,f1846])).
% 1.46/1.50 thf(f1846,plain,(
% 1.46/1.50 ($true = (sK4 @ sK23 @ sK24)) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1844])).
% 1.46/1.50 thf(f1844,plain,(
% 1.46/1.50 ($false = ((sK4 @ sK23 @ sK24) => (sK20 @ sK23 @ sK24))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1843])).
% 1.46/1.50 thf(f1843,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: ((sK4 @ sK23 @ Y0) => (sK20 @ sK23 @ Y0))) @ sK24)) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1840])).
% 1.46/1.50 thf(f1840,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: ((sK4 @ sK23 @ Y0) => (sK20 @ sK23 @ Y0))))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1838])).
% 1.46/1.50 thf(f1838,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1))))) @ sK23)) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1835])).
% 1.46/1.50 thf(f1835,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1))))))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(not_proxy_clausification,[status(thm)],[f1807])).
% 1.46/1.50 thf(f1807,plain,(
% 1.46/1.50 ($true = (~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1806])).
% 1.46/1.50 thf(f1806,plain,(
% 1.46/1.50 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))) & $true))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f1805,f1744])).
% 1.46/1.50 thf(f1744,plain,(
% 1.46/1.50 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1739])).
% 1.46/1.50 thf(f1739,plain,(
% 1.46/1.50 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))) = $true) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1734])).
% 1.46/1.50 thf(f1734,plain,(
% 1.46/1.50 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))) => (sK20 @ sK19 @ sK18)) = $false) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1733])).
% 1.46/1.50 thf(f1733,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))) @ sK20)) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1717])).
% 1.46/1.50 thf(f1717,plain,(
% 1.46/1.50 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1716])).
% 1.46/1.50 thf(f1716,plain,(
% 1.46/1.50 ($false = ($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1715])).
% 1.46/1.50 thf(f1715,plain,(
% 1.46/1.50 ((($true | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK19 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))))) = $false) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f1714,f844])).
% 1.46/1.50 thf(f844,plain,(
% 1.46/1.50 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))))) | ~spl0_13),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f843])).
% 1.46/1.50 thf(f843,definition,(
% 1.46/1.50 spl0_13 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.46/1.50 thf(f1805,plain,(
% 1.46/1.50 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1804])).
% 1.46/1.50 thf(f1804,plain,(
% 1.46/1.50 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))) => $false) = $true) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(superposition,[status(thm)],[f1799,f1738])).
% 1.46/1.50 thf(f1738,plain,(
% 1.46/1.50 ((sK20 @ sK19 @ sK18) = $false) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1734])).
% 1.46/1.50 thf(f1799,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y2 @ Y1) & (X1 @ Y0 @ Y2)) => (X1 @ Y0 @ Y1))))))))) => (X1 @ sK19 @ sK18)))) ) | ~spl0_13),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1798])).
% 1.46/1.50 thf(f1798,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))) @ X1) = $true)) ) | ~spl0_13),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f844])).
% 1.46/1.50 thf(f1858,plain,(
% 1.46/1.50 ($true = (~ ((sK2 @ sK23 @ sK24) | (sK4 @ sK23 @ sK24)))) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1857])).
% 1.46/1.50 thf(f1857,plain,(
% 1.46/1.50 ($true = (((sK2 @ sK23 @ sK24) | (sK4 @ sK23 @ sK24)) => $false)) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(superposition,[status(thm)],[f1761,f1845])).
% 1.46/1.50 thf(f1845,plain,(
% 1.46/1.50 ((sK20 @ sK23 @ sK24) = $false) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1844])).
% 1.46/1.50 thf(f1761,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = (((sK2 @ X2 @ X1) | (sK4 @ X2 @ X1)) => (sK20 @ X2 @ X1)))) ) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1760])).
% 1.46/1.50 thf(f1760,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK4 @ Y0 @ X1)) => (sK20 @ Y0 @ X1))) @ X2) = $true)) ) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f1755])).
% 1.46/1.50 thf(f1755,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK4 @ Y0 @ X1)) => (sK20 @ Y0 @ X1)))))) ) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1754])).
% 1.46/1.50 thf(f1754,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0))))) @ X1))) ) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f1747])).
% 1.46/1.50 thf(f1747,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0)))))) = $true) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1746])).
% 1.46/1.50 thf(f1746,plain,(
% 1.46/1.50 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0)))))) & $true)) | (~spl0_10 | ~spl0_13)),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1739,f1744])).
% 1.46/1.50 thf(f1671,plain,(
% 1.46/1.50 ~spl0_15 | ~spl0_29),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f1670])).
% 1.46/1.50 thf(f1670,plain,(
% 1.46/1.50 $false | (~spl0_15 | ~spl0_29)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f1669])).
% 1.46/1.50 thf(f1669,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_15 | ~spl0_29)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1668])).
% 1.46/1.50 thf(f1668,plain,(
% 1.46/1.50 ((~ $true) = $true) | (~spl0_15 | ~spl0_29)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1665])).
% 1.46/1.50 thf(f1665,plain,(
% 1.46/1.50 ($true = (~ ((sK4 @ sK30 @ sK31) | $true))) | (~spl0_15 | ~spl0_29)),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1647,f1656])).
% 1.46/1.50 thf(f1656,plain,(
% 1.46/1.50 ($true = (sK2 @ sK30 @ sK31)) | ~spl0_29),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f1655])).
% 1.46/1.50 thf(f1655,definition,(
% 1.46/1.50 spl0_29 <=> ($true = (sK2 @ sK30 @ sK31))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition])).
% 1.46/1.50 thf(f1647,plain,(
% 1.46/1.50 ($true = (~ ((sK4 @ sK30 @ sK31) | (sK2 @ sK30 @ sK31)))) | ~spl0_15),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1643])).
% 1.46/1.50 thf(f1643,plain,(
% 1.46/1.50 ($true = (((sK4 @ sK30 @ sK31) | (sK2 @ sK30 @ sK31)) => $false)) | ~spl0_15),
% 1.46/1.50 inference(superposition,[status(thm)],[f61,f1634])).
% 1.46/1.50 thf(f1634,plain,(
% 1.46/1.50 ($false = (sK6 @ sK30 @ sK31)) | ~spl0_15),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1633])).
% 1.46/1.50 thf(f1633,plain,(
% 1.46/1.50 ((((sK2 @ sK30 @ sK31) | (sK4 @ sK30 @ sK31)) => (sK6 @ sK30 @ sK31)) = $false) | ~spl0_15),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1632])).
% 1.46/1.50 thf(f1632,plain,(
% 1.46/1.50 (((^[Y0 : a]: (((sK2 @ sK30 @ Y0) | (sK4 @ sK30 @ Y0)) => (sK6 @ sK30 @ Y0))) @ sK31) = $false) | ~spl0_15),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1613])).
% 1.46/1.50 thf(f1613,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK30 @ Y0) | (sK4 @ sK30 @ Y0)) => (sK6 @ sK30 @ Y0)))) = $false) | ~spl0_15),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1612])).
% 1.46/1.50 thf(f1612,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))) @ sK30)) | ~spl0_15),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f876])).
% 1.46/1.50 thf(f876,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) = $false) | ~spl0_15),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f875])).
% 1.46/1.50 thf(f875,definition,(
% 1.46/1.50 spl0_15 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) = $false)),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.46/1.50 thf(f61,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (((((sK4 @ X1 @ X2) | (sK2 @ X1 @ X2)) => (sK6 @ X1 @ X2)) = $true)) )),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.46/1.50 thf(f60,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK4 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK6 @ X1 @ Y0))) @ X2))) )),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f57])).
% 1.46/1.50 thf(f57,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK6 @ X1 @ Y0)))))) )),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.46/1.50 thf(f56,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))) @ X1))) )),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f45])).
% 1.46/1.50 thf(f45,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) = $true)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.46/1.50 thf(f37,plain,(
% 1.46/1.50 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y2 @ Y1)) => (sK6 @ Y0 @ Y1))))))))) = $true)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.46/1.50 thf(f33,plain,(
% 1.46/1.50 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y2 @ Y1)) => (sK6 @ Y0 @ Y1))))))))) => (sK6 @ sK3 @ sK5)))),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.46/1.50 thf(f32,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK3 @ sK5))) @ sK6))),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f18])).
% 1.46/1.50 thf(f18,plain,(
% 1.46/1.50 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK3 @ sK5)))))),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.46/1.50 thf(f17,plain,(
% 1.46/1.50 (((((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))))))))))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK3 @ sK5))))) = $false)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.46/1.50 thf(f16,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK3 @ Y0))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK4 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y2 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y3 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y5 @ Y6) | (sK4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y2 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK4 @ Y6 @ Y5) | (sK2 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y2 @ Y1)))))))))))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ sK3 @ Y0)))))) @ sK5))),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f15])).
% 1.46/1.50 thf(f15,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK3 @ Y0))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK4 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y2 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y3 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y5 @ Y6) | (sK4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y2 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK4 @ Y6 @ Y5) | (sK2 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y2 @ Y1)))))))))))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ sK3 @ Y0))))))) = $false)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.46/1.50 thf(f14,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (Y0 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ sK3 @ Y1))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y3 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y8 @ Y6)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y4 @ Y2)))) & (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y6 @ Y7) | (Y0 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y3 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y7 @ Y6) | (sK2 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y7 @ Y6))))))))) => (Y5 @ Y3 @ Y2)))))))))))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ sK3 @ Y1)))))))) @ sK4))),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f13])).
% 1.46/1.50 thf(f13,plain,(
% 1.46/1.50 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (Y0 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ sK3 @ Y1))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y3 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y3 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y8 @ Y6)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y4 @ Y2)))) & (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y6 @ Y7) | (Y0 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y3 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y7 @ Y6) | (sK2 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y7 @ Y6))))))))) => (Y5 @ Y3 @ Y2)))))))))))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ sK3 @ Y1))))))))) = $false)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.46/1.50 thf(f12,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (Y1 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y0 @ Y2))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y1 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y6 @ Y7))))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y4 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y6 @ Y7))))))))) => (Y5 @ Y4 @ Y3)))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y5 @ Y3)))) & (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y7 @ Y8) | (Y1 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y4 @ Y5))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y8 @ Y7) | (sK2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y8 @ Y7))))))))) => (Y6 @ Y4 @ Y3)))))))))))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y0 @ Y2)))))))))) @ sK3))),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f11])).
% 1.46/1.50 thf(f11,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (Y1 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y0 @ Y2))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y1 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y6 @ Y7))))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y4 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y6 @ Y7))))))))) => (Y5 @ Y4 @ Y3)))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y5 @ Y3)))) & (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y7 @ Y8) | (Y1 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y4 @ Y5))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y8 @ Y7) | (sK2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y8 @ Y7))))))))) => (Y6 @ Y4 @ Y3)))))))))))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))) = $false)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.46/1.50 thf(f10,plain,(
% 1.46/1.50 (((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y1 @ Y3))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y5 @ Y4)))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y6 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) | (Y2 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y10))))))))) => (Y7 @ Y5 @ Y6))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y9 @ Y8) | (Y0 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y9 @ Y8))))))))) => (Y7 @ Y5 @ Y4)))))))))))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y2 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y1 @ Y3)))))))))))) @ sK2) = $false)),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f7])).
% 1.46/1.50 thf(f7,plain,(
% 1.46/1.50 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y1 @ Y3))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y5 @ Y4)))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y6 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) | (Y2 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y10))))))))) => (Y7 @ Y5 @ Y6))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y9 @ Y8) | (Y0 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y9 @ Y8))))))))) => (Y7 @ Y5 @ Y4)))))))))))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y2 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y1 @ Y3))))))))))))))),
% 1.46/1.50 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.46/1.50 thf(f6,plain,(
% 1.46/1.50 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y1 @ Y3))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y5 @ Y4)))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y6 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) | (Y2 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y10))))))))) => (Y7 @ Y5 @ Y6))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y9 @ Y8) | (Y0 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y9 @ Y8))))))))) => (Y7 @ Y5 @ Y4)))))))))))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y2 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y1 @ Y3)))))))))))))))),
% 1.46/1.50 inference(cnf_transformation,[status(thm)],[f5])).
% 1.46/1.50 thf(f5,plain,(
% 1.46/1.50 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((~ (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y1 @ Y3))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8))))))))) => (Y6 @ Y5 @ Y4)))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y6 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) | (Y2 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y10))))))))) => (Y7 @ Y5 @ Y6))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y9 @ Y8) | (Y0 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y9 @ Y8))))))))) => (Y7 @ Y5 @ Y4)))))))))))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y2 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y1 @ Y3)))))))))))))))),
% 1.46/1.50 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.50 thf(f4,plain,(
% 1.46/1.50 ~! [X0 : a,X1 : a > a > $o,X2 : a,X3 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a,X7 : a] : (((X4 @ X5 @ X6) & (X4 @ X7 @ X5)) => (X4 @ X7 @ X6)) & ! [X8 : a,X9 : a] : (((X3 @ X9 @ X8) | (X1 @ X9 @ X8)) => (X4 @ X9 @ X8))) => (X4 @ X2 @ X0)) | (! [X10 : a,X11 : a,X12 : a] : ((! [X13 : a > a > $o] : ((! [X14 : a,X15 : a,X16 : a] : (((X13 @ X15 @ X16) & (X13 @ X16 @ X14)) => (X13 @ X15 @ X14)) & ! [X17 : a,X18 : a] : (((X1 @ X18 @ X17) | (X3 @ X18 @ X17)) => (X13 @ X18 @ X17))) => (X13 @ X11 @ X10)) & ! [X19 : a > a > $o] : ((! [X20 : a,X21 : a,X22 : a] : (((X19 @ X20 @ X22) & (X19 @ X22 @ X21)) => (X19 @ X20 @ X21)) & ! [X23 : a,X24 : a] : (((X1 @ X23 @ X24) | (X3 @ X23 @ X24)) => (X19 @ X23 @ X24))) => (X19 @ X10 @ X12))) => ! [X25 : a > a > $o] : ((! [X26 : a,X27 : a,X28 : a] : (((X25 @ X27 @ X26) & (X25 @ X26 @ X28)) => (X25 @ X27 @ X28)) & ! [X29 : a,X30 : a] : (((X3 @ X29 @ X30) | (X1 @ X29 @ X30)) => (X25 @ X29 @ X30))) => (X25 @ X11 @ X12))) & ! [X31 : a,X32 : a] : ((! [X33 : a > a > $o] : ((! [X34 : a,X35 : a,X36 : a] : (((X33 @ X36 @ X34) & (X33 @ X35 @ X36)) => (X33 @ X35 @ X34)) & ! [X37 : a,X38 : a] : ((X3 @ X38 @ X37) => (X33 @ X38 @ X37))) => (X33 @ X31 @ X32)) | ! [X39 : a > a > $o] : ((! [X40 : a,X41 : a,X42 : a] : (((X39 @ X42 @ X40) & (X39 @ X40 @ X41)) => (X39 @ X42 @ X41)) & ! [X43 : a,X44 : a] : ((X1 @ X44 @ X43) => (X39 @ X44 @ X43))) => (X39 @ X31 @ X32))) => ! [X45 : a > a > $o] : ((! [X46 : a,X47 : a,X48 : a] : (((X45 @ X48 @ X46) & (X45 @ X46 @ X47)) => (X45 @ X48 @ X47)) & ! [X49 : a,X50 : a] : (((X1 @ X49 @ X50) | (X3 @ X49 @ X50)) => (X45 @ X49 @ X50))) => (X45 @ X31 @ X32))) & ~! [X51 : a > a > $o] : ((! [X52 : a,X53 : a,X54 : a] : (((X51 @ X52 @ X54) & (X51 @ X53 @ X52)) => (X51 @ X53 @ X54)) & ! [X55 : a,X56 : a] : (((X1 @ X56 @ X55) | (X3 @ X56 @ X55)) => (X51 @ X56 @ X55))) => (X51 @ X2 @ X0))))),
% 1.46/1.50 inference(rectify,[status(thm)],[f2])).
% 1.46/1.50 thf(f2,negated_conjecture,(
% 1.46/1.50 ~! [X3 : a,X1 : a > a > $o,X2 : a,X0 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X6 : a,X7 : a,X5 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) | (! [X6 : a,X5 : a,X7 : a] : ((! [X4 : a > a > $o] : ((! [X10 : a,X8 : a,X9 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6)) & ! [X4 : a > a > $o] : ((! [X8 : a,X10 : a,X9 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X6 @ X7))) => ! [X4 : a > a > $o] : ((! [X9 : a,X8 : a,X10 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X7))) & ! [X5 : a,X6 : a] : ((! [X4 : a > a > $o] : ((! [X7 : a,X8 : a,X9 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X9 : a,X8 : a] : ((X0 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6)) | ! [X4 : a > a > $o] : ((! [X9 : a,X7 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X7)) => (X4 @ X8 @ X7)) & ! [X9 : a,X8 : a] : ((X1 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) => ! [X4 : a > a > $o] : ((! [X9 : a,X7 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X7)) => (X4 @ X8 @ X7)) & ! [X8 : a,X9 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) & ~! [X4 : a > a > $o] : ((! [X6 : a,X5 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X6 : a,X5 : a] : (((X1 @ X5 @ X6) | (X0 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3))))),
% 1.46/1.50 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.50 thf(f1,conjecture,(
% 1.46/1.50 ! [X3 : a,X1 : a > a > $o,X2 : a,X0 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X6 : a,X7 : a,X5 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) | (! [X6 : a,X5 : a,X7 : a] : ((! [X4 : a > a > $o] : ((! [X10 : a,X8 : a,X9 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6)) & ! [X4 : a > a > $o] : ((! [X8 : a,X10 : a,X9 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X6 @ X7))) => ! [X4 : a > a > $o] : ((! [X9 : a,X8 : a,X10 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X7))) & ! [X5 : a,X6 : a] : ((! [X4 : a > a > $o] : ((! [X7 : a,X8 : a,X9 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X9 : a,X8 : a] : ((X0 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6)) | ! [X4 : a > a > $o] : ((! [X9 : a,X7 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X7)) => (X4 @ X8 @ X7)) & ! [X9 : a,X8 : a] : ((X1 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) => ! [X4 : a > a > $o] : ((! [X9 : a,X7 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X7)) => (X4 @ X8 @ X7)) & ! [X8 : a,X9 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) & ~! [X4 : a > a > $o] : ((! [X6 : a,X5 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X6 : a,X5 : a] : (((X1 @ X5 @ X6) | (X0 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3))))),
% 1.46/1.50 file('/export/starexec/sandbox2/tmp/tmp.6Vfhle69yx/DTF2THF_27930.p',cTHM250H_pme)).
% 1.46/1.50 thf(f1664,plain,(
% 1.46/1.50 ~spl0_15 | ~spl0_28),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f1663])).
% 1.46/1.50 thf(f1663,plain,(
% 1.46/1.50 $false | (~spl0_15 | ~spl0_28)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f1662])).
% 1.46/1.50 thf(f1662,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_15 | ~spl0_28)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1661])).
% 1.46/1.50 thf(f1661,plain,(
% 1.46/1.50 ((~ $true) = $true) | (~spl0_15 | ~spl0_28)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1658])).
% 1.46/1.50 thf(f1658,plain,(
% 1.46/1.50 ((~ ($true | (sK2 @ sK30 @ sK31))) = $true) | (~spl0_15 | ~spl0_28)),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1647,f1653])).
% 1.46/1.50 thf(f1653,plain,(
% 1.46/1.50 ($true = (sK4 @ sK30 @ sK31)) | ~spl0_28),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f1652])).
% 1.46/1.50 thf(f1652,definition,(
% 1.46/1.50 spl0_28 <=> ($true = (sK4 @ sK30 @ sK31))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition])).
% 1.46/1.50 thf(f1657,plain,(
% 1.46/1.50 spl0_28 | spl0_29 | ~spl0_15),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f1650,f875,f1655,f1652])).
% 1.46/1.50 thf(f1650,plain,(
% 1.46/1.50 ($true = (sK2 @ sK30 @ sK31)) | ($true = (sK4 @ sK30 @ sK31)) | ~spl0_15),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1635])).
% 1.46/1.50 thf(f1635,plain,(
% 1.46/1.50 ($true = ((sK2 @ sK30 @ sK31) | (sK4 @ sK30 @ sK31))) | ~spl0_15),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1633])).
% 1.46/1.50 thf(f1565,plain,(
% 1.46/1.50 ~spl0_2 | ~spl0_9 | ~spl0_24),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f1564])).
% 1.46/1.50 thf(f1564,plain,(
% 1.46/1.50 $false | (~spl0_2 | ~spl0_9 | ~spl0_24)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f1563])).
% 1.46/1.50 thf(f1563,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_2 | ~spl0_9 | ~spl0_24)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f1551,f1270])).
% 1.46/1.50 thf(f1270,plain,(
% 1.46/1.50 ($false = (sK11 @ sK29 @ sK28)) | ~spl0_9),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1269])).
% 1.46/1.50 thf(f1269,plain,(
% 1.46/1.50 ($false = ($true => (sK11 @ sK29 @ sK28))) | ~spl0_9),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1260,f1268])).
% 1.46/1.50 thf(f1268,plain,(
% 1.46/1.50 ($true = ((sK2 @ sK29 @ sK28) | (sK4 @ sK29 @ sK28))) | ~spl0_9),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1260])).
% 1.46/1.50 thf(f1260,plain,(
% 1.46/1.50 ((((sK2 @ sK29 @ sK28) | (sK4 @ sK29 @ sK28)) => (sK11 @ sK29 @ sK28)) = $false) | ~spl0_9),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1259])).
% 1.46/1.50 thf(f1259,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (((sK2 @ Y0 @ sK28) | (sK4 @ Y0 @ sK28)) => (sK11 @ Y0 @ sK28))) @ sK29)) | ~spl0_9),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1256])).
% 1.46/1.50 thf(f1256,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK28) | (sK4 @ Y0 @ sK28)) => (sK11 @ Y0 @ sK28))))) | ~spl0_9),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1255])).
% 1.46/1.50 thf(f1255,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0))))) @ sK28)) | ~spl0_9),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f462])).
% 1.46/1.50 thf(f1551,plain,(
% 1.46/1.50 ($true = (sK11 @ sK29 @ sK28)) | (~spl0_2 | ~spl0_24)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1550])).
% 1.46/1.50 thf(f1550,plain,(
% 1.46/1.50 ($true = ($true => (sK11 @ sK29 @ sK28))) | (~spl0_2 | ~spl0_24)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1543])).
% 1.46/1.50 thf(f1543,plain,(
% 1.46/1.50 ((((sK4 @ sK29 @ sK28) | $true) => (sK11 @ sK29 @ sK28)) = $true) | (~spl0_2 | ~spl0_24)),
% 1.46/1.50 inference(superposition,[status(thm)],[f1526,f1284])).
% 1.46/1.50 thf(f1284,plain,(
% 1.46/1.50 ($true = (sK2 @ sK29 @ sK28)) | ~spl0_24),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f1283])).
% 1.46/1.50 thf(f1283,definition,(
% 1.46/1.50 spl0_24 <=> ($true = (sK2 @ sK29 @ sK28))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])).
% 1.46/1.50 thf(f1526,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = (((sK4 @ X2 @ X1) | (sK2 @ X2 @ X1)) => (sK11 @ X2 @ X1)))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1525])).
% 1.46/1.50 thf(f1525,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK4 @ Y0 @ X1) | (sK2 @ Y0 @ X1)) => (sK11 @ Y0 @ X1))) @ X2))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f1513])).
% 1.46/1.50 thf(f1513,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ Y0 @ X1) | (sK2 @ Y0 @ X1)) => (sK11 @ Y0 @ X1)))))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1512])).
% 1.46/1.50 thf(f1512,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0))))) @ X1))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f1330])).
% 1.46/1.50 thf(f1330,plain,(
% 1.46/1.50 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0))))))) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1274])).
% 1.46/1.50 thf(f1274,plain,(
% 1.46/1.50 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0)))))))))) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1272])).
% 1.46/1.50 thf(f1272,plain,(
% 1.46/1.50 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0))))))))) => (sK11 @ sK8 @ sK7))) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1271])).
% 1.46/1.50 thf(f1271,plain,(
% 1.46/1.50 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))) @ sK11) = $false) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1264])).
% 1.46/1.50 thf(f1264,plain,(
% 1.46/1.50 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) = $false) | ~spl0_2),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1263])).
% 1.46/1.50 thf(f1263,plain,(
% 1.46/1.50 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1258,f1262])).
% 1.46/1.50 thf(f1262,plain,(
% 1.46/1.50 ($true = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK9 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK9)))))) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1258])).
% 1.46/1.50 thf(f1258,plain,(
% 1.46/1.50 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK9 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK9))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1257])).
% 1.46/1.50 thf(f1257,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK8 @ sK7)))))) @ sK9)) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1254])).
% 1.46/1.50 thf(f1254,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK8 @ sK7))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1253])).
% 1.46/1.50 thf(f1253,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ sK7)))))))) @ sK8)) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1252])).
% 1.46/1.50 thf(f1252,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ sK7))))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1251])).
% 1.46/1.50 thf(f1251,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))))))))) @ sK7) = $false) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f28])).
% 1.46/1.50 thf(f1288,plain,(
% 1.46/1.50 spl0_24 | spl0_25 | ~spl0_9),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f1281,f461,f1286,f1283])).
% 1.46/1.50 thf(f1281,plain,(
% 1.46/1.50 ($true = (sK2 @ sK29 @ sK28)) | ($true = (sK4 @ sK29 @ sK28)) | ~spl0_9),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1268])).
% 1.46/1.50 thf(f1247,plain,(
% 1.46/1.50 ~spl0_14),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f1246])).
% 1.46/1.50 thf(f1246,plain,(
% 1.46/1.50 $false | ~spl0_14),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f1243])).
% 1.46/1.50 thf(f1243,plain,(
% 1.46/1.50 ($true = $false) | ~spl0_14),
% 1.46/1.50 inference(superposition,[status(thm)],[f106,f1222])).
% 1.46/1.50 thf(f1222,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((sK6 @ sK26 @ Y0) & (sK6 @ Y0 @ sK25)) => (sK6 @ sK26 @ sK25)))) = $false) | ~spl0_14),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1221])).
% 1.46/1.50 thf(f1221,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ sK25)) => (sK6 @ Y0 @ sK25))))) @ sK26)) | ~spl0_14),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1218])).
% 1.46/1.50 thf(f1218,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ sK25)) => (sK6 @ Y0 @ sK25))))))) | ~spl0_14),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1217])).
% 1.46/1.50 thf(f1217,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))) @ sK25) = $false) | ~spl0_14),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f873])).
% 1.46/1.50 thf(f873,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) = $false) | ~spl0_14),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f872])).
% 1.46/1.50 thf(f872,definition,(
% 1.46/1.50 spl0_14 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) = $false)),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.46/1.50 thf(f106,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK6 @ X1 @ Y0) & (sK6 @ Y0 @ X2)) => (sK6 @ X1 @ X2)))))) )),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.46/1.50 thf(f105,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ X1 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ X1 @ Y0))))) @ X2) = $true)) )),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f103])).
% 1.46/1.50 thf(f103,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ X1 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ X1 @ Y0)))))))) )),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.46/1.50 thf(f102,plain,(
% 1.46/1.50 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y2 @ Y1)) => (sK6 @ Y0 @ Y1))))))) @ X1) = $true)) )),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f47])).
% 1.46/1.50 thf(f47,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y2 @ Y1)) => (sK6 @ Y0 @ Y1)))))))) = $true)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f46])).
% 1.46/1.50 thf(f46,plain,(
% 1.46/1.50 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y2 @ Y1)) => (sK6 @ Y0 @ Y1))))))))))),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f37,f45])).
% 1.46/1.50 thf(f1105,plain,(
% 1.46/1.50 spl0_20 | spl0_21 | ~spl0_10 | ~spl0_12),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f1096,f840,f495,f1103,f1100])).
% 1.46/1.50 thf(f1096,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y1 @ Y0) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y1 @ Y2))))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))) = $false) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1087])).
% 1.46/1.50 thf(f1087,plain,(
% 1.46/1.50 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y1 @ Y0) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y1 @ Y2)))))))))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(not_proxy_clausification,[status(thm)],[f1061])).
% 1.46/1.50 thf(f1061,plain,(
% 1.46/1.50 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y1 @ Y0) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y1 @ Y2)))))))))) = $true) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1060])).
% 1.46/1.50 thf(f1060,plain,(
% 1.46/1.50 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK20 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y1 @ Y0) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y1 @ Y2))))))))) => $false)) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(superposition,[status(thm)],[f1047,f1011])).
% 1.46/1.50 thf(f1011,plain,(
% 1.46/1.50 ((sK20 @ sK19 @ sK18) = $false) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1010])).
% 1.46/1.50 thf(f1010,plain,(
% 1.46/1.50 ($false = ($true => (sK20 @ sK19 @ sK18))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f1005,f1009])).
% 1.46/1.50 thf(f1009,plain,(
% 1.46/1.50 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))) = $true) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f1005])).
% 1.46/1.50 thf(f1005,plain,(
% 1.46/1.50 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK20 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK20 @ Y2 @ Y1) & (sK20 @ Y0 @ Y2)) => (sK20 @ Y0 @ Y1))))))))) => (sK20 @ sK19 @ sK18)) = $false) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1004])).
% 1.46/1.50 thf(f1004,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))) @ sK20)) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f1001])).
% 1.46/1.50 thf(f1001,plain,(
% 1.46/1.50 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f1000])).
% 1.46/1.50 thf(f1000,plain,(
% 1.46/1.50 ($false = ($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f999])).
% 1.46/1.50 thf(f999,plain,(
% 1.46/1.50 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))) | $true) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))))) | (~spl0_10 | ~spl0_12)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f998,f841])).
% 1.46/1.50 thf(f998,plain,(
% 1.46/1.50 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK19 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))))) = $false) | ~spl0_10),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f997])).
% 1.46/1.50 thf(f997,plain,(
% 1.46/1.50 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))))) @ sK19) = $false) | ~spl0_10),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f994])).
% 1.46/1.50 thf(f994,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))))))) | ~spl0_10),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f993])).
% 1.46/1.50 thf(f993,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK18) = $false) | ~spl0_10),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f496])).
% 1.46/1.50 thf(f1047,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y0) & (X1 @ Y0 @ Y2)) => (X1 @ Y1 @ Y2))))))))) => (X1 @ sK19 @ sK18)))) ) | ~spl0_12),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f1046])).
% 1.46/1.50 thf(f1046,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK19 @ sK18))) @ X1))) ) | ~spl0_12),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f841])).
% 1.46/1.50 thf(f912,plain,(
% 1.46/1.50 spl0_16 | spl0_17 | ~spl0_7),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f905,f283,f910,f907])).
% 1.46/1.50 thf(f905,plain,(
% 1.46/1.50 ($true = (sK2 @ sK21 @ sK22)) | ((sK4 @ sK21 @ sK22) = $true) | ~spl0_7),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f894])).
% 1.46/1.50 thf(f894,plain,(
% 1.46/1.50 (((sK2 @ sK21 @ sK22) | (sK4 @ sK21 @ sK22)) = $true) | ~spl0_7),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f890])).
% 1.46/1.50 thf(f890,plain,(
% 1.46/1.50 ((((sK2 @ sK21 @ sK22) | (sK4 @ sK21 @ sK22)) => (sK11 @ sK21 @ sK22)) = $false) | ~spl0_7),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f889])).
% 1.46/1.50 thf(f889,plain,(
% 1.46/1.50 (((^[Y0 : a]: (((sK2 @ sK21 @ Y0) | (sK4 @ sK21 @ Y0)) => (sK11 @ sK21 @ Y0))) @ sK22) = $false) | ~spl0_7),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f886])).
% 1.46/1.50 thf(f886,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK21 @ Y0) | (sK4 @ sK21 @ Y0)) => (sK11 @ sK21 @ Y0)))) = $false) | ~spl0_7),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f885])).
% 1.46/1.50 thf(f885,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1))))) @ sK21) = $false) | ~spl0_7),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f284])).
% 1.46/1.50 thf(f877,plain,(
% 1.46/1.50 spl0_14 | spl0_15 | ~spl0_11),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f868,f498,f875,f872])).
% 1.46/1.50 thf(f498,definition,(
% 1.46/1.50 spl0_11 <=> ($false = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5))))))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.46/1.50 thf(f868,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) = $false) | ~spl0_11),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f865])).
% 1.46/1.50 thf(f865,plain,(
% 1.46/1.50 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))))) | ~spl0_11),
% 1.46/1.50 inference(not_proxy_clausification,[status(thm)],[f864])).
% 1.46/1.50 thf(f864,plain,(
% 1.46/1.50 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))))))) | ~spl0_11),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f858])).
% 1.46/1.50 thf(f858,plain,(
% 1.46/1.50 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))))) => $false)) | ~spl0_11),
% 1.46/1.50 inference(superposition,[status(thm)],[f855,f39])).
% 1.46/1.50 thf(f39,plain,(
% 1.46/1.50 ($false = (sK6 @ sK3 @ sK5))),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f38])).
% 1.46/1.50 thf(f38,plain,(
% 1.46/1.50 (($true => (sK6 @ sK3 @ sK5)) = $false)),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f33,f37])).
% 1.46/1.50 thf(f855,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y2) & (X1 @ Y2 @ Y0)) => (X1 @ Y1 @ Y0))))))))) => (X1 @ sK3 @ sK5)))) ) | ~spl0_11),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f854])).
% 1.46/1.50 thf(f854,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5))) @ X1))) ) | ~spl0_11),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f851])).
% 1.46/1.50 thf(f851,plain,(
% 1.46/1.50 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5))))) | ~spl0_11),
% 1.46/1.50 inference(not_proxy_clausification,[status(thm)],[f499])).
% 1.46/1.50 thf(f499,plain,(
% 1.46/1.50 ($false = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5)))))) | ~spl0_11),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f498])).
% 1.46/1.50 thf(f845,plain,(
% 1.46/1.50 spl0_12 | spl0_13 | ~spl0_10),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f838,f495,f843,f840])).
% 1.46/1.50 thf(f838,plain,(
% 1.46/1.50 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))))) | ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK19 @ sK18))))) | ~spl0_10),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f786])).
% 1.46/1.50 thf(f786,plain,(
% 1.46/1.50 ($true = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK19 @ sK18)))))) | ~spl0_10),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f784])).
% 1.46/1.50 thf(f784,plain,(
% 1.46/1.50 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK19 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK19 @ sK18))))) = $false) | ~spl0_10),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f783])).
% 1.46/1.50 thf(f783,plain,(
% 1.46/1.50 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))))) @ sK19) = $false) | ~spl0_10),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f782])).
% 1.46/1.50 thf(f782,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK18))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ Y0 @ sK18)))))))) | ~spl0_10),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f781])).
% 1.46/1.50 thf(f781,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK18) = $false) | ~spl0_10),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f496])).
% 1.46/1.50 thf(f775,plain,(
% 1.46/1.50 ~spl0_2 | ~spl0_8),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f774])).
% 1.46/1.50 thf(f774,plain,(
% 1.46/1.50 $false | (~spl0_2 | ~spl0_8)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f773])).
% 1.46/1.50 thf(f773,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_2 | ~spl0_8)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f772])).
% 1.46/1.50 thf(f772,plain,(
% 1.46/1.50 ((~ $true) = $true) | (~spl0_2 | ~spl0_8)),
% 1.46/1.50 inference(forward_demodulation,[status(thm)],[f766,f533])).
% 1.46/1.50 thf(f533,plain,(
% 1.46/1.50 ((sK11 @ sK15 @ sK16) = $true) | ~spl0_8),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f524])).
% 1.46/1.50 thf(f524,plain,(
% 1.46/1.50 ($true = ((sK11 @ sK15 @ sK16) & (sK11 @ sK17 @ sK15))) | ~spl0_8),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f514])).
% 1.46/1.50 thf(f514,plain,(
% 1.46/1.50 ($false = (((sK11 @ sK15 @ sK16) & (sK11 @ sK17 @ sK15)) => (sK11 @ sK17 @ sK16))) | ~spl0_8),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f513])).
% 1.46/1.50 thf(f513,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (((sK11 @ sK15 @ sK16) & (sK11 @ Y0 @ sK15)) => (sK11 @ Y0 @ sK16))) @ sK17)) | ~spl0_8),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f510])).
% 1.46/1.50 thf(f510,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((sK11 @ sK15 @ sK16) & (sK11 @ Y0 @ sK15)) => (sK11 @ Y0 @ sK16)))) = $false) | ~spl0_8),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f509])).
% 1.46/1.50 thf(f509,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ sK15 @ Y0) & (sK11 @ Y1 @ sK15)) => (sK11 @ Y1 @ Y0))))) @ sK16) = $false) | ~spl0_8),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f506])).
% 1.46/1.50 thf(f506,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ sK15 @ Y0) & (sK11 @ Y1 @ sK15)) => (sK11 @ Y1 @ Y0))))))) | ~spl0_8),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f505])).
% 1.46/1.50 thf(f505,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y2 @ Y0)) => (sK11 @ Y2 @ Y1))))))) @ sK15) = $false) | ~spl0_8),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f459])).
% 1.46/1.50 thf(f459,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y2 @ Y0)) => (sK11 @ Y2 @ Y1)))))))) = $false) | ~spl0_8),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f458])).
% 1.46/1.50 thf(f458,definition,(
% 1.46/1.50 spl0_8 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y2 @ Y0)) => (sK11 @ Y2 @ Y1)))))))) = $false)),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.46/1.50 thf(f766,plain,(
% 1.46/1.50 ((~ (sK11 @ sK15 @ sK16)) = $true) | (~spl0_2 | ~spl0_8)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f764])).
% 1.46/1.50 thf(f764,plain,(
% 1.46/1.50 (((sK11 @ sK15 @ sK16) => $false) = $true) | (~spl0_2 | ~spl0_8)),
% 1.46/1.50 inference(superposition,[status(thm)],[f681,f526])).
% 1.46/1.50 thf(f526,plain,(
% 1.46/1.50 ((sK11 @ sK17 @ sK16) = $false) | ~spl0_8),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f525])).
% 1.46/1.50 thf(f525,plain,(
% 1.46/1.50 ($false = ($true => (sK11 @ sK17 @ sK16))) | ~spl0_8),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f514,f524])).
% 1.46/1.50 thf(f681,plain,(
% 1.46/1.50 ( ! [X0 : a] : (($true = ((sK11 @ sK15 @ X0) => (sK11 @ sK17 @ X0)))) ) | (~spl0_2 | ~spl0_8)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f663])).
% 1.46/1.50 thf(f663,plain,(
% 1.46/1.50 ( ! [X0 : a] : (($true = (((sK11 @ sK15 @ X0) & $true) => (sK11 @ sK17 @ X0)))) ) | (~spl0_2 | ~spl0_8)),
% 1.46/1.50 inference(superposition,[status(thm)],[f644,f535])).
% 1.46/1.50 thf(f535,plain,(
% 1.46/1.50 ((sK11 @ sK17 @ sK15) = $true) | ~spl0_8),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f534])).
% 1.46/1.50 thf(f534,plain,(
% 1.46/1.50 (($true & (sK11 @ sK17 @ sK15)) = $true) | ~spl0_8),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f524,f533])).
% 1.46/1.50 thf(f644,plain,(
% 1.46/1.50 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK11 @ X3 @ X1) & (sK11 @ X2 @ X3)) => (sK11 @ X2 @ X1)))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f643])).
% 1.46/1.50 thf(f643,plain,(
% 1.46/1.50 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK11 @ Y0 @ X1) & (sK11 @ X2 @ Y0)) => (sK11 @ X2 @ X1))) @ X3))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f639])).
% 1.46/1.50 thf(f639,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK11 @ Y0 @ X1) & (sK11 @ X2 @ Y0)) => (sK11 @ X2 @ X1)))))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f638])).
% 1.46/1.50 thf(f638,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ Y1 @ X1) & (sK11 @ Y0 @ Y1)) => (sK11 @ Y0 @ X1))))) @ X2))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f629])).
% 1.46/1.50 thf(f629,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ Y1 @ X1) & (sK11 @ Y0 @ Y1)) => (sK11 @ Y0 @ X1)))))))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f628])).
% 1.46/1.50 thf(f628,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0))))))) @ X1))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f553])).
% 1.46/1.50 thf(f553,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0)))))))) = $true) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f546])).
% 1.46/1.50 thf(f546,plain,(
% 1.46/1.50 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0)))))))))) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f544])).
% 1.46/1.50 thf(f544,plain,(
% 1.46/1.50 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0))))))))) => (sK11 @ sK8 @ sK7))) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f543])).
% 1.46/1.50 thf(f543,plain,(
% 1.46/1.50 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))) @ sK11) = $false) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f515])).
% 1.46/1.50 thf(f515,plain,(
% 1.46/1.50 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) = $false) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f512])).
% 1.46/1.50 thf(f512,plain,(
% 1.46/1.50 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK9 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK9))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f511])).
% 1.46/1.50 thf(f511,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK8 @ sK7)))))) @ sK9)) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f508])).
% 1.46/1.50 thf(f508,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK8 @ sK7))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f507])).
% 1.46/1.50 thf(f507,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ sK7)))))))) @ sK8)) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f504])).
% 1.46/1.50 thf(f504,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ sK7))))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f503])).
% 1.46/1.50 thf(f503,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))))))))) @ sK7) = $false) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f28])).
% 1.46/1.50 thf(f500,plain,(
% 1.46/1.50 spl0_10 | spl0_11 | ~spl0_1),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f493,f24,f498,f495])).
% 1.46/1.50 thf(f24,definition,(
% 1.46/1.50 spl0_1 <=> ($false = ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))))))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.46/1.50 thf(f493,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false) | ($false = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5)))))) | ~spl0_1),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.46/1.50 thf(f25,plain,(
% 1.46/1.50 ($false = ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0))))))))))) | ~spl0_1),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.46/1.50 thf(f488,plain,(
% 1.46/1.50 ~spl0_2 | ~spl0_6),
% 1.46/1.50 inference(avatar_contradiction_clause,[status(thm)],[f487])).
% 1.46/1.50 thf(f487,plain,(
% 1.46/1.50 $false | (~spl0_2 | ~spl0_6)),
% 1.46/1.50 inference(trivial_inequality_removal,[status(thm)],[f483])).
% 1.46/1.50 thf(f483,plain,(
% 1.46/1.50 ($true = $false) | (~spl0_2 | ~spl0_6)),
% 1.46/1.50 inference(superposition,[status(thm)],[f480,f195])).
% 1.46/1.50 thf(f195,plain,(
% 1.46/1.50 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK11 @ X3 @ X1) & (sK11 @ X2 @ X3)) => (sK11 @ X2 @ X1)))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f194])).
% 1.46/1.50 thf(f194,plain,(
% 1.46/1.50 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK11 @ Y0 @ X1) & (sK11 @ X2 @ Y0)) => (sK11 @ X2 @ X1))) @ X3))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f193])).
% 1.46/1.50 thf(f193,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK11 @ Y0 @ X1) & (sK11 @ X2 @ Y0)) => (sK11 @ X2 @ X1)))))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f192])).
% 1.46/1.50 thf(f192,plain,(
% 1.46/1.50 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ Y1 @ X1) & (sK11 @ Y0 @ Y1)) => (sK11 @ Y0 @ X1))))) @ X2))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f183])).
% 1.46/1.50 thf(f183,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ Y1 @ X1) & (sK11 @ Y0 @ Y1)) => (sK11 @ Y0 @ X1)))))))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f182])).
% 1.46/1.50 thf(f182,plain,(
% 1.46/1.50 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0))))))) @ X1))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f134])).
% 1.46/1.50 thf(f134,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0)))))))) = $true) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.46/1.50 thf(f95,plain,(
% 1.46/1.50 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0)))))))))) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.46/1.50 thf(f89,plain,(
% 1.46/1.50 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y2 @ Y0) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y1 @ Y0))))))))) => (sK11 @ sK8 @ sK7))) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.46/1.50 thf(f88,plain,(
% 1.46/1.50 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))) @ sK11) = $false) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f48])).
% 1.46/1.50 thf(f48,plain,(
% 1.46/1.50 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) = $false) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.46/1.50 thf(f43,plain,(
% 1.46/1.50 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK9 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK9))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.46/1.50 thf(f42,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK8 @ sK7)))))) @ sK9)) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f41])).
% 1.46/1.50 thf(f41,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ sK8 @ sK7))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.46/1.50 thf(f40,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ sK7)))))))) @ sK8)) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f35])).
% 1.46/1.50 thf(f35,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y0 @ sK7))))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.46/1.50 thf(f34,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))))))))) @ sK7) = $false) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f28])).
% 1.46/1.50 thf(f480,plain,(
% 1.46/1.50 ($false = (((sK11 @ (sK12 @ sK11) @ sK14) & (sK11 @ sK13 @ (sK12 @ sK11))) => (sK11 @ sK13 @ sK14))) | ~spl0_6),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f479])).
% 1.46/1.50 thf(f479,plain,(
% 1.46/1.50 (((^[Y0 : a]: (((sK11 @ (sK12 @ sK11) @ Y0) & (sK11 @ sK13 @ (sK12 @ sK11))) => (sK11 @ sK13 @ Y0))) @ sK14) = $false) | ~spl0_6),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f478])).
% 1.46/1.50 thf(f478,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (((sK11 @ (sK12 @ sK11) @ Y0) & (sK11 @ sK13 @ (sK12 @ sK11))) => (sK11 @ sK13 @ Y0))))) | ~spl0_6),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f477])).
% 1.46/1.50 thf(f477,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ (sK12 @ sK11) @ Y1) & (sK11 @ Y0 @ (sK12 @ sK11))) => (sK11 @ Y0 @ Y1))))) @ sK13)) | ~spl0_6),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f476])).
% 1.46/1.50 thf(f476,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ (sK12 @ sK11) @ Y1) & (sK11 @ Y0 @ (sK12 @ sK11))) => (sK11 @ Y0 @ Y1))))))) | ~spl0_6),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f467])).
% 1.46/1.50 thf(f467,plain,(
% 1.46/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y2) & (sK11 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y2))))))) @ (sK12 @ sK11)) = $false) | ~spl0_6),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f281])).
% 1.46/1.50 thf(f281,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y2) & (sK11 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y2)))))))) = $false) | ~spl0_6),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f280])).
% 1.46/1.50 thf(f280,definition,(
% 1.46/1.50 spl0_6 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y2) & (sK11 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y2)))))))) = $false)),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.46/1.50 thf(f463,plain,(
% 1.46/1.50 spl0_8 | spl0_9 | ~spl0_2 | ~spl0_4),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f452,f262,f27,f461,f458])).
% 1.46/1.50 thf(f262,definition,(
% 1.46/1.50 spl0_4 <=> ($false = (sK11 @ sK10 @ sK7))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.46/1.50 thf(f452,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y2 @ Y0)) => (sK11 @ Y2 @ Y1)))))))) = $false) | (~spl0_2 | ~spl0_4)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f439])).
% 1.46/1.50 thf(f439,plain,(
% 1.46/1.50 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y2 @ Y0)) => (sK11 @ Y2 @ Y1)))))))))) | (~spl0_2 | ~spl0_4)),
% 1.46/1.50 inference(not_proxy_clausification,[status(thm)],[f292])).
% 1.46/1.50 thf(f292,plain,(
% 1.46/1.50 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y2 @ Y0)) => (sK11 @ Y2 @ Y1))))))))))) | (~spl0_2 | ~spl0_4)),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f291])).
% 1.46/1.50 thf(f291,plain,(
% 1.46/1.50 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y2 @ Y0)) => (sK11 @ Y2 @ Y1))))))))) => $false) = $true) | (~spl0_2 | ~spl0_4)),
% 1.46/1.50 inference(superposition,[status(thm)],[f101,f263])).
% 1.46/1.50 thf(f263,plain,(
% 1.46/1.50 ($false = (sK11 @ sK10 @ sK7)) | ~spl0_4),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f262])).
% 1.46/1.50 thf(f101,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y1) & (X1 @ Y2 @ Y0)) => (X1 @ Y2 @ Y1))))))))) => (X1 @ sK10 @ sK7)))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.46/1.50 thf(f100,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK7))) @ X1))) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f69])).
% 1.46/1.50 thf(f69,plain,(
% 1.46/1.50 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK7))))) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.46/1.50 thf(f62,plain,(
% 1.46/1.50 ($true = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK10)))))) | ~spl0_2),
% 1.46/1.50 inference(not_proxy_clausification,[status(thm)],[f59])).
% 1.46/1.50 thf(f59,plain,(
% 1.46/1.50 ((~ ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK10)))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.46/1.50 thf(f58,plain,(
% 1.46/1.50 ($false = ((^[Y0 : a]: (~ ((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))))) @ sK10)) | ~spl0_2),
% 1.46/1.50 inference(sigma_clausification,[status(thm)],[f52])).
% 1.46/1.50 thf(f52,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (~ ((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0)))))))) = $false) | ~spl0_2),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f51])).
% 1.46/1.50 thf(f51,plain,(
% 1.46/1.50 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK7)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK8 @ Y0))))) => $false))) = $false) | ~spl0_2),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f41,f48])).
% 1.46/1.50 thf(f285,plain,(
% 1.46/1.50 spl0_6 | spl0_7 | ~spl0_3),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f274,f259,f283,f280])).
% 1.46/1.50 thf(f259,definition,(
% 1.46/1.50 spl0_3 <=> ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y2) & (sK11 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y2)))))))))))),
% 1.46/1.50 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.46/1.50 thf(f274,plain,(
% 1.46/1.50 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y2) & (sK11 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y2)))))))) = $false) | ~spl0_3),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f269])).
% 1.46/1.50 thf(f269,plain,(
% 1.46/1.50 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y2) & (sK11 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y2)))))))))) | ~spl0_3),
% 1.46/1.50 inference(not_proxy_clausification,[status(thm)],[f260])).
% 1.46/1.50 thf(f260,plain,(
% 1.46/1.50 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y2) & (sK11 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y2))))))))))) | ~spl0_3),
% 1.46/1.50 inference(avatar_component_clause,[status(thm)],[f259])).
% 1.46/1.50 thf(f264,plain,(
% 1.46/1.50 spl0_3 | spl0_4 | ~spl0_2),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f253,f27,f262,f259])).
% 1.46/1.50 thf(f253,plain,(
% 1.46/1.50 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y2) & (sK11 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y2))))))))))) | ($false = (sK11 @ sK10 @ sK7)) | ~spl0_2),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f247])).
% 1.46/1.50 thf(f247,plain,(
% 1.46/1.50 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK11 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y2) & (sK11 @ Y1 @ Y0)) => (sK11 @ Y1 @ Y2))))))))) => $false)) | ($false = (sK11 @ sK10 @ sK7)) | ~spl0_2),
% 1.46/1.50 inference(superposition,[status(thm)],[f76,f214])).
% 1.46/1.50 thf(f214,plain,(
% 1.46/1.50 ( ! [X0 : a] : (((sK11 @ sK8 @ X0) = $false) | ((sK11 @ X0 @ sK7) = $false)) ) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f205])).
% 1.46/1.50 thf(f205,plain,(
% 1.46/1.50 ( ! [X0 : a] : (($false = ((sK11 @ X0 @ sK7) & (sK11 @ sK8 @ X0)))) ) | ~spl0_2),
% 1.46/1.50 inference(not_proxy_clausification,[status(thm)],[f204])).
% 1.46/1.50 thf(f204,plain,(
% 1.46/1.50 ( ! [X0 : a] : (($true = (~ ((sK11 @ X0 @ sK7) & (sK11 @ sK8 @ X0))))) ) | ~spl0_2),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f197])).
% 1.46/1.50 thf(f197,plain,(
% 1.46/1.50 ( ! [X0 : a] : (($true = (((sK11 @ X0 @ sK7) & (sK11 @ sK8 @ X0)) => $false))) ) | ~spl0_2),
% 1.46/1.50 inference(superposition,[status(thm)],[f195,f94])).
% 1.46/1.50 thf(f94,plain,(
% 1.46/1.50 ($false = (sK11 @ sK8 @ sK7)) | ~spl0_2),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.46/1.50 thf(f76,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y2) & (X1 @ Y1 @ Y0)) => (X1 @ Y1 @ Y2))))))))) => (X1 @ sK8 @ sK10)))) ) | ~spl0_2),
% 1.46/1.50 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.46/1.50 thf(f75,plain,(
% 1.46/1.50 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK10))) @ X1) = $true)) ) | ~spl0_2),
% 1.46/1.50 inference(pi_clausification,[status(thm)],[f71])).
% 1.46/1.50 thf(f71,plain,(
% 1.46/1.50 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK10)))) = $true) | ~spl0_2),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f70])).
% 1.46/1.50 thf(f70,plain,(
% 1.46/1.50 ($true = ($true & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK10)))))) | ~spl0_2),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f62,f69])).
% 1.46/1.50 thf(f29,plain,(
% 1.46/1.50 spl0_1 | spl0_2),
% 1.46/1.50 inference(avatar_split_clause,[status(thm)],[f22,f27,f24])).
% 1.46/1.50 thf(f22,plain,(
% 1.46/1.50 ($false = ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0))))))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0))))))))))) = $false)),
% 1.46/1.50 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.46/1.50 thf(f21,plain,(
% 1.46/1.50 ($false = (((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))))))))))))),
% 1.46/1.50 inference(boolean_simplification,[status(thm)],[f20])).
% 1.46/1.50 thf(f20,plain,(
% 1.46/1.50 ($false = ((((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK3 @ sK5))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))))))))))) | $false))),
% 1.46/1.50 inference(backward_demodulation,[status(thm)],[f17,f18])).
% 1.46/1.50 % SZS output end Proof for DTF2THF_27930
% 1.46/1.50 % (28039)------------------------------
% 1.46/1.50 % (28039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.50 % (28039)Termination reason: Refutation
% 1.46/1.50
% 1.46/1.50 % (28039)Memory used [KB]: 7291
% 1.46/1.50 % (28039)Time elapsed: 0.260 s
% 1.46/1.50 % (28039)Instructions burned: 683 (million)
% 1.46/1.50 % (28039)------------------------------
% 1.46/1.50 % (28039)------------------------------
% 1.46/1.50 % (28026)Success in time 0.302 s
%------------------------------------------------------------------------------