%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV153^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:24 AM UTC 2026
% Result : Theorem 1.67s 1.55s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 29
% Syntax : Number of formulae : 482 ( 30 unt; 0 typ; 28 def)
% Number of atoms : 4891 ( 453 equ; 0 cnn)
% Maximal formula atoms : 5 ( 10 avg)
% Number of connectives : 13467 ( 702 ~;1365 |; 902 &;7735 @)
% ( 28 <=>;1279 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 656 ( 656 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 59 con; 0-2 aty)
% (1456 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1702 (1531 ^; 171 !; 0 ?;1702 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a > a > $o ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: 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 > $o ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a > $o ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
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(f3373,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f44,f245,f414,f424,f613,f643,f674,f704,f779,f879,f958,f1183,f1248,f1273,f1507,f2009,f2041,f2101,f2117,f2403,f2669,f2696,f2748,f2760,f2867,f2876,f3233,f3332,f3372]) ).
thf(f3372,plain,
( ~ spl0_11
| ~ spl0_17
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[status(thm)],[f3371]) ).
thf(f3371,plain,
( $false
| ~ spl0_11
| ~ spl0_17
| ~ spl0_65 ),
inference(trivial_inequality_removal,[status(thm)],[f3370]) ).
thf(f3370,plain,
( ( $false = $true )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_65 ),
inference(boolean_simplification,[status(thm)],[f3369]) ).
thf(f3369,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_65 ),
inference(boolean_simplification,[status(thm)],[f3368]) ).
thf(f3368,plain,
( ( $true
= ( ~ ( ( sK4 @ sK16 @ sK34 )
| $true ) ) )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_65 ),
inference(forward_demodulation,[status(thm)],[f3364,f3356]) ).
thf(f3356,plain,
( ( $true
= ( sK3 @ sK16 @ sK34 ) )
| ~ spl0_65 ),
inference(binary_proxy_clausification,[status(thm)],[f3344]) ).
thf(f3344,plain,
( ( $false
= ( ( sK3 @ sK16 @ sK34 )
=> ( sK17 @ sK34 ) ) )
| ~ spl0_65 ),
inference(beta_eta_normalization,[status(thm)],[f3342]) ).
thf(f3342,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) )
@ sK34 ) )
| ~ spl0_65 ),
inference(sigma_clausification,[status(thm)],[f3232]) ).
thf(f3232,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) )
= $false )
| ~ spl0_65 ),
inference(avatar_component_clause,[status(thm)],[f3231]) ).
thf(f3231,definition,
( spl0_65
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_65])],[avatar_definition]) ).
thf(f3364,plain,
( ( ( ~ ( ( sK4 @ sK16 @ sK34 )
| ( sK3 @ sK16 @ sK34 ) ) )
= $true )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_65 ),
inference(boolean_simplification,[status(thm)],[f3363]) ).
thf(f3363,plain,
( ( ( ( ( sK4 @ sK16 @ sK34 )
| ( sK3 @ sK16 @ sK34 ) )
=> $false )
= $true )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_65 ),
inference(superposition,[status(thm)],[f2982,f3355]) ).
thf(f3355,plain,
( ( $false
= ( sK17 @ sK34 ) )
| ~ spl0_65 ),
inference(binary_proxy_clausification,[status(thm)],[f3344]) ).
thf(f2982,plain,
( ! [X1: a] :
( ( ( ( sK4 @ sK16 @ X1 )
| ( sK3 @ sK16 @ X1 ) )
=> ( sK17 @ X1 ) )
= $true )
| ~ spl0_11
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f2981]) ).
thf(f2981,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ sK16 @ Y0 )
| ( sK3 @ sK16 @ Y0 ) )
=> ( sK17 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_11
| ~ spl0_17 ),
inference(pi_clausification,[status(thm)],[f2968]) ).
thf(f2968,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK16 @ Y0 )
| ( sK3 @ sK16 @ Y0 ) )
=> ( sK17 @ Y0 ) ) ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f2967]) ).
thf(f2967,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK16 @ Y0 )
| ( sK3 @ sK16 @ Y0 ) )
=> ( sK17 @ Y0 ) ) )
& $true ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f2930,f2965]) ).
thf(f2965,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK17 @ Y0 ) ) ) ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f2930]) ).
thf(f2930,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK16 @ Y0 )
| ( sK3 @ sK16 @ Y0 ) )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK17 @ Y0 ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f2921]) ).
thf(f2921,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK16 @ Y0 )
| ( sK3 @ sK16 @ Y0 ) )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK17 @ Y0 ) ) ) ) )
=> ( sK17 @ sK15 ) ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f2920]) ).
thf(f2920,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) )
@ sK17 ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(sigma_clausification,[status(thm)],[f2908]) ).
thf(f2908,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
= $false )
| ~ spl0_11
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f2907]) ).
thf(f2907,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f2906]) ).
thf(f2906,plain,
( ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) )
= $false )
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f2905,f639]) ).
thf(f639,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f638]) ).
thf(f638,definition,
( spl0_17
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f2905,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f2904]) ).
thf(f2904,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) )
@ sK16 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f2895]) ).
thf(f2895,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f2894]) ).
thf(f2894,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK15 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f420]) ).
thf(f420,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f419]) ).
thf(f419,definition,
( spl0_11
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f3332,plain,
( ~ spl0_11
| ~ spl0_17
| ~ spl0_64 ),
inference(avatar_contradiction_clause,[status(thm)],[f3331]) ).
thf(f3331,plain,
( $false
| ~ spl0_11
| ~ spl0_17
| ~ spl0_64 ),
inference(trivial_inequality_removal,[status(thm)],[f3330]) ).
thf(f3330,plain,
( ( $false = $true )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_64 ),
inference(forward_demodulation,[status(thm)],[f3329,f3280]) ).
thf(f3280,plain,
( ( $false
= ( sK17 @ sK33 ) )
| ~ spl0_64 ),
inference(boolean_simplification,[status(thm)],[f3279]) ).
thf(f3279,plain,
( ( ( $true
=> ( sK17 @ sK33 ) )
= $false )
| ~ spl0_64 ),
inference(backward_demodulation,[status(thm)],[f3266,f3278]) ).
thf(f3278,plain,
( ( ( ( sK17 @ sK32 )
& ( sK3 @ sK32 @ sK33 ) )
= $true )
| ~ spl0_64 ),
inference(binary_proxy_clausification,[status(thm)],[f3266]) ).
thf(f3266,plain,
( ( $false
= ( ( ( sK17 @ sK32 )
& ( sK3 @ sK32 @ sK33 ) )
=> ( sK17 @ sK33 ) ) )
| ~ spl0_64 ),
inference(beta_eta_normalization,[status(thm)],[f3265]) ).
thf(f3265,plain,
( ( ( ^ [Y0: a] :
( ( ( sK17 @ sK32 )
& ( sK3 @ sK32 @ Y0 ) )
=> ( sK17 @ Y0 ) )
@ sK33 )
= $false )
| ~ spl0_64 ),
inference(sigma_clausification,[status(thm)],[f3255]) ).
thf(f3255,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK17 @ sK32 )
& ( sK3 @ sK32 @ Y0 ) )
=> ( sK17 @ Y0 ) ) )
= $false )
| ~ spl0_64 ),
inference(beta_eta_normalization,[status(thm)],[f3253]) ).
thf(f3253,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK17 @ Y1 ) ) )
@ sK32 ) )
| ~ spl0_64 ),
inference(sigma_clausification,[status(thm)],[f3229]) ).
thf(f3229,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK17 @ Y1 ) ) ) )
= $false )
| ~ spl0_64 ),
inference(avatar_component_clause,[status(thm)],[f3228]) ).
thf(f3228,definition,
( spl0_64
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK17 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_64])],[avatar_definition]) ).
thf(f3329,plain,
( ( $true
= ( sK17 @ sK33 ) )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_64 ),
inference(boolean_simplification,[status(thm)],[f3328]) ).
thf(f3328,plain,
( ( ( $true
=> ( sK17 @ sK33 ) )
= $true )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_64 ),
inference(forward_demodulation,[status(thm)],[f3327,f3313]) ).
thf(f3313,plain,
( ( ( sK17 @ sK32 )
= $true )
| ~ spl0_64 ),
inference(binary_proxy_clausification,[status(thm)],[f3278]) ).
thf(f3327,plain,
( ( $true
= ( ( sK17 @ sK32 )
=> ( sK17 @ sK33 ) ) )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_64 ),
inference(boolean_simplification,[status(thm)],[f3326]) ).
thf(f3326,plain,
( ( ( ( ( sK17 @ sK32 )
& $true )
=> ( sK17 @ sK33 ) )
= $true )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_64 ),
inference(boolean_simplification,[status(thm)],[f3322]) ).
thf(f3322,plain,
( ( $true
= ( ( ( sK17 @ sK32 )
& ( $true
| ( sK4 @ sK32 @ sK33 ) ) )
=> ( sK17 @ sK33 ) ) )
| ~ spl0_11
| ~ spl0_17
| ~ spl0_64 ),
inference(superposition,[status(thm)],[f3048,f3315]) ).
thf(f3315,plain,
( ( ( sK3 @ sK32 @ sK33 )
= $true )
| ~ spl0_64 ),
inference(boolean_simplification,[status(thm)],[f3314]) ).
thf(f3314,plain,
( ( $true
= ( $true
& ( sK3 @ sK32 @ sK33 ) ) )
| ~ spl0_64 ),
inference(backward_demodulation,[status(thm)],[f3278,f3313]) ).
thf(f3048,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK17 @ X2 )
& ( ( sK3 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) ) )
=> ( sK17 @ X1 ) ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f3047]) ).
thf(f3047,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK17 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK17 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_11
| ~ spl0_17 ),
inference(pi_clausification,[status(thm)],[f3034]) ).
thf(f3034,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK17 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK17 @ X1 ) ) )
= $true )
| ~ spl0_11
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f3033]) ).
thf(f3033,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK17 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_11
| ~ spl0_17 ),
inference(pi_clausification,[status(thm)],[f2965]) ).
thf(f3233,plain,
( spl0_64
| spl0_65
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[status(thm)],[f3224,f638,f419,f3231,f3228]) ).
thf(f3224,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK17 @ Y1 ) ) ) )
= $false )
| ~ spl0_11
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f3214]) ).
thf(f3214,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK17 @ Y1 ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(not_proxy_clausification,[status(thm)],[f2957]) ).
thf(f2957,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK17 @ Y1 ) ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f2953]) ).
thf(f2953,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK17 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_11
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f2936,f2929]) ).
thf(f2929,plain,
( ( $false
= ( sK17 @ sK15 ) )
| ~ spl0_11
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f2921]) ).
thf(f2936,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK16 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK15 ) )
= $true )
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f2935]) ).
thf(f2935,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 ) )
@ X1 )
= $true )
| ~ spl0_17 ),
inference(pi_clausification,[status(thm)],[f639]) ).
thf(f2876,plain,
( ~ spl0_20
| ~ spl0_31
| ~ spl0_56 ),
inference(avatar_contradiction_clause,[status(thm)],[f2875]) ).
thf(f2875,plain,
( $false
| ~ spl0_20
| ~ spl0_31
| ~ spl0_56 ),
inference(trivial_inequality_removal,[status(thm)],[f2874]) ).
thf(f2874,plain,
( ( $false = $true )
| ~ spl0_20
| ~ spl0_31
| ~ spl0_56 ),
inference(boolean_simplification,[status(thm)],[f2873]) ).
thf(f2873,plain,
( ( ( ( sK6 @ sK22 )
=> $true )
= $false )
| ~ spl0_20
| ~ spl0_31
| ~ spl0_56 ),
inference(forward_demodulation,[status(thm)],[f2872,f2097]) ).
thf(f2097,plain,
( ( ( sK6 @ sK23 )
= $true )
| ~ spl0_56 ),
inference(avatar_component_clause,[status(thm)],[f2096]) ).
thf(f2096,definition,
( spl0_56
<=> ( ( sK6 @ sK23 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_56])],[avatar_definition]) ).
thf(f2872,plain,
( ( $false
= ( ( sK6 @ sK22 )
=> ( sK6 @ sK23 ) ) )
| ~ spl0_20
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f2871]) ).
thf(f2871,plain,
( ( ( ( ( sK6 @ sK22 )
& $true )
=> ( sK6 @ sK23 ) )
= $false )
| ~ spl0_20
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f2870]) ).
thf(f2870,plain,
( ( ( ( ( sK6 @ sK22 )
& ( $true
| ( sK3 @ sK22 @ sK23 ) ) )
=> ( sK6 @ sK23 ) )
= $false )
| ~ spl0_20
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f2862,f957]) ).
thf(f957,plain,
( ( ( sK4 @ sK22 @ sK23 )
= $true )
| ~ spl0_31 ),
inference(avatar_component_clause,[status(thm)],[f956]) ).
thf(f956,definition,
( spl0_31
<=> ( ( sK4 @ sK22 @ sK23 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition]) ).
thf(f2862,plain,
( ( ( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ sK23 )
| ( sK3 @ sK22 @ sK23 ) ) )
=> ( sK6 @ sK23 ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[status(thm)],[f2861]) ).
thf(f2861,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ Y0 )
| ( sK3 @ sK22 @ Y0 ) ) )
=> ( sK6 @ Y0 ) )
@ sK23 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[status(thm)],[f2848]) ).
thf(f2848,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ Y0 )
| ( sK3 @ sK22 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_20 ),
inference(beta_eta_normalization,[status(thm)],[f2844]) ).
thf(f2844,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) )
@ sK22 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[status(thm)],[f673]) ).
thf(f673,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f672]) ).
thf(f672,definition,
( spl0_20
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition]) ).
thf(f2867,plain,
( ~ spl0_20
| ~ spl0_57 ),
inference(avatar_contradiction_clause,[status(thm)],[f2866]) ).
thf(f2866,plain,
( $false
| ~ spl0_20
| ~ spl0_57 ),
inference(trivial_inequality_removal,[status(thm)],[f2865]) ).
thf(f2865,plain,
( ( $false = $true )
| ~ spl0_20
| ~ spl0_57 ),
inference(boolean_simplification,[status(thm)],[f2864]) ).
thf(f2864,plain,
( ( $false
= ( $false
=> ( sK6 @ sK23 ) ) )
| ~ spl0_20
| ~ spl0_57 ),
inference(boolean_simplification,[status(thm)],[f2863]) ).
thf(f2863,plain,
( ( ( ( $false
& ( ( sK4 @ sK22 @ sK23 )
| ( sK3 @ sK22 @ sK23 ) ) )
=> ( sK6 @ sK23 ) )
= $false )
| ~ spl0_20
| ~ spl0_57 ),
inference(forward_demodulation,[status(thm)],[f2862,f2100]) ).
thf(f2100,plain,
( ( $false
= ( sK6 @ sK22 ) )
| ~ spl0_57 ),
inference(avatar_component_clause,[status(thm)],[f2099]) ).
thf(f2099,definition,
( spl0_57
<=> ( $false
= ( sK6 @ sK22 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_57])],[avatar_definition]) ).
thf(f2760,plain,
( ~ spl0_2
| ~ spl0_16
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f2759]) ).
thf(f2759,plain,
( $false
| ~ spl0_2
| ~ spl0_16
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f2758]) ).
thf(f2758,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_16
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f2757,f2751]) ).
thf(f2751,plain,
( ( $false
= ( ( sK10 @ sK19 )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_16
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f2750]) ).
thf(f2750,plain,
( ( ( ( ( sK10 @ sK19 )
& $true )
=> ( sK10 @ sK20 ) )
= $false )
| ~ spl0_16
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f2749]) ).
thf(f2749,plain,
( ( $false
= ( ( ( sK10 @ sK19 )
& ( $true
| ( sK4 @ sK19 @ sK20 ) ) )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_16
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f2743,f775]) ).
thf(f775,plain,
( ( $true
= ( sK3 @ sK19 @ sK20 ) )
| ~ spl0_25 ),
inference(avatar_component_clause,[status(thm)],[f774]) ).
thf(f774,definition,
( spl0_25
<=> ( $true
= ( sK3 @ sK19 @ sK20 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition]) ).
thf(f2743,plain,
( ( $false
= ( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ sK20 )
| ( sK4 @ sK19 @ sK20 ) ) )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f2742]) ).
thf(f2742,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ Y0 )
| ( sK4 @ sK19 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ sK20 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f2731]) ).
thf(f2731,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ Y0 )
| ( sK4 @ sK19 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f2727]) ).
thf(f2727,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ sK19 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f612]) ).
thf(f612,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $false )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f611]) ).
thf(f611,definition,
( spl0_16
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f2757,plain,
( ( $true
= ( ( sK10 @ sK19 )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_2
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f2756]) ).
thf(f2756,plain,
( ( ( ( ( sK10 @ sK19 )
& $true )
=> ( sK10 @ sK20 ) )
= $true )
| ~ spl0_2
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f2752]) ).
thf(f2752,plain,
( ( $true
= ( ( ( sK10 @ sK19 )
& ( ( sK4 @ sK19 @ sK20 )
| $true ) )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_2
| ~ spl0_25 ),
inference(superposition,[status(thm)],[f2277,f775]) ).
thf(f2277,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) ) )
=> ( sK10 @ X2 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2276]) ).
thf(f2276,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f2261]) ).
thf(f2261,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2260]) ).
thf(f2260,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f2249]) ).
thf(f2249,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f2248]) ).
thf(f2248,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f2185,f2247]) ).
thf(f2247,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f2185]) ).
thf(f2185,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f2173]) ).
thf(f2173,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
=> ( sK10 @ sK8 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2172]) ).
thf(f2172,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ sK10 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f2157]) ).
thf(f2157,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f2141]) ).
thf(f2141,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2140]) ).
thf(f2140,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f2129]) ).
thf(f2129,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2128]) ).
thf(f2128,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f2124]) ).
thf(f2124,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f2123]) ).
thf(f2123,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl0_2
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f2748,plain,
( ~ spl0_16
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[status(thm)],[f2747]) ).
thf(f2747,plain,
( $false
| ~ spl0_16
| ~ spl0_40 ),
inference(trivial_inequality_removal,[status(thm)],[f2746]) ).
thf(f2746,plain,
( ( $false = $true )
| ~ spl0_16
| ~ spl0_40 ),
inference(boolean_simplification,[status(thm)],[f2745]) ).
thf(f2745,plain,
( ( ( $false
=> ( sK10 @ sK20 ) )
= $false )
| ~ spl0_16
| ~ spl0_40 ),
inference(boolean_simplification,[status(thm)],[f2744]) ).
thf(f2744,plain,
( ( ( ( $false
& ( ( sK3 @ sK19 @ sK20 )
| ( sK4 @ sK19 @ sK20 ) ) )
=> ( sK10 @ sK20 ) )
= $false )
| ~ spl0_16
| ~ spl0_40 ),
inference(forward_demodulation,[status(thm)],[f2743,f1506]) ).
thf(f1506,plain,
( ( ( sK10 @ sK19 )
= $false )
| ~ spl0_40 ),
inference(avatar_component_clause,[status(thm)],[f1505]) ).
thf(f1505,definition,
( spl0_40
<=> ( ( sK10 @ sK19 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_40])],[avatar_definition]) ).
thf(f2696,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f2695]) ).
thf(f2695,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f2694]) ).
thf(f2694,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f2693,f2643]) ).
thf(f2643,plain,
( ( $false
= ( sK10 @ sK12 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f2625]) ).
thf(f2625,plain,
( ( $false
= ( ( ( ( sK3 @ sK13 @ sK12 )
| ( sK4 @ sK13 @ sK12 ) )
& ( sK10 @ sK13 ) )
=> ( sK10 @ sK12 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f2624]) ).
thf(f2624,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ sK12 ) )
@ sK13 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f2579]) ).
thf(f2579,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ sK12 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f2577]) ).
thf(f2577,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
& ( sK10 @ Y1 ) )
=> ( sK10 @ Y0 ) ) )
@ sK12 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f241]) ).
thf(f241,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
& ( sK10 @ Y1 ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f240]) ).
thf(f240,definition,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
& ( sK10 @ Y1 ) )
=> ( sK10 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f2693,plain,
( ( ( sK10 @ sK12 )
= $true )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f2692]) ).
thf(f2692,plain,
( ( $true
= ( $true
=> ( sK10 @ sK12 ) ) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f2687,f2673]) ).
thf(f2673,plain,
( ( ( sK10 @ sK14 )
= $true )
| ~ spl0_3
| ~ spl0_9 ),
inference(not_proxy_clausification,[status(thm)],[f2672]) ).
thf(f2672,plain,
( ( ( ~ ( sK10 @ sK14 ) )
= $false )
| ~ spl0_3
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f2671]) ).
thf(f2671,plain,
( ( ( ~ ( $true
& ( sK10 @ sK14 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f2670]) ).
thf(f2670,plain,
( ( $false
= ( ~ ( ( ( sK3 @ sK14 @ sK12 )
| $true )
& ( sK10 @ sK14 ) ) ) )
| ~ spl0_3
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f2663,f410]) ).
thf(f410,plain,
( ( ( sK4 @ sK14 @ sK12 )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f409]) ).
thf(f409,definition,
( spl0_9
<=> ( ( sK4 @ sK14 @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f2663,plain,
( ( ( ~ ( ( ( sK3 @ sK14 @ sK12 )
| ( sK4 @ sK14 @ sK12 ) )
& ( sK10 @ sK14 ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f2662]) ).
thf(f2662,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) )
@ sK14 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f2650]) ).
thf(f2650,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f2646]) ).
thf(f2646,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) )
=> $false ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f2579,f2643]) ).
thf(f2687,plain,
( ( $true
= ( ( sK10 @ sK14 )
=> ( sK10 @ sK12 ) ) )
| ~ spl0_2
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f2686]) ).
thf(f2686,plain,
( ( $true
= ( ( ( sK10 @ sK14 )
& $true )
=> ( sK10 @ sK12 ) ) )
| ~ spl0_2
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f2684]) ).
thf(f2684,plain,
( ( $true
= ( ( ( sK10 @ sK14 )
& ( $true
| ( sK3 @ sK14 @ sK12 ) ) )
=> ( sK10 @ sK12 ) ) )
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f2277,f410]) ).
thf(f2669,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f2668]) ).
thf(f2668,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f2667]) ).
thf(f2667,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f2649,f2666]) ).
thf(f2666,plain,
( ( ( ~ ( sK10 @ sK14 ) )
= $false )
| ~ spl0_3
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f2665]) ).
thf(f2665,plain,
( ( ( ~ ( $true
& ( sK10 @ sK14 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f2664]) ).
thf(f2664,plain,
( ( $false
= ( ~ ( ( $true
| ( sK4 @ sK14 @ sK12 ) )
& ( sK10 @ sK14 ) ) ) )
| ~ spl0_3
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f2663,f413]) ).
thf(f413,plain,
( ( $true
= ( sK3 @ sK14 @ sK12 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f412]) ).
thf(f412,definition,
( spl0_10
<=> ( $true
= ( sK3 @ sK14 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f2649,plain,
( ( ( ~ ( sK10 @ sK14 ) )
= $true )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f2647]) ).
thf(f2647,plain,
( ( ( ( sK10 @ sK14 )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f2546,f2643]) ).
thf(f2546,plain,
( ( $true
= ( ( sK10 @ sK14 )
=> ( sK10 @ sK12 ) ) )
| ~ spl0_2
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f2545]) ).
thf(f2545,plain,
( ( $true
= ( ( ( sK10 @ sK14 )
& $true )
=> ( sK10 @ sK12 ) ) )
| ~ spl0_2
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f2543]) ).
thf(f2543,plain,
( ( $true
= ( ( ( sK10 @ sK14 )
& ( ( sK4 @ sK14 @ sK12 )
| $true ) )
=> ( sK10 @ sK12 ) ) )
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f2277,f413]) ).
thf(f2403,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_15
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f2402]) ).
thf(f2402,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_15
| ~ spl0_22 ),
inference(trivial_inequality_removal,[status(thm)],[f2401]) ).
thf(f2401,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f2400,f2120]) ).
thf(f2120,plain,
( ( $false
= ( sK10 @ sK18 ) )
| ~ spl0_15
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f2119]) ).
thf(f2119,plain,
( ( ( $true
=> ( sK10 @ sK18 ) )
= $false )
| ~ spl0_15
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f2118]) ).
thf(f2118,plain,
( ( ( ( $true
| ( sK4 @ sK7 @ sK18 ) )
=> ( sK10 @ sK18 ) )
= $false )
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f2035,f703]) ).
thf(f703,plain,
( ( ( sK3 @ sK7 @ sK18 )
= $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[status(thm)],[f702]) ).
thf(f702,definition,
( spl0_22
<=> ( ( sK3 @ sK7 @ sK18 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition]) ).
thf(f2035,plain,
( ( ( ( ( sK3 @ sK7 @ sK18 )
| ( sK4 @ sK7 @ sK18 ) )
=> ( sK10 @ sK18 ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f2031]) ).
thf(f2031,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) )
@ sK18 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f609]) ).
thf(f609,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f608]) ).
thf(f608,definition,
( spl0_15
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f2400,plain,
( ( $true
= ( sK10 @ sK18 ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f2399]) ).
thf(f2399,plain,
( ( ( $true
=> ( sK10 @ sK18 ) )
= $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f2328,f244]) ).
thf(f244,plain,
( ( ( sK10 @ sK7 )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f243]) ).
thf(f243,definition,
( spl0_4
<=> ( ( sK10 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f2328,plain,
( ( $true
= ( ( sK10 @ sK7 )
=> ( sK10 @ sK18 ) ) )
| ~ spl0_2
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f2327]) ).
thf(f2327,plain,
( ( ( ( ( sK10 @ sK7 )
& $true )
=> ( sK10 @ sK18 ) )
= $true )
| ~ spl0_2
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f2297]) ).
thf(f2297,plain,
( ( ( ( ( sK10 @ sK7 )
& ( ( sK4 @ sK7 @ sK18 )
| $true ) )
=> ( sK10 @ sK18 ) )
= $true )
| ~ spl0_2
| ~ spl0_22 ),
inference(superposition,[status(thm)],[f2277,f703]) ).
thf(f2117,plain,
( ~ spl0_20
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[status(thm)],[f2116]) ).
thf(f2116,plain,
( $false
| ~ spl0_20
| ~ spl0_30 ),
inference(trivial_inequality_removal,[status(thm)],[f2115]) ).
thf(f2115,plain,
( ( $false = $true )
| ~ spl0_20
| ~ spl0_30 ),
inference(backward_demodulation,[status(thm)],[f2109,f2114]) ).
thf(f2114,plain,
( ( $false
= ( ( sK6 @ sK22 )
=> ( sK6 @ sK23 ) ) )
| ~ spl0_20
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f2113]) ).
thf(f2113,plain,
( ( ( ( ( sK6 @ sK22 )
& $true )
=> ( sK6 @ sK23 ) )
= $false )
| ~ spl0_20
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f2112]) ).
thf(f2112,plain,
( ( $false
= ( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ sK23 )
| $true ) )
=> ( sK6 @ sK23 ) ) )
| ~ spl0_20
| ~ spl0_30 ),
inference(forward_demodulation,[status(thm)],[f2111,f954]) ).
thf(f954,plain,
( ( ( sK3 @ sK22 @ sK23 )
= $true )
| ~ spl0_30 ),
inference(avatar_component_clause,[status(thm)],[f953]) ).
thf(f953,definition,
( spl0_30
<=> ( ( sK3 @ sK22 @ sK23 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition]) ).
thf(f2111,plain,
( ( ( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ sK23 )
| ( sK3 @ sK22 @ sK23 ) ) )
=> ( sK6 @ sK23 ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[status(thm)],[f2110]) ).
thf(f2110,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ Y0 )
| ( sK3 @ sK22 @ Y0 ) ) )
=> ( sK6 @ Y0 ) )
@ sK23 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[status(thm)],[f2106]) ).
thf(f2106,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ Y0 )
| ( sK3 @ sK22 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_20 ),
inference(beta_eta_normalization,[status(thm)],[f2102]) ).
thf(f2102,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) )
@ sK22 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[status(thm)],[f673]) ).
thf(f2109,plain,
( ( $true
= ( ( sK6 @ sK22 )
=> ( sK6 @ sK23 ) ) )
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f2108]) ).
thf(f2108,plain,
( ( ( ( ( sK6 @ sK22 )
& $true )
=> ( sK6 @ sK23 ) )
= $true )
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f2107]) ).
thf(f2107,plain,
( ( ( ( ( sK6 @ sK22 )
& ( $true
| ( sK4 @ sK22 @ sK23 ) ) )
=> ( sK6 @ sK23 ) )
= $true )
| ~ spl0_30 ),
inference(superposition,[status(thm)],[f79,f954]) ).
thf(f79,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK6 @ X1 )
& ( ( sK3 @ X1 @ X2 )
| ( sK4 @ X1 @ X2 ) ) )
=> ( sK6 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ X1 )
& ( ( sK3 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 )
& ( ( sK3 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( $false
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f17,f19]) ).
thf(f19,plain,
( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK4 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK3 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK4 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK3 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y3 @ Y5 )
| ( sK3 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y3 @ Y5 )
| ( sK3 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK4 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK2 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK4 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK3 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK4 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK3 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y3 @ Y5 )
| ( sK3 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y3 @ Y5 )
| ( sK3 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK4 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK2 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( Y0 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( sK3 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK3 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( Y0 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK3 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y4 @ Y6 )
| ( sK3 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y4 @ Y6 )
| ( sK3 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( Y0 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( Y0 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK2 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( Y0 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( sK3 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK3 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( Y0 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK3 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y4 @ Y6 )
| ( sK3 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y4 @ Y6 )
| ( sK3 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( Y0 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( Y0 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( Y1 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y4 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y4 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y4 @ Y6 )
| ( Y0 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( Y1 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y5 @ Y7 )
| ( Y0 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y5 @ Y7 )
| ( Y0 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( Y0 @ Y4 @ Y5 )
| ( Y1 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
| ( Y0 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ sK2 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( Y1 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y4 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y4 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y4 @ Y6 )
| ( Y0 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( Y1 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y5 @ Y7 )
| ( Y0 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y5 @ Y7 )
| ( Y0 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( Y0 @ Y4 @ Y5 )
| ( Y1 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
| ( Y0 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ sK2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y5 @ Y7 )
| ( Y1 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y6 @ Y8 )
| ( Y1 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y6 @ Y8 )
| ( Y1 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y1 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y5 @ Y7 )
| ( Y1 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y6 @ Y8 )
| ( Y1 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y6 @ Y8 )
| ( Y1 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y1 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y5 @ Y7 )
| ( Y1 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y6 @ Y8 )
| ( Y1 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y6 @ Y8 )
| ( Y1 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y1 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ~ ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y5 @ Y7 )
| ( Y1 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y6 @ Y8 )
| ( Y1 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y6 @ Y8 )
| ( Y1 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y1 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a > a > $o,X3: a] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X2 @ X0 @ X5 )
| ( X1 @ X0 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X1 @ X7 @ X6 )
| ( X2 @ X7 @ X6 ) )
& ( X4 @ X7 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
| ( ! [X8: a,X9: a,X10: a] :
( ( ! [X11: a > $o] :
( ( ! [X12: a] :
( ( ( X2 @ X8 @ X12 )
| ( X1 @ X8 @ X12 ) )
=> ( X11 @ X12 ) )
& ! [X13: a,X14: a] :
( ( ( X11 @ X13 )
& ( ( X1 @ X13 @ X14 )
| ( X2 @ X13 @ X14 ) ) )
=> ( X11 @ X14 ) ) )
=> ( X11 @ X10 ) )
& ! [X15: a > $o] :
( ( ! [X16: a] :
( ( ( X1 @ X10 @ X16 )
| ( X2 @ X10 @ X16 ) )
=> ( X15 @ X16 ) )
& ! [X17: a,X18: a] :
( ( ( ( X1 @ X18 @ X17 )
| ( X2 @ X18 @ X17 ) )
& ( X15 @ X18 ) )
=> ( X15 @ X17 ) ) )
=> ( X15 @ X9 ) ) )
=> ! [X19: a > $o] :
( ( ! [X20: a,X21: a] :
( ( ( ( X2 @ X21 @ X20 )
| ( X1 @ X21 @ X20 ) )
& ( X19 @ X21 ) )
=> ( X19 @ X20 ) )
& ! [X22: a] :
( ( ( X2 @ X8 @ X22 )
| ( X1 @ X8 @ X22 ) )
=> ( X19 @ X22 ) ) )
=> ( X19 @ X9 ) ) )
& ! [X23: a,X24: a] :
( ( ! [X25: a > $o] :
( ( ! [X26: a,X27: a] :
( ( ( X25 @ X26 )
& ( X1 @ X26 @ X27 ) )
=> ( X25 @ X27 ) )
& ! [X28: a] :
( ( X1 @ X23 @ X28 )
=> ( X25 @ X28 ) ) )
=> ( X25 @ X24 ) )
| ! [X29: a > $o] :
( ( ! [X30: a,X31: a] :
( ( ( X2 @ X31 @ X30 )
& ( X29 @ X31 ) )
=> ( X29 @ X30 ) )
& ! [X32: a] :
( ( X2 @ X23 @ X32 )
=> ( X29 @ X32 ) ) )
=> ( X29 @ X24 ) ) )
=> ! [X33: a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( ( X1 @ X34 @ X35 )
| ( X2 @ X34 @ X35 ) )
& ( X33 @ X34 ) )
=> ( X33 @ X35 ) )
& ! [X36: a] :
( ( ( X2 @ X23 @ X36 )
| ( X1 @ X23 @ X36 ) )
=> ( X33 @ X36 ) ) )
=> ( X33 @ X24 ) ) )
& ~ ! [X37: a > $o] :
( ( ! [X38: a,X39: a] :
( ( ( ( X2 @ X39 @ X38 )
| ( X1 @ X39 @ X38 ) )
& ( X37 @ X39 ) )
=> ( X37 @ X38 ) )
& ! [X40: a] :
( ( ( X1 @ X0 @ X40 )
| ( X2 @ X0 @ X40 ) )
=> ( X37 @ X40 ) ) )
=> ( X37 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X0: a > a > $o,X1: a > a > $o,X3: a] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) )
| ( ! [X8: a,X10: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
& ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X9 @ X5 )
| ( X1 @ X9 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
=> ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X8: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X1 @ X6 @ X7 )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) )
& ~ ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a,X0: a > a > $o,X1: a > a > $o,X3: a] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) )
| ( ! [X8: a,X10: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
& ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X9 @ X5 )
| ( X1 @ X9 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
=> ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X8: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X1 @ X6 @ X7 )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) )
& ~ ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WPOE9q203G/DTF2THF_6844.p',cTHM251H_pme) ).
thf(f2101,plain,
( spl0_56
| spl0_57
| ~ spl0_31 ),
inference(avatar_split_clause,[status(thm)],[f2094,f956,f2099,f2096]) ).
thf(f2094,plain,
( ( $false
= ( sK6 @ sK22 ) )
| ( ( sK6 @ sK23 )
= $true )
| ~ spl0_31 ),
inference(binary_proxy_clausification,[status(thm)],[f2051]) ).
thf(f2051,plain,
( ( $true
= ( ( sK6 @ sK22 )
=> ( sK6 @ sK23 ) ) )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f2050]) ).
thf(f2050,plain,
( ( ( ( ( sK6 @ sK22 )
& $true )
=> ( sK6 @ sK23 ) )
= $true )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f2049]) ).
thf(f2049,plain,
( ( ( ( ( sK6 @ sK22 )
& ( ( sK3 @ sK22 @ sK23 )
| $true ) )
=> ( sK6 @ sK23 ) )
= $true )
| ~ spl0_31 ),
inference(superposition,[status(thm)],[f79,f957]) ).
thf(f2041,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_15
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f2040]) ).
thf(f2040,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_15
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f2039]) ).
thf(f2039,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_15
| ~ spl0_21 ),
inference(backward_demodulation,[status(thm)],[f2030,f2038]) ).
thf(f2038,plain,
( ( $false
= ( sK10 @ sK18 ) )
| ~ spl0_15
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f2037]) ).
thf(f2037,plain,
( ( ( $true
=> ( sK10 @ sK18 ) )
= $false )
| ~ spl0_15
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f2036]) ).
thf(f2036,plain,
( ( ( ( ( sK3 @ sK7 @ sK18 )
| $true )
=> ( sK10 @ sK18 ) )
= $false )
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f2035,f700]) ).
thf(f700,plain,
( ( ( sK4 @ sK7 @ sK18 )
= $true )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f699]) ).
thf(f699,definition,
( spl0_21
<=> ( ( sK4 @ sK7 @ sK18 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f2030,plain,
( ( $true
= ( sK10 @ sK18 ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f2029]) ).
thf(f2029,plain,
( ( ( $true
=> ( sK10 @ sK18 ) )
= $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f2026,f244]) ).
thf(f2026,plain,
( ( $true
= ( ( sK10 @ sK7 )
=> ( sK10 @ sK18 ) ) )
| ~ spl0_2
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f2025]) ).
thf(f2025,plain,
( ( ( ( ( sK10 @ sK7 )
& $true )
=> ( sK10 @ sK18 ) )
= $true )
| ~ spl0_2
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f2021]) ).
thf(f2021,plain,
( ( $true
= ( ( ( sK10 @ sK7 )
& ( $true
| ( sK3 @ sK7 @ sK18 ) ) )
=> ( sK10 @ sK18 ) ) )
| ~ spl0_2
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f1408,f700]) ).
thf(f1408,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) ) )
=> ( sK10 @ X2 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1407]) ).
thf(f1407,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f1397]) ).
thf(f1397,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1396]) ).
thf(f1396,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f1336]) ).
thf(f1336,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1333]) ).
thf(f1333,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1321]) ).
thf(f1321,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
=> ( sK10 @ sK8 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1320]) ).
thf(f1320,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ sK10 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f1310]) ).
thf(f1310,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f1309]) ).
thf(f1309,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f1294,f1308]) ).
thf(f1308,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1294]) ).
thf(f1294,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1293]) ).
thf(f1293,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f1282]) ).
thf(f1282,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1281]) ).
thf(f1281,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f1277]) ).
thf(f1277,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f1276]) ).
thf(f1276,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f2009,plain,
( ~ spl0_16
| ~ spl0_26
| ~ spl0_39 ),
inference(avatar_contradiction_clause,[status(thm)],[f2008]) ).
thf(f2008,plain,
( $false
| ~ spl0_16
| ~ spl0_26
| ~ spl0_39 ),
inference(trivial_inequality_removal,[status(thm)],[f2007]) ).
thf(f2007,plain,
( ( $false = $true )
| ~ spl0_16
| ~ spl0_26
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f2006]) ).
thf(f2006,plain,
( ( $false
= ( ( sK10 @ sK19 )
=> $true ) )
| ~ spl0_16
| ~ spl0_26
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f2005,f1503]) ).
thf(f1503,plain,
( ( $true
= ( sK10 @ sK20 ) )
| ~ spl0_39 ),
inference(avatar_component_clause,[status(thm)],[f1502]) ).
thf(f1502,definition,
( spl0_39
<=> ( $true
= ( sK10 @ sK20 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_39])],[avatar_definition]) ).
thf(f2005,plain,
( ( $false
= ( ( sK10 @ sK19 )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_16
| ~ spl0_26 ),
inference(boolean_simplification,[status(thm)],[f2004]) ).
thf(f2004,plain,
( ( ( ( ( sK10 @ sK19 )
& $true )
=> ( sK10 @ sK20 ) )
= $false )
| ~ spl0_16
| ~ spl0_26 ),
inference(boolean_simplification,[status(thm)],[f2003]) ).
thf(f2003,plain,
( ( ( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ sK20 )
| $true ) )
=> ( sK10 @ sK20 ) )
= $false )
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_demodulation,[status(thm)],[f2002,f778]) ).
thf(f778,plain,
( ( ( sK4 @ sK19 @ sK20 )
= $true )
| ~ spl0_26 ),
inference(avatar_component_clause,[status(thm)],[f777]) ).
thf(f777,definition,
( spl0_26
<=> ( ( sK4 @ sK19 @ sK20 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition]) ).
thf(f2002,plain,
( ( $false
= ( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ sK20 )
| ( sK4 @ sK19 @ sK20 ) ) )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f2001]) ).
thf(f2001,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ Y0 )
| ( sK4 @ sK19 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ sK20 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f1985]) ).
thf(f1985,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ Y0 )
| ( sK4 @ sK19 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f1981]) ).
thf(f1981,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ sK19 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f612]) ).
thf(f1507,plain,
( spl0_39
| spl0_40
| ~ spl0_2
| ~ spl0_26 ),
inference(avatar_split_clause,[status(thm)],[f1500,f777,f42,f1505,f1502]) ).
thf(f1500,plain,
( ( $true
= ( sK10 @ sK20 ) )
| ( ( sK10 @ sK19 )
= $false )
| ~ spl0_2
| ~ spl0_26 ),
inference(binary_proxy_clausification,[status(thm)],[f1463]) ).
thf(f1463,plain,
( ( $true
= ( ( sK10 @ sK19 )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_2
| ~ spl0_26 ),
inference(boolean_simplification,[status(thm)],[f1462]) ).
thf(f1462,plain,
( ( ( ( ( sK10 @ sK19 )
& $true )
=> ( sK10 @ sK20 ) )
= $true )
| ~ spl0_2
| ~ spl0_26 ),
inference(boolean_simplification,[status(thm)],[f1445]) ).
thf(f1445,plain,
( ( ( ( ( sK10 @ sK19 )
& ( $true
| ( sK3 @ sK19 @ sK20 ) ) )
=> ( sK10 @ sK20 ) )
= $true )
| ~ spl0_2
| ~ spl0_26 ),
inference(superposition,[status(thm)],[f1408,f778]) ).
thf(f1273,plain,
( ~ spl0_11
| ~ spl0_18
| ~ spl0_34 ),
inference(avatar_contradiction_clause,[status(thm)],[f1272]) ).
thf(f1272,plain,
( $false
| ~ spl0_11
| ~ spl0_18
| ~ spl0_34 ),
inference(trivial_inequality_removal,[status(thm)],[f1271]) ).
thf(f1271,plain,
( ( $false = $true )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_34 ),
inference(boolean_simplification,[status(thm)],[f1270]) ).
thf(f1270,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_34 ),
inference(boolean_simplification,[status(thm)],[f1269]) ).
thf(f1269,plain,
( ( ( ~ ( $true
| ( sK3 @ sK16 @ sK27 ) ) )
= $true )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_34 ),
inference(forward_demodulation,[status(thm)],[f1268,f1257]) ).
thf(f1257,plain,
( ( $true
= ( sK4 @ sK16 @ sK27 ) )
| ~ spl0_34 ),
inference(binary_proxy_clausification,[status(thm)],[f1255]) ).
thf(f1255,plain,
( ( ( ( sK4 @ sK16 @ sK27 )
=> ( sK17 @ sK27 ) )
= $false )
| ~ spl0_34 ),
inference(beta_eta_normalization,[status(thm)],[f1251]) ).
thf(f1251,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) )
@ sK27 )
= $false )
| ~ spl0_34 ),
inference(sigma_clausification,[status(thm)],[f1179]) ).
thf(f1179,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) ) )
| ~ spl0_34 ),
inference(avatar_component_clause,[status(thm)],[f1178]) ).
thf(f1178,definition,
( spl0_34
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_34])],[avatar_definition]) ).
thf(f1268,plain,
( ( ( ~ ( ( sK4 @ sK16 @ sK27 )
| ( sK3 @ sK16 @ sK27 ) ) )
= $true )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_34 ),
inference(boolean_simplification,[status(thm)],[f1263]) ).
thf(f1263,plain,
( ( ( ( ( sK4 @ sK16 @ sK27 )
| ( sK3 @ sK16 @ sK27 ) )
=> $false )
= $true )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_34 ),
inference(superposition,[status(thm)],[f1062,f1259]) ).
thf(f1259,plain,
( ( $false
= ( sK17 @ sK27 ) )
| ~ spl0_34 ),
inference(boolean_simplification,[status(thm)],[f1258]) ).
thf(f1258,plain,
( ( ( $true
=> ( sK17 @ sK27 ) )
= $false )
| ~ spl0_34 ),
inference(backward_demodulation,[status(thm)],[f1255,f1257]) ).
thf(f1062,plain,
( ! [X1: a] :
( ( ( ( sK4 @ sK16 @ X1 )
| ( sK3 @ sK16 @ X1 ) )
=> ( sK17 @ X1 ) )
= $true )
| ~ spl0_11
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f1061]) ).
thf(f1061,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ sK16 @ Y0 )
| ( sK3 @ sK16 @ Y0 ) )
=> ( sK17 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_11
| ~ spl0_18 ),
inference(pi_clausification,[status(thm)],[f1037]) ).
thf(f1037,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK16 @ Y0 )
| ( sK3 @ sK16 @ Y0 ) )
=> ( sK17 @ Y0 ) ) ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f1004]) ).
thf(f1004,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK16 @ Y0 )
| ( sK3 @ sK16 @ Y0 ) )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK17 @ Y0 ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f993]) ).
thf(f993,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK16 @ Y0 )
| ( sK3 @ sK16 @ Y0 ) )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK17 @ Y0 ) ) ) ) )
=> ( sK17 @ sK15 ) ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f992]) ).
thf(f992,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) )
@ sK17 ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(sigma_clausification,[status(thm)],[f981]) ).
thf(f981,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
= $false )
| ~ spl0_11
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f980]) ).
thf(f980,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f979]) ).
thf(f979,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
| $true )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) )
= $false )
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[status(thm)],[f978,f642]) ).
thf(f642,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
= $true )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f641]) ).
thf(f641,definition,
( spl0_18
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f978,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f977]) ).
thf(f977,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) )
@ sK16 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f968]) ).
thf(f968,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f967]) ).
thf(f967,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK15 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f420]) ).
thf(f1248,plain,
( ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[status(thm)],[f1247]) ).
thf(f1247,plain,
( $false
| ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(trivial_inequality_removal,[status(thm)],[f1246]) ).
thf(f1246,plain,
( ( $false = $true )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(forward_demodulation,[status(thm)],[f1245,f1193]) ).
thf(f1193,plain,
( ( ( sK17 @ sK24 )
= $false )
| ~ spl0_35 ),
inference(binary_proxy_clausification,[status(thm)],[f1192]) ).
thf(f1192,plain,
( ( $false
= ( ( ( sK4 @ sK25 @ sK24 )
& ( sK17 @ sK25 ) )
=> ( sK17 @ sK24 ) ) )
| ~ spl0_35 ),
inference(beta_eta_normalization,[status(thm)],[f1191]) ).
thf(f1191,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ sK24 )
& ( sK17 @ Y0 ) )
=> ( sK17 @ sK24 ) )
@ sK25 ) )
| ~ spl0_35 ),
inference(sigma_clausification,[status(thm)],[f1190]) ).
thf(f1190,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ sK24 )
& ( sK17 @ Y0 ) )
=> ( sK17 @ sK24 ) ) ) )
| ~ spl0_35 ),
inference(beta_eta_normalization,[status(thm)],[f1186]) ).
thf(f1186,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK17 @ Y1 ) )
=> ( sK17 @ Y0 ) ) )
@ sK24 ) )
| ~ spl0_35 ),
inference(sigma_clausification,[status(thm)],[f1182]) ).
thf(f1182,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK17 @ Y1 ) )
=> ( sK17 @ Y0 ) ) ) ) )
| ~ spl0_35 ),
inference(avatar_component_clause,[status(thm)],[f1181]) ).
thf(f1181,definition,
( spl0_35
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK17 @ Y1 ) )
=> ( sK17 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_35])],[avatar_definition]) ).
thf(f1245,plain,
( ( ( sK17 @ sK24 )
= $true )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f1244]) ).
thf(f1244,plain,
( ( ( $true
=> ( sK17 @ sK24 ) )
= $true )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(forward_demodulation,[status(thm)],[f1243,f1215]) ).
thf(f1215,plain,
( ( $true
= ( sK17 @ sK26 ) )
| ~ spl0_35 ),
inference(binary_proxy_clausification,[status(thm)],[f1212]) ).
thf(f1212,plain,
( ( ( ( sK4 @ sK26 @ sK24 )
& ( sK17 @ sK26 ) )
= $true )
| ~ spl0_35 ),
inference(not_proxy_clausification,[status(thm)],[f1202]) ).
thf(f1202,plain,
( ( ( ~ ( ( sK4 @ sK26 @ sK24 )
& ( sK17 @ sK26 ) ) )
= $false )
| ~ spl0_35 ),
inference(beta_eta_normalization,[status(thm)],[f1201]) ).
thf(f1201,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK4 @ Y0 @ sK24 )
& ( sK17 @ Y0 ) )
@ sK26 )
= $false )
| ~ spl0_35 ),
inference(sigma_clausification,[status(thm)],[f1197]) ).
thf(f1197,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK4 @ Y0 @ sK24 )
& ( sK17 @ Y0 ) ) )
= $false )
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f1196]) ).
thf(f1196,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ sK24 )
& ( sK17 @ Y0 ) )
=> $false ) ) )
| ~ spl0_35 ),
inference(backward_demodulation,[status(thm)],[f1190,f1193]) ).
thf(f1243,plain,
( ( ( ( sK17 @ sK26 )
=> ( sK17 @ sK24 ) )
= $true )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f1242]) ).
thf(f1242,plain,
( ( $true
= ( ( ( sK17 @ sK26 )
& $true )
=> ( sK17 @ sK24 ) ) )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f1238]) ).
thf(f1238,plain,
( ( $true
= ( ( ( sK17 @ sK26 )
& ( ( sK3 @ sK26 @ sK24 )
| $true ) )
=> ( sK17 @ sK24 ) ) )
| ~ spl0_11
| ~ spl0_18
| ~ spl0_35 ),
inference(superposition,[status(thm)],[f1064,f1218]) ).
thf(f1218,plain,
( ( ( sK4 @ sK26 @ sK24 )
= $true )
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f1217]) ).
thf(f1217,plain,
( ( $true
= ( ( sK4 @ sK26 @ sK24 )
& $true ) )
| ~ spl0_35 ),
inference(backward_demodulation,[status(thm)],[f1212,f1215]) ).
thf(f1064,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK17 @ X2 )
& ( ( sK3 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) ) )
=> ( sK17 @ X1 ) ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f1063]) ).
thf(f1063,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK17 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK17 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_11
| ~ spl0_18 ),
inference(pi_clausification,[status(thm)],[f1060]) ).
thf(f1060,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK17 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK17 @ X1 ) ) )
= $true )
| ~ spl0_11
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f1059]) ).
thf(f1059,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK17 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_11
| ~ spl0_18 ),
inference(pi_clausification,[status(thm)],[f1039]) ).
thf(f1039,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK17 @ Y0 ) ) ) ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1038]) ).
thf(f1038,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK17 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK17 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_11
| ~ spl0_18 ),
inference(backward_demodulation,[status(thm)],[f1004,f1037]) ).
thf(f1183,plain,
( spl0_34
| spl0_35
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_split_clause,[status(thm)],[f1174,f641,f419,f1181,f1178]) ).
thf(f1174,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK17 @ Y1 ) )
=> ( sK17 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f1150]) ).
thf(f1150,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK17 @ Y1 ) )
=> ( sK17 @ Y0 ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(not_proxy_clausification,[status(thm)],[f1024]) ).
thf(f1024,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK17 @ Y1 ) )
=> ( sK17 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_11
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1022]) ).
thf(f1022,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK16 @ Y0 )
=> ( sK17 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK17 @ Y1 ) )
=> ( sK17 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f1008,f1006]) ).
thf(f1006,plain,
( ( $false
= ( sK17 @ sK15 ) )
| ~ spl0_11
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1005]) ).
thf(f1005,plain,
( ( ( $true
=> ( sK17 @ sK15 ) )
= $false )
| ~ spl0_11
| ~ spl0_18 ),
inference(backward_demodulation,[status(thm)],[f993,f1004]) ).
thf(f1008,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK16 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK15 ) )
= $true )
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f1007]) ).
thf(f1007,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) )
@ X1 ) )
| ~ spl0_18 ),
inference(pi_clausification,[status(thm)],[f642]) ).
thf(f958,plain,
( spl0_30
| spl0_31
| ~ spl0_20 ),
inference(avatar_split_clause,[status(thm)],[f951,f672,f956,f953]) ).
thf(f951,plain,
( ( ( sK3 @ sK22 @ sK23 )
= $true )
| ( ( sK4 @ sK22 @ sK23 )
= $true )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[status(thm)],[f940]) ).
thf(f940,plain,
( ( $true
= ( ( sK4 @ sK22 @ sK23 )
| ( sK3 @ sK22 @ sK23 ) ) )
| ~ spl0_20 ),
inference(boolean_simplification,[status(thm)],[f939]) ).
thf(f939,plain,
( ( ( $true
& ( ( sK4 @ sK22 @ sK23 )
| ( sK3 @ sK22 @ sK23 ) ) )
= $true )
| ~ spl0_20 ),
inference(backward_demodulation,[status(thm)],[f893,f938]) ).
thf(f938,plain,
( ( $true
= ( sK6 @ sK22 ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[status(thm)],[f893]) ).
thf(f893,plain,
( ( $true
= ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ sK23 )
| ( sK3 @ sK22 @ sK23 ) ) ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[status(thm)],[f891]) ).
thf(f891,plain,
( ( ( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ sK23 )
| ( sK3 @ sK22 @ sK23 ) ) )
=> ( sK6 @ sK23 ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[status(thm)],[f890]) ).
thf(f890,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ Y0 )
| ( sK3 @ sK22 @ Y0 ) ) )
=> ( sK6 @ Y0 ) )
@ sK23 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[status(thm)],[f887]) ).
thf(f887,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK22 )
& ( ( sK4 @ sK22 @ Y0 )
| ( sK3 @ sK22 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_20 ),
inference(beta_eta_normalization,[status(thm)],[f885]) ).
thf(f885,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) )
@ sK22 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[status(thm)],[f673]) ).
thf(f879,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[status(thm)],[f878]) ).
thf(f878,plain,
( $false
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f877]) ).
thf(f877,plain,
( ( $false = $true )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f876]) ).
thf(f876,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f873]) ).
thf(f873,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK5 @ sK21 ) ) ) )
| ~ spl0_19 ),
inference(backward_demodulation,[status(thm)],[f866,f872]) ).
thf(f872,plain,
( ( ( sK4 @ sK5 @ sK21 )
= $true )
| ~ spl0_19 ),
inference(not_proxy_clausification,[status(thm)],[f839]) ).
thf(f839,plain,
( ( ( ~ ( sK4 @ sK5 @ sK21 ) )
= $false )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f838]) ).
thf(f838,plain,
( ( ( ( sK4 @ sK5 @ sK21 )
=> $false )
= $false )
| ~ spl0_19 ),
inference(forward_demodulation,[status(thm)],[f837,f828]) ).
thf(f828,plain,
( ( $false
= ( sK6 @ sK21 ) )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[status(thm)],[f825]) ).
thf(f825,plain,
( ( ( ( ( sK3 @ sK5 @ sK21 )
| ( sK4 @ sK5 @ sK21 ) )
=> ( sK6 @ sK21 ) )
= $false )
| ~ spl0_19 ),
inference(beta_eta_normalization,[status(thm)],[f824]) ).
thf(f824,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ sK21 )
= $false )
| ~ spl0_19 ),
inference(sigma_clausification,[status(thm)],[f670]) ).
thf(f670,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f669]) ).
thf(f669,definition,
( spl0_19
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f837,plain,
( ( $false
= ( ( sK4 @ sK5 @ sK21 )
=> ( sK6 @ sK21 ) ) )
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f836]) ).
thf(f836,plain,
( ( $false
= ( ( sK4 @ sK5 @ sK21 )
=> ( sK6 @ sK21 ) ) )
| ( $false = $true )
| ~ spl0_19 ),
inference(forward_demodulation,[status(thm)],[f831,f828]) ).
thf(f831,plain,
( ( $true
= ( sK6 @ sK21 ) )
| ( $false
= ( ( sK4 @ sK5 @ sK21 )
=> ( sK6 @ sK21 ) ) )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f830]) ).
thf(f830,plain,
( ( $true
= ( sK6 @ sK21 ) )
| ( ( ( $false
| ( sK4 @ sK5 @ sK21 ) )
=> ( sK6 @ sK21 ) )
= $false )
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f825,f392]) ).
thf(f392,plain,
! [X1: a] :
( ( ( sK3 @ sK5 @ X1 )
= $false )
| ( ( sK6 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: a] :
( ( $false
= ( ( sK4 @ sK5 @ X1 )
| ( sK3 @ sK5 @ X1 ) ) )
| ( ( sK6 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: a] :
( ( ( ( sK4 @ sK5 @ X1 )
| ( sK3 @ sK5 @ X1 ) )
=> ( sK6 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f25,f29]) ).
thf(f866,plain,
( ( ( ~ ( ( sK4 @ sK5 @ sK21 )
| ( sK3 @ sK5 @ sK21 ) ) )
= $true )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f865]) ).
thf(f865,plain,
( ( ( ( ( sK4 @ sK5 @ sK21 )
| ( sK3 @ sK5 @ sK21 ) )
=> $false )
= $true )
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f33,f828]) ).
thf(f779,plain,
( spl0_25
| spl0_26
| ~ spl0_16 ),
inference(avatar_split_clause,[status(thm)],[f770,f611,f777,f774]) ).
thf(f770,plain,
( ( ( sK4 @ sK19 @ sK20 )
= $true )
| ( $true
= ( sK3 @ sK19 @ sK20 ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f732]) ).
thf(f732,plain,
( ( ( ( sK3 @ sK19 @ sK20 )
| ( sK4 @ sK19 @ sK20 ) )
= $true )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f722]) ).
thf(f722,plain,
( ( $true
= ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ sK20 )
| ( sK4 @ sK19 @ sK20 ) ) ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f718]) ).
thf(f718,plain,
( ( $false
= ( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ sK20 )
| ( sK4 @ sK19 @ sK20 ) ) )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f717]) ).
thf(f717,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ Y0 )
| ( sK4 @ sK19 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ sK20 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f708]) ).
thf(f708,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ Y0 )
| ( sK4 @ sK19 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f707]) ).
thf(f707,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ sK19 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f612]) ).
thf(f704,plain,
( spl0_21
| spl0_22
| ~ spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f695,f608,f702,f699]) ).
thf(f695,plain,
( ( ( sK4 @ sK7 @ sK18 )
= $true )
| ( ( sK3 @ sK7 @ sK18 )
= $true )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f684]) ).
thf(f684,plain,
( ( ( ( sK3 @ sK7 @ sK18 )
| ( sK4 @ sK7 @ sK18 ) )
= $true )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f680]) ).
thf(f680,plain,
( ( ( ( ( sK3 @ sK7 @ sK18 )
| ( sK4 @ sK7 @ sK18 ) )
=> ( sK10 @ sK18 ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f679]) ).
thf(f679,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) )
@ sK18 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f609]) ).
thf(f674,plain,
( spl0_19
| spl0_20
| ~ spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f665,f422,f672,f669]) ).
thf(f422,definition,
( spl0_12
<=> ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f665,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f662]) ).
thf(f662,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_12 ),
inference(not_proxy_clausification,[status(thm)],[f661]) ).
thf(f661,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f652]) ).
thf(f652,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f650,f27]) ).
thf(f27,plain,
( $false
= ( sK6 @ sK2 ) ),
inference(boolean_simplification,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
= ( $true
=> ( sK6 @ sK2 ) ) ),
inference(backward_demodulation,[status(thm)],[f23,f25]) ).
thf(f650,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK2 ) )
= $true )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f649]) ).
thf(f649,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) )
@ X1 ) )
| ~ spl0_12 ),
inference(pi_clausification,[status(thm)],[f646]) ).
thf(f646,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
= $true )
| ~ spl0_12 ),
inference(not_proxy_clausification,[status(thm)],[f423]) ).
thf(f423,plain,
( ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) ) ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f422]) ).
thf(f643,plain,
( spl0_17
| spl0_18
| ~ spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f636,f419,f641,f638]) ).
thf(f636,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
= $true )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
= $true )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f623]) ).
thf(f623,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) )
= $true )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f621]) ).
thf(f621,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK16 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK16 @ Y1 )
| ( sK3 @ sK16 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK15 ) ) ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f620]) ).
thf(f620,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) )
@ sK16 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f619]) ).
thf(f619,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK15 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK15 ) ) ) ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f618]) ).
thf(f618,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK15 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f420]) ).
thf(f613,plain,
( spl0_15
| spl0_16
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f604,f42,f611,f608]) ).
thf(f604,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f598]) ).
thf(f598,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f496]) ).
thf(f496,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f494]) ).
thf(f494,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f489,f474]) ).
thf(f474,plain,
( ( $false
= ( sK10 @ sK8 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f456]) ).
thf(f456,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
=> ( sK10 @ sK8 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f455]) ).
thf(f455,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ sK10 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f449]) ).
thf(f449,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f446]) ).
thf(f446,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f445]) ).
thf(f445,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f441]) ).
thf(f441,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f440]) ).
thf(f440,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f431]) ).
thf(f431,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f430]) ).
thf(f430,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f489,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK8 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f488]) ).
thf(f488,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f483]) ).
thf(f483,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f482]) ).
thf(f482,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
& $true )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f450,f480]) ).
thf(f480,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f450]) ).
thf(f450,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f446]) ).
thf(f424,plain,
( spl0_11
| spl0_12
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f417,f39,f422,f419]) ).
thf(f39,definition,
( spl0_1
<=> ( $false
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f417,plain,
( ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $false
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f414,plain,
( spl0_9
| spl0_10
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f405,f240,f412,f409]) ).
thf(f405,plain,
( ( ( sK4 @ sK14 @ sK12 )
= $true )
| ( $true
= ( sK3 @ sK14 @ sK12 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f378]) ).
thf(f378,plain,
( ( ( ( sK3 @ sK14 @ sK12 )
| ( sK4 @ sK14 @ sK12 ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f359]) ).
thf(f359,plain,
( ( $true
= ( ( ( sK3 @ sK14 @ sK12 )
| ( sK4 @ sK14 @ sK12 ) )
& ( sK10 @ sK14 ) ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f343]) ).
thf(f343,plain,
( ( ( ~ ( ( ( sK3 @ sK14 @ sK12 )
| ( sK4 @ sK14 @ sK12 ) )
& ( sK10 @ sK14 ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f342]) ).
thf(f342,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) )
@ sK14 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f332]) ).
thf(f332,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f331]) ).
thf(f331,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) )
=> $false ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f282,f330]) ).
thf(f330,plain,
( ( $false
= ( sK10 @ sK12 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f329]) ).
thf(f329,plain,
( ( $false
= ( $true
=> ( sK10 @ sK12 ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f293,f328]) ).
thf(f328,plain,
( ( $true
= ( ( ( sK3 @ sK13 @ sK12 )
| ( sK4 @ sK13 @ sK12 ) )
& ( sK10 @ sK13 ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f293]) ).
thf(f293,plain,
( ( $false
= ( ( ( ( sK3 @ sK13 @ sK12 )
| ( sK4 @ sK13 @ sK12 ) )
& ( sK10 @ sK13 ) )
=> ( sK10 @ sK12 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f292]) ).
thf(f292,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ sK12 ) )
@ sK13 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f282]) ).
thf(f282,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK3 @ Y0 @ sK12 )
| ( sK4 @ Y0 @ sK12 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ sK12 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f278]) ).
thf(f278,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
& ( sK10 @ Y1 ) )
=> ( sK10 @ Y0 ) ) )
@ sK12 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f241]) ).
thf(f245,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f238,f42,f243,f240]) ).
thf(f238,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
& ( sK10 @ Y1 ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ( ( sK10 @ sK7 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f192]) ).
thf(f192,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
& ( sK10 @ Y1 ) )
=> ( sK10 @ Y0 ) ) ) )
=> ( sK10 @ sK7 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f191]) ).
thf(f191,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
& ( sK10 @ Y1 ) )
=> ( sK10 @ Y0 ) ) ) )
& $true )
=> ( sK10 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f175,f117]) ).
thf(f117,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
=> ( sK10 @ sK8 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ sK10 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f65,f71]) ).
thf(f71,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f175,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK9 @ Y0 )
| ( sK3 @ sK9 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f174]) ).
thf(f174,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f163]) ).
thf(f163,plain,
( ( ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK9 @ Y1 )
| ( sK3 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f71,f162]) ).
thf(f162,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f44,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f37,f42,f39]) ).
thf(f37,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV153^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n001.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 12:41:50 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SEV153^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.48 % Domain : Set Theory (Relations)
% 0.20/0.48 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bro09]
% 0.20/0.48 % Names : tps_1220 [Bro09]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.42 v8.2.0, 0.36 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, 0.62 v6.4.0, 0.71 v6.3.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.50 v5.2.0, 0.75 v4.1.0, 1.00 v4.0.0
% 0.20/0.48 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.48 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.48 % Number of connectives : 148 ( 1 ~; 14 |; 19 &; 88 @)
% 0.20/0.48 % ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 23 ( 23 avg)
% 0.20/0.48 % Number of types : 2 ( 1 usr)
% 0.20/0.48 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.48 % Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% 0.20/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(a_type,type,
% 0.20/0.48 a: $tType ).
% 0.20/0.48
% 0.20/0.48 thf(cTHM251H_pme,conjecture,
% 0.20/0.48 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.20/0.48 ( ! [Xq: a > $o] :
% 0.20/0.48 ( ( ! [Xw: a] :
% 0.20/0.48 ( ( ( R @ Xx @ Xw )
% 0.20/0.48 | ( S @ Xx @ Xw ) )
% 0.20/0.48 => ( Xq @ Xw ) )
% 0.20/0.48 & ! [Xu: a,Xv: a] :
% 0.20/0.48 ( ( ( Xq @ Xu )
% 0.20/0.48 & ( ( R @ Xu @ Xv )
% 0.20/0.48 | ( S @ Xu @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xy ) )
% 0.20/0.48 | ( ~ ! [Xq: a > $o] :
% 0.20/0.48 ( ( ! [Xw: a] :
% 0.20/0.48 ( ( ( R @ Xx @ Xw )
% 0.20/0.48 | ( S @ Xx @ Xw ) )
% 0.20/0.48 => ( Xq @ Xw ) )
% 0.20/0.48 & ! [Xu: a,Xv: a] :
% 0.20/0.48 ( ( ( Xq @ Xu )
% 0.20/0.48 & ( ( R @ Xu @ Xv )
% 0.20/0.48 | ( S @ Xu @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xy ) )
% 0.20/0.48 & ! [Xx0: a,Xy0: a] :
% 0.20/0.48 ( ( ! [Xq: a > $o] :
% 0.20/0.48 ( ( ! [Xw: a] :
% 0.20/0.48 ( ( R @ Xx0 @ Xw )
% 0.20/0.48 => ( Xq @ Xw ) )
% 0.20/0.48 & ! [Xu: a,Xv: a] :
% 0.20/0.48 ( ( ( Xq @ Xu )
% 0.20/0.48 & ( R @ Xu @ Xv ) )
% 0.20/0.48 => ( Xq @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xy0 ) )
% 0.20/0.48 | ! [Xq: a > $o] :
% 0.20/0.48 ( ( ! [Xw: a] :
% 0.20/0.48 ( ( S @ Xx0 @ Xw )
% 0.20/0.48 => ( Xq @ Xw ) )
% 0.20/0.48 & ! [Xu: a,Xv: a] :
% 0.20/0.48 ( ( ( Xq @ Xu )
% 0.20/0.48 & ( S @ Xu @ Xv ) )
% 0.20/0.48 => ( Xq @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xy0 ) ) )
% 0.20/0.48 => ! [Xq: a > $o] :
% 0.20/0.48 ( ( ! [Xw: a] :
% 0.20/0.48 ( ( ( R @ Xx0 @ Xw )
% 0.20/0.48 | ( S @ Xx0 @ Xw ) )
% 0.20/0.48 => ( Xq @ Xw ) )
% 0.20/0.48 & ! [Xu: a,Xv: a] :
% 0.20/0.48 ( ( ( Xq @ Xu )
% 0.20/0.48 & ( ( R @ Xu @ Xv )
% 0.20/0.48 | ( S @ Xu @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xy0 ) ) )
% 0.20/0.48 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.20/0.48 ( ( ! [Xq: a > $o] :
% 0.20/0.48 ( ( ! [Xw: a] :
% 0.20/0.48 ( ( ( R @ Xx0 @ Xw )
% 0.20/0.48 | ( S @ Xx0 @ Xw ) )
% 0.20/0.48 => ( Xq @ Xw ) )
% 0.20/0.48 & ! [Xu: a,Xv: a] :
% 0.20/0.48 ( ( ( Xq @ Xu )
% 0.20/0.48 & ( ( R @ Xu @ Xv )
% 0.20/0.48 | ( S @ Xu @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xy0 ) )
% 0.20/0.48 & ! [Xq: a > $o] :
% 0.20/0.48 ( ( ! [Xw: a] :
% 0.20/0.48 ( ( ( R @ Xy0 @ Xw )
% 0.20/0.48 | ( S @ Xy0 @ Xw ) )
% 0.20/0.48 => ( Xq @ Xw ) )
% 0.20/0.48 & ! [Xu: a,Xv: a] :
% 0.20/0.48 ( ( ( Xq @ Xu )
% 0.20/0.48 & ( ( R @ Xu @ Xv )
% 0.20/0.48 | ( S @ Xu @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xz ) ) )
% 0.20/0.48 => ! [Xq: a > $o] :
% 0.20/0.48 ( ( ! [Xw: a] :
% 0.20/0.48 ( ( ( R @ Xx0 @ Xw )
% 0.20/0.48 | ( S @ Xx0 @ Xw ) )
% 0.20/0.48 => ( Xq @ Xw ) )
% 0.20/0.48 & ! [Xu: a,Xv: a] :
% 0.20/0.48 ( ( ( Xq @ Xu )
% 0.20/0.48 & ( ( R @ Xu @ Xv )
% 0.20/0.48 | ( S @ Xu @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xv ) ) )
% 0.20/0.48 => ( Xq @ Xz ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.50/1.28 ---- Embedded in THF ---
% 1.50/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.28 %%% Generated on Tue Feb 24 12:41:51 EST 2026
% 1.50/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.28 %%% Logic specification used:
% 1.50/1.28 %%% thf(spec, logic, $$dhol).
% 1.50/1.28
% 1.50/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WPOE9q203G/DTF2DTF6844.p
% See solution above
% 1.50/1.28 ------------------------
% 1.50/1.29 ---- Cleaned THF ---
% 1.50/1.29 thf(a_type,type,
% 1.50/1.29 a: $tType ).
% 1.50/1.29
% 1.50/1.29 thf(cTHM251H_pme,conjecture,
% 1.50/1.29 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.50/1.29 ( ! [Xq: a > $o] :
% 1.50/1.29 ( ( ! [Xw: a] :
% 1.50/1.29 ( ( ( R @ Xx @ Xw )
% 1.50/1.29 | ( S @ Xx @ Xw ) )
% 1.50/1.29 => ( Xq @ Xw ) )
% 1.50/1.29 & ! [Xu: a,Xv: a] :
% 1.50/1.29 ( ( ( Xq @ Xu )
% 1.50/1.29 & ( ( R @ Xu @ Xv )
% 1.50/1.29 | ( S @ Xu @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xy ) )
% 1.50/1.29 | ( ~ ! [Xq: a > $o] :
% 1.50/1.29 ( ( ! [Xw: a] :
% 1.50/1.29 ( ( ( R @ Xx @ Xw )
% 1.50/1.29 | ( S @ Xx @ Xw ) )
% 1.50/1.29 => ( Xq @ Xw ) )
% 1.50/1.29 & ! [Xu: a,Xv: a] :
% 1.50/1.29 ( ( ( Xq @ Xu )
% 1.50/1.29 & ( ( R @ Xu @ Xv )
% 1.50/1.29 | ( S @ Xu @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xy ) )
% 1.50/1.29 & ! [Xx0: a,Xy0: a] :
% 1.50/1.29 ( ( ! [Xq: a > $o] :
% 1.50/1.29 ( ( ! [Xw: a] :
% 1.50/1.29 ( ( R @ Xx0 @ Xw )
% 1.50/1.29 => ( Xq @ Xw ) )
% 1.50/1.29 & ! [Xu: a,Xv: a] :
% 1.50/1.29 ( ( ( Xq @ Xu )
% 1.50/1.29 & ( R @ Xu @ Xv ) )
% 1.50/1.29 => ( Xq @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xy0 ) )
% 1.50/1.29 | ! [Xq: a > $o] :
% 1.50/1.29 ( ( ! [Xw: a] :
% 1.50/1.29 ( ( S @ Xx0 @ Xw )
% 1.50/1.29 => ( Xq @ Xw ) )
% 1.50/1.29 & ! [Xu: a,Xv: a] :
% 1.50/1.29 ( ( ( Xq @ Xu )
% 1.50/1.29 & ( S @ Xu @ Xv ) )
% 1.50/1.29 => ( Xq @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xy0 ) ) )
% 1.50/1.29 => ! [Xq: a > $o] :
% 1.50/1.29 ( ( ! [Xw: a] :
% 1.50/1.29 ( ( ( R @ Xx0 @ Xw )
% 1.50/1.29 | ( S @ Xx0 @ Xw ) )
% 1.50/1.29 => ( Xq @ Xw ) )
% 1.50/1.29 & ! [Xu: a,Xv: a] :
% 1.50/1.29 ( ( ( Xq @ Xu )
% 1.50/1.29 & ( ( R @ Xu @ Xv )
% 1.50/1.29 | ( S @ Xu @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xy0 ) ) )
% 1.50/1.29 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.50/1.29 ( ( ! [Xq: a > $o] :
% 1.50/1.29 ( ( ! [Xw: a] :
% 1.50/1.29 ( ( ( R @ Xx0 @ Xw )
% 1.50/1.29 | ( S @ Xx0 @ Xw ) )
% 1.50/1.29 => ( Xq @ Xw ) )
% 1.50/1.29 & ! [Xu: a,Xv: a] :
% 1.50/1.29 ( ( ( Xq @ Xu )
% 1.50/1.29 & ( ( R @ Xu @ Xv )
% 1.50/1.29 | ( S @ Xu @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xy0 ) )
% 1.50/1.29 & ! [Xq: a > $o] :
% 1.50/1.29 ( ( ! [Xw: a] :
% 1.50/1.29 ( ( ( R @ Xy0 @ Xw )
% 1.50/1.29 | ( S @ Xy0 @ Xw ) )
% 1.50/1.29 => ( Xq @ Xw ) )
% 1.50/1.29 & ! [Xu: a,Xv: a] :
% 1.50/1.29 ( ( ( Xq @ Xu )
% 1.50/1.29 & ( ( R @ Xu @ Xv )
% 1.50/1.29 | ( S @ Xu @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xz ) ) )
% 1.50/1.29 => ! [Xq: a > $o] :
% 1.50/1.29 ( ( ! [Xw: a] :
% 1.50/1.29 ( ( ( R @ Xx0 @ Xw )
% 1.50/1.29 | ( S @ Xx0 @ Xw ) )
% 1.50/1.29 => ( Xq @ Xw ) )
% 1.50/1.29 & ! [Xu: a,Xv: a] :
% 1.50/1.29 ( ( ( Xq @ Xu )
% 1.50/1.29 & ( ( R @ Xu @ Xv )
% 1.50/1.29 | ( S @ Xu @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xv ) ) )
% 1.50/1.29 => ( Xq @ Xz ) ) ) ) ) ).
% 1.50/1.29 ------------------------
% 1.67/1.31 % (6945)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_6844 for (2999ds/4Mi)
% 1.67/1.31 % (6944)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/183Mi)
% 1.67/1.31 % (6947)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/2Mi)
% 1.67/1.31 % (6945)Instruction limit reached!
% 1.67/1.31 % (6945)------------------------------
% 1.67/1.31 % (6945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (6945)Termination reason: Unknown
% 1.67/1.31 % (6945)Termination phase: Preprocessing 3
% 1.67/1.31
% 1.67/1.31 % (6945)Memory used [KB]: 1023
% 1.67/1.31 % (6945)Time elapsed: 0.003 s
% 1.67/1.31 % (6945)Instructions burned: 4 (million)
% 1.67/1.31 % (6945)------------------------------
% 1.67/1.31 % (6945)------------------------------
% 1.67/1.31 % (6947)Instruction limit reached!
% 1.67/1.31 % (6947)------------------------------
% 1.67/1.31 % (6947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (6947)Termination reason: Unknown
% 1.67/1.31 % (6947)Termination phase: Naming
% 1.67/1.31
% 1.67/1.31 % (6947)Memory used [KB]: 1023
% 1.67/1.31 % (6947)Time elapsed: 0.002 s
% 1.67/1.31 % (6947)Instructions burned: 3 (million)
% 1.67/1.31 % (6947)------------------------------
% 1.67/1.31 % (6947)------------------------------
% 1.67/1.31 % (6948)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_6844 for (2999ds/2Mi)
% 1.67/1.31 % (6950)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/18Mi)
% 1.67/1.32 % (6949)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_6844 for (2999ds/275Mi)
% 1.67/1.32 % (6948)Instruction limit reached!
% 1.67/1.32 % (6948)------------------------------
% 1.67/1.32 % (6948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (6948)Termination reason: Unknown
% 1.67/1.32 % (6948)Termination phase: shuffling
% 1.67/1.32
% 1.67/1.32 % (6948)Memory used [KB]: 1023
% 1.67/1.32 % (6948)Time elapsed: 0.003 s
% 1.67/1.32 % (6948)Instructions burned: 2 (million)
% 1.67/1.32 % (6948)------------------------------
% 1.67/1.32 % (6948)------------------------------
% 1.67/1.32 % (6946)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_6844 for (2999ds/27Mi)
% 1.67/1.32 % (6951)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/3Mi)
% 1.67/1.32 % (6951)Instruction limit reached!
% 1.67/1.32 % (6951)------------------------------
% 1.67/1.32 % (6951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (6951)Termination reason: Unknown
% 1.67/1.32 % (6951)Termination phase: Property scanning
% 1.67/1.32 % (6952)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_6844 for (2999ds/37Mi)
% 1.67/1.32
% 1.67/1.32 % (6951)Memory used [KB]: 1023
% 1.67/1.32 % (6951)Time elapsed: 0.002 s
% 1.67/1.32 % (6951)Instructions burned: 3 (million)
% 1.67/1.32 % (6951)------------------------------
% 1.67/1.32 % (6951)------------------------------
% 1.67/1.32 % (6950)Instruction limit reached!
% 1.67/1.32 % (6950)------------------------------
% 1.67/1.32 % (6950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (6950)Termination reason: Unknown
% 1.67/1.32 % (6950)Termination phase: Saturation
% 1.67/1.32
% 1.67/1.32 % (6950)Memory used [KB]: 5628
% 1.67/1.32 % (6950)Time elapsed: 0.011 s
% 1.67/1.32 % (6950)Instructions burned: 18 (million)
% 1.67/1.32 % (6950)------------------------------
% 1.67/1.32 % (6950)------------------------------
% 1.67/1.33 % (6954)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_6844 for (2999ds/3Mi)
% 1.67/1.33 % (6954)Instruction limit reached!
% 1.67/1.33 % (6954)------------------------------
% 1.67/1.33 % (6954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (6954)Termination reason: Unknown
% 1.67/1.33 % (6954)Termination phase: Preprocessing 2
% 1.67/1.33
% 1.67/1.33 % (6954)Memory used [KB]: 1023
% 1.67/1.33 % (6954)Time elapsed: 0.002 s
% 1.67/1.33 % (6954)Instructions burned: 3 (million)
% 1.67/1.33 % (6954)------------------------------
% 1.67/1.33 % (6954)------------------------------
% 1.67/1.33 % (6952)Instruction limit reached!
% 1.67/1.33 % (6952)------------------------------
% 1.67/1.33 % (6952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (6952)Termination reason: Unknown
% 1.67/1.33 % (6952)Termination phase: Saturation
% 1.67/1.33
% 1.67/1.33 % (6952)Memory used [KB]: 5628
% 1.67/1.33 % (6952)Time elapsed: 0.013 s
% 1.67/1.33 % (6952)Instructions burned: 39 (million)
% 1.67/1.33 % (6952)------------------------------
% 1.67/1.33 % (6952)------------------------------
% 1.67/1.33 % (6946)Instruction limit reached!
% 1.67/1.33 % (6946)------------------------------
% 1.67/1.33 % (6946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (6946)Termination reason: Unknown
% 1.67/1.33 % (6946)Termination phase: Saturation
% 1.67/1.33
% 1.67/1.33 % (6946)Memory used [KB]: 5756
% 1.67/1.33 % (6946)Time elapsed: 0.018 s
% 1.67/1.33 % (6946)Instructions burned: 28 (million)
% 1.67/1.33 % (6946)------------------------------
% 1.67/1.33 % (6946)------------------------------
% 1.67/1.33 % (6953)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_6844 for (2999ds/15Mi)
% 1.67/1.34 % (6955)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_6844 for (2999ds/1041Mi)
% 1.67/1.34 % (6956)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/7Mi)
% 1.67/1.34 % (6953)Instruction limit reached!
% 1.67/1.34 % (6953)------------------------------
% 1.67/1.34 % (6953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (6953)Termination reason: Unknown
% 1.67/1.34 % (6953)Termination phase: Saturation
% 1.67/1.34
% 1.67/1.34 % (6953)Memory used [KB]: 5756
% 1.67/1.34 % (6953)Time elapsed: 0.011 s
% 1.67/1.34 % (6953)Instructions burned: 15 (million)
% 1.67/1.34 % (6953)------------------------------
% 1.67/1.34 % (6953)------------------------------
% 1.67/1.34 % (6956)Instruction limit reached!
% 1.67/1.34 % (6956)------------------------------
% 1.67/1.34 % (6956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (6956)Termination reason: Unknown
% 1.67/1.34 % (6956)Termination phase: Property scanning
% 1.67/1.34
% 1.67/1.34 % (6956)Memory used [KB]: 1151
% 1.67/1.34 % (6956)Time elapsed: 0.004 s
% 1.67/1.34 % (6956)Instructions burned: 7 (million)
% 1.67/1.34 % (6956)------------------------------
% 1.67/1.34 % (6956)------------------------------
% 1.67/1.35 % (6957)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/16Mi)
% 1.67/1.35 % (6958)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_6844 for (2999ds/3Mi)
% 1.67/1.35 % (6958)Instruction limit reached!
% 1.67/1.35 % (6958)------------------------------
% 1.67/1.35 % (6958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (6958)Termination reason: Unknown
% 1.67/1.35 % (6958)Termination phase: Naming
% 1.67/1.35
% 1.67/1.35 % (6958)Memory used [KB]: 1023
% 1.67/1.35 % (6958)Time elapsed: 0.004 s
% 1.67/1.35 % (6958)Instructions burned: 3 (million)
% 1.67/1.35 % (6958)------------------------------
% 1.67/1.35 % (6958)------------------------------
% 1.67/1.35 % (6959)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_6844 for (2999ds/3Mi)
% 1.67/1.35 % (6957)Instruction limit reached!
% 1.67/1.35 % (6957)------------------------------
% 1.67/1.35 % (6957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (6957)Termination reason: Unknown
% 1.67/1.35 % (6957)Termination phase: Property scanning
% 1.67/1.35
% 1.67/1.35 % (6957)Memory used [KB]: 1151
% 1.67/1.35 % (6957)Time elapsed: 0.008 s
% 1.67/1.35 % (6957)Instructions burned: 16 (million)
% 1.67/1.35 % (6957)------------------------------
% 1.67/1.35 % (6957)------------------------------
% 1.67/1.35 % (6960)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/7Mi)
% 1.67/1.35 % (6959)Instruction limit reached!
% 1.67/1.35 % (6959)------------------------------
% 1.67/1.35 % (6959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (6959)Termination reason: Unknown
% 1.67/1.35 % (6959)Termination phase: Preprocessing 3
% 1.67/1.35
% 1.67/1.35 % (6959)Memory used [KB]: 1023
% 1.67/1.35 % (6959)Time elapsed: 0.003 s
% 1.67/1.35 % (6959)Instructions burned: 4 (million)
% 1.67/1.35 % (6959)------------------------------
% 1.67/1.35 % (6959)------------------------------
% 1.67/1.36 % (6960)Instruction limit reached!
% 1.67/1.36 % (6960)------------------------------
% 1.67/1.36 % (6960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (6960)Termination reason: Unknown
% 1.67/1.36 % (6960)Termination phase: Property scanning
% 1.67/1.36
% 1.67/1.36 % (6960)Memory used [KB]: 1151
% 1.67/1.36 % (6960)Time elapsed: 0.004 s
% 1.67/1.36 % (6960)Instructions burned: 7 (million)
% 1.67/1.36 % (6960)------------------------------
% 1.67/1.36 % (6960)------------------------------
% 1.67/1.36 % (6944)Instruction limit reached!
% 1.67/1.36 % (6944)------------------------------
% 1.67/1.36 % (6944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (6944)Termination reason: Unknown
% 1.67/1.36 % (6944)Termination phase: Saturation
% 1.67/1.36
% 1.67/1.36 % (6944)Memory used [KB]: 6396
% 1.67/1.36 % (6944)Time elapsed: 0.056 s
% 1.67/1.36 % (6944)Instructions burned: 183 (million)
% 1.67/1.36 % (6944)------------------------------
% 1.67/1.36 % (6944)------------------------------
% 1.67/1.37 % (6963)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/18Mi)
% 1.67/1.37 % (6964)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/710Mi)
% 1.67/1.37 % (6961)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/3Mi)
% 1.67/1.37 % (6962)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/4Mi)
% 1.67/1.37 % (6961)Instruction limit reached!
% 1.67/1.37 % (6961)------------------------------
% 1.67/1.37 % (6961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (6961)Termination reason: Unknown
% 1.67/1.37 % (6961)Termination phase: shuffling
% 1.67/1.37
% 1.67/1.37 % (6961)Memory used [KB]: 1023
% 1.67/1.37 % (6961)Time elapsed: 0.004 s
% 1.67/1.37 % (6961)Instructions burned: 4 (million)
% 1.67/1.37 % (6961)------------------------------
% 1.67/1.37 % (6961)------------------------------
% 1.67/1.37 % (6962)Instruction limit reached!
% 1.67/1.37 % (6962)------------------------------
% 1.67/1.37 % (6962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (6962)Termination reason: Unknown
% 1.67/1.37 % (6962)Termination phase: Naming
% 1.67/1.37
% 1.67/1.37 % (6962)Memory used [KB]: 1023
% 1.67/1.37 % (6962)Time elapsed: 0.003 s
% 1.67/1.37 % (6962)Instructions burned: 4 (million)
% 1.67/1.37 % (6962)------------------------------
% 1.67/1.37 % (6962)------------------------------
% 1.67/1.37 % (6965)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/6Mi)
% 1.67/1.37 % (6963)Instruction limit reached!
% 1.67/1.37 % (6963)------------------------------
% 1.67/1.37 % (6963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (6963)Termination reason: Unknown
% 1.67/1.37 % (6963)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (6963)Memory used [KB]: 5628
% 1.67/1.37 % (6963)Time elapsed: 0.011 s
% 1.67/1.37 % (6963)Instructions burned: 18 (million)
% 1.67/1.37 % (6963)------------------------------
% 1.67/1.37 % (6963)------------------------------
% 1.67/1.37 % (6965)Instruction limit reached!
% 1.67/1.37 % (6965)------------------------------
% 1.67/1.37 % (6965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (6965)Termination reason: Unknown
% 1.67/1.37 % (6965)Termination phase: Property scanning
% 1.67/1.37
% 1.67/1.37 % (6965)Memory used [KB]: 1151
% 1.67/1.37 % (6965)Time elapsed: 0.004 s
% 1.67/1.37 % (6965)Instructions burned: 9 (million)
% 1.67/1.37 % (6965)------------------------------
% 1.67/1.37 % (6965)------------------------------
% 1.67/1.38 % (6967)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_6844 for (2999ds/21Mi)
% 1.67/1.38 % (6969)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_6844 for (2999ds/6Mi)
% 1.67/1.39 % (6968)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/5Mi)
% 1.67/1.39 % (6969)Instruction limit reached!
% 1.67/1.39 % (6969)------------------------------
% 1.67/1.39 % (6969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (6969)Termination reason: Unknown
% 1.67/1.39 % (6969)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (6969)Memory used [KB]: 5500
% 1.67/1.39 % (6969)Time elapsed: 0.003 s
% 1.67/1.39 % (6969)Instructions burned: 7 (million)
% 1.67/1.39 % (6969)------------------------------
% 1.67/1.39 % (6969)------------------------------
% 1.67/1.39 % (6968)Instruction limit reached!
% 1.67/1.39 % (6968)------------------------------
% 1.67/1.39 % (6968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (6968)Termination reason: Unknown
% 1.67/1.39 % (6968)Termination phase: Property scanning
% 1.67/1.39
% 1.67/1.39 % (6968)Memory used [KB]: 1023
% 1.67/1.39 % (6968)Time elapsed: 0.004 s
% 1.67/1.39 % (6968)Instructions burned: 5 (million)
% 1.67/1.39 % (6968)------------------------------
% 1.67/1.39 % (6968)------------------------------
% 1.67/1.39 % (6966)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_6844 for (2999ds/902Mi)
% 1.67/1.39 % (6967)Instruction limit reached!
% 1.67/1.39 % (6967)------------------------------
% 1.67/1.39 % (6967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.39 % (6967)Termination reason: Unknown
% 1.67/1.39 % (6967)Termination phase: Saturation
% 1.67/1.39
% 1.67/1.39 % (6967)Memory used [KB]: 5756
% 1.67/1.39 % (6967)Time elapsed: 0.008 s
% 1.67/1.39 % (6967)Instructions burned: 22 (million)
% 1.67/1.39 % (6967)------------------------------
% 1.67/1.39 % (6967)------------------------------
% 1.67/1.40 % (6970)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/377Mi)
% 1.67/1.40 % (6972)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_6844 for (2999ds/19Mi)
% 1.67/1.41 % (6971)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_6844 for (2999ds/779Mi)
% 1.67/1.41 % (6972)Instruction limit reached!
% 1.67/1.41 % (6972)------------------------------
% 1.67/1.41 % (6972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (6972)Termination reason: Unknown
% 1.67/1.41 % (6972)Termination phase: Saturation
% 1.67/1.41
% 1.67/1.41 % (6972)Memory used [KB]: 5500
% 1.67/1.41 % (6972)Time elapsed: 0.008 s
% 1.67/1.41 % (6972)Instructions burned: 22 (million)
% 1.67/1.41 % (6972)------------------------------
% 1.67/1.41 % (6972)------------------------------
% 1.67/1.42 % (6973)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6844 for (2999ds/879Mi)
% 1.67/1.45 % (6949)Instruction limit reached!
% 1.67/1.45 % (6949)------------------------------
% 1.67/1.45 % (6949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (6949)Termination reason: Unknown
% 1.67/1.45 % (6949)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (6949)Memory used [KB]: 6268
% 1.67/1.45 % (6949)Time elapsed: 0.139 s
% 1.67/1.45 % (6949)Instructions burned: 275 (million)
% 1.67/1.45 % (6949)------------------------------
% 1.67/1.45 % (6949)------------------------------
% 1.67/1.47 % (6974)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6844 for (2998ds/17Mi)
% 1.67/1.48 % (6974)Instruction limit reached!
% 1.67/1.48 % (6974)------------------------------
% 1.67/1.48 % (6974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.48 % (6974)Termination reason: Unknown
% 1.67/1.48 % (6974)Termination phase: Saturation
% 1.67/1.48
% 1.67/1.48 % (6974)Memory used [KB]: 5756
% 1.67/1.48 % (6974)Time elapsed: 0.011 s
% 1.67/1.48 % (6974)Instructions burned: 18 (million)
% 1.67/1.48 % (6974)------------------------------
% 1.67/1.48 % (6974)------------------------------
% 1.67/1.50 % (6975)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6844 for (2998ds/3Mi)
% 1.67/1.50 % (6975)Instruction limit reached!
% 1.67/1.50 % (6975)------------------------------
% 1.67/1.50 % (6975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.50 % (6975)Termination reason: Unknown
% 1.67/1.50 % (6975)Termination phase: shuffling
% 1.67/1.50
% 1.67/1.50 % (6975)Memory used [KB]: 1023
% 1.67/1.50 % (6975)Time elapsed: 0.003 s
% 1.67/1.50 % (6975)Instructions burned: 3 (million)
% 1.67/1.50 % (6975)------------------------------
% 1.67/1.50 % (6975)------------------------------
% 1.67/1.51 % (6970)Instruction limit reached!
% 1.67/1.51 % (6970)------------------------------
% 1.67/1.51 % (6970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.51 % (6970)Termination reason: Unknown
% 1.67/1.51 % (6970)Termination phase: Saturation
% 1.67/1.51
% 1.67/1.51 % (6970)Memory used [KB]: 6652
% 1.67/1.51 % (6970)Time elapsed: 0.115 s
% 1.67/1.51 % (6970)Instructions burned: 379 (million)
% 1.67/1.51 % (6970)------------------------------
% 1.67/1.51 % (6970)------------------------------
% 1.67/1.51 % (6976)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_6844 for (2998ds/30Mi)
% 1.67/1.52 % (6977)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_6844 for (2998ds/127Mi)
% 1.67/1.53 % (6976)Instruction limit reached!
% 1.67/1.53 % (6976)------------------------------
% 1.67/1.53 % (6976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.53 % (6976)Termination reason: Unknown
% 1.67/1.53 % (6976)Termination phase: Saturation
% 1.67/1.53
% 1.67/1.53 % (6976)Memory used [KB]: 5756
% 1.67/1.53 % (6976)Time elapsed: 0.017 s
% 1.67/1.53 % (6976)Instructions burned: 31 (million)
% 1.67/1.53 % (6976)------------------------------
% 1.67/1.53 % (6976)------------------------------
% 1.67/1.54 % (6955)First to succeed.
% 1.67/1.55 % (6978)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_6844 for (2997ds/100Mi)
% 1.67/1.55 % (6955)Refutation found. Thanks to Tanya!
% 1.67/1.55 % SZS status Theorem for DTF2THF_6844
% 1.67/1.55 % SZS output start Proof for DTF2THF_6844
% 1.67/1.55 thf(type_def_5, type, a: $tType).
% 1.67/1.55 thf(func_def_0, type, a: $tType).
% 1.67/1.55 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.67/1.55 thf(func_def_21, type, sK2: a).
% 1.67/1.55 thf(func_def_22, type, sK3: a > a > $o).
% 1.67/1.55 thf(func_def_23, type, sK4: a > a > $o).
% 1.67/1.55 thf(func_def_24, type, sK5: a).
% 1.67/1.55 thf(func_def_25, type, sK6: a > $o).
% 1.67/1.55 thf(func_def_26, type, sK7: a).
% 1.67/1.55 thf(func_def_27, type, sK8: a).
% 1.67/1.55 thf(func_def_28, type, sK9: a).
% 1.67/1.55 thf(func_def_29, type, sK10: a > $o).
% 1.67/1.55 thf(func_def_30, type, sK11: a).
% 1.67/1.55 thf(func_def_31, type, sK12: a).
% 1.67/1.55 thf(func_def_32, type, sK13: a).
% 1.67/1.55 thf(func_def_33, type, sK14: a).
% 1.67/1.55 thf(func_def_34, type, sK15: a).
% 1.67/1.55 thf(func_def_35, type, sK16: a).
% 1.67/1.55 thf(func_def_36, type, sK17: a > $o).
% 1.67/1.55 thf(func_def_37, type, sK18: a).
% 1.67/1.55 thf(func_def_38, type, sK19: a).
% 1.67/1.55 thf(func_def_39, type, sK20: a).
% 1.67/1.55 thf(func_def_40, type, sK21: a).
% 1.67/1.55 thf(func_def_41, type, sK22: a).
% 1.67/1.55 thf(func_def_42, type, sK23: a).
% 1.67/1.55 thf(func_def_43, type, sK24: a).
% 1.67/1.55 thf(func_def_44, type, sK25: a).
% 1.67/1.55 thf(func_def_45, type, sK26: a).
% 1.67/1.55 thf(func_def_46, type, sK27: a).
% 1.67/1.55 thf(func_def_47, type, sK28: a).
% 1.67/1.55 thf(func_def_48, type, sK29: a).
% 1.67/1.55 thf(func_def_49, type, sK30: a).
% 1.67/1.55 thf(func_def_50, type, sK31: a).
% 1.67/1.55 thf(func_def_51, type, sK32: a).
% 1.67/1.55 thf(func_def_52, type, sK33: a).
% 1.67/1.55 thf(func_def_53, type, sK34: a).
% 1.67/1.55 thf(f3373,plain,(
% 1.67/1.55 $false),
% 1.67/1.55 inference(avatar_sat_refutation,[status(thm)],[f44,f245,f414,f424,f613,f643,f674,f704,f779,f879,f958,f1183,f1248,f1273,f1507,f2009,f2041,f2101,f2117,f2403,f2669,f2696,f2748,f2760,f2867,f2876,f3233,f3332,f3372])).
% 1.67/1.55 thf(f3372,plain,(
% 1.67/1.55 ~spl0_11 | ~spl0_17 | ~spl0_65),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3371])).
% 1.67/1.55 thf(f3371,plain,(
% 1.67/1.55 $false | (~spl0_11 | ~spl0_17 | ~spl0_65)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f3370])).
% 1.67/1.55 thf(f3370,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_11 | ~spl0_17 | ~spl0_65)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f3369])).
% 1.67/1.55 thf(f3369,plain,(
% 1.67/1.55 ((~ $true) = $true) | (~spl0_11 | ~spl0_17 | ~spl0_65)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f3368])).
% 1.67/1.55 thf(f3368,plain,(
% 1.67/1.55 ($true = (~ ((sK4 @ sK16 @ sK34) | $true))) | (~spl0_11 | ~spl0_17 | ~spl0_65)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f3364,f3356])).
% 1.67/1.55 thf(f3356,plain,(
% 1.67/1.55 ($true = (sK3 @ sK16 @ sK34)) | ~spl0_65),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f3344])).
% 1.67/1.55 thf(f3344,plain,(
% 1.67/1.55 ($false = ((sK3 @ sK16 @ sK34) => (sK17 @ sK34))) | ~spl0_65),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f3342])).
% 1.67/1.55 thf(f3342,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a]: ((sK3 @ sK16 @ Y0) => (sK17 @ Y0))) @ sK34)) | ~spl0_65),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f3232])).
% 1.67/1.55 thf(f3232,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK16 @ Y0) => (sK17 @ Y0)))) = $false) | ~spl0_65),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f3231])).
% 1.67/1.55 thf(f3231,definition,(
% 1.67/1.55 spl0_65 <=> ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK16 @ Y0) => (sK17 @ Y0)))) = $false)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_65])],[avatar_definition])).
% 1.67/1.55 thf(f3364,plain,(
% 1.67/1.55 ((~ ((sK4 @ sK16 @ sK34) | (sK3 @ sK16 @ sK34))) = $true) | (~spl0_11 | ~spl0_17 | ~spl0_65)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f3363])).
% 1.67/1.55 thf(f3363,plain,(
% 1.67/1.55 ((((sK4 @ sK16 @ sK34) | (sK3 @ sK16 @ sK34)) => $false) = $true) | (~spl0_11 | ~spl0_17 | ~spl0_65)),
% 1.67/1.55 inference(superposition,[status(thm)],[f2982,f3355])).
% 1.67/1.55 thf(f3355,plain,(
% 1.67/1.55 ($false = (sK17 @ sK34)) | ~spl0_65),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f3344])).
% 1.67/1.55 thf(f2982,plain,(
% 1.67/1.55 ( ! [X1 : a] : (((((sK4 @ sK16 @ X1) | (sK3 @ sK16 @ X1)) => (sK17 @ X1)) = $true)) ) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2981])).
% 1.67/1.55 thf(f2981,plain,(
% 1.67/1.55 ( ! [X1 : a] : ((((^[Y0 : a]: (((sK4 @ sK16 @ Y0) | (sK3 @ sK16 @ Y0)) => (sK17 @ Y0))) @ X1) = $true)) ) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(pi_clausification,[status(thm)],[f2968])).
% 1.67/1.55 thf(f2968,plain,(
% 1.67/1.55 ($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ sK16 @ Y0) | (sK3 @ sK16 @ Y0)) => (sK17 @ Y0))))) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2967])).
% 1.67/1.55 thf(f2967,plain,(
% 1.67/1.55 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK16 @ Y0) | (sK3 @ sK16 @ Y0)) => (sK17 @ Y0)))) & $true)) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f2930,f2965])).
% 1.67/1.55 thf(f2965,plain,(
% 1.67/1.55 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK17 @ Y0))))))) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f2930])).
% 1.67/1.55 thf(f2930,plain,(
% 1.67/1.55 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK16 @ Y0) | (sK3 @ sK16 @ Y0)) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK17 @ Y0)))))))) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f2921])).
% 1.67/1.55 thf(f2921,plain,(
% 1.67/1.55 ($false = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK16 @ Y0) | (sK3 @ sK16 @ Y0)) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK17 @ Y0))))))) => (sK17 @ sK15))) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2920])).
% 1.67/1.55 thf(f2920,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15))) @ sK17)) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2908])).
% 1.67/1.55 thf(f2908,plain,(
% 1.67/1.55 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15)))) = $false) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2907])).
% 1.67/1.55 thf(f2907,plain,(
% 1.67/1.55 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15)))))) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2906])).
% 1.67/1.55 thf(f2906,plain,(
% 1.67/1.55 ((($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK15))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15))))) = $false) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2905,f639])).
% 1.67/1.55 thf(f639,plain,(
% 1.67/1.55 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) = $true) | ~spl0_17),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f638])).
% 1.67/1.55 thf(f638,definition,(
% 1.67/1.55 spl0_17 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) = $true)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.67/1.55 thf(f2905,plain,(
% 1.67/1.55 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK15))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15)))))) | ~spl0_11),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2904])).
% 1.67/1.55 thf(f2904,plain,(
% 1.67/1.55 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK15))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK15)))))) @ sK16) = $false) | ~spl0_11),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2895])).
% 1.67/1.55 thf(f2895,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK15))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK15))))))) = $false) | ~spl0_11),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2894])).
% 1.67/1.55 thf(f2894,plain,(
% 1.67/1.55 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))) @ sK15) = $false) | ~spl0_11),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f420])).
% 1.67/1.55 thf(f420,plain,(
% 1.67/1.55 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))))) | ~spl0_11),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f419])).
% 1.67/1.55 thf(f419,definition,(
% 1.67/1.55 spl0_11 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0))))))))))),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.67/1.55 thf(f3332,plain,(
% 1.67/1.55 ~spl0_11 | ~spl0_17 | ~spl0_64),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f3331])).
% 1.67/1.55 thf(f3331,plain,(
% 1.67/1.55 $false | (~spl0_11 | ~spl0_17 | ~spl0_64)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f3330])).
% 1.67/1.55 thf(f3330,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_11 | ~spl0_17 | ~spl0_64)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f3329,f3280])).
% 1.67/1.55 thf(f3280,plain,(
% 1.67/1.55 ($false = (sK17 @ sK33)) | ~spl0_64),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f3279])).
% 1.67/1.55 thf(f3279,plain,(
% 1.67/1.55 (($true => (sK17 @ sK33)) = $false) | ~spl0_64),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f3266,f3278])).
% 1.67/1.55 thf(f3278,plain,(
% 1.67/1.55 (((sK17 @ sK32) & (sK3 @ sK32 @ sK33)) = $true) | ~spl0_64),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f3266])).
% 1.67/1.55 thf(f3266,plain,(
% 1.67/1.55 ($false = (((sK17 @ sK32) & (sK3 @ sK32 @ sK33)) => (sK17 @ sK33))) | ~spl0_64),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f3265])).
% 1.67/1.55 thf(f3265,plain,(
% 1.67/1.55 (((^[Y0 : a]: (((sK17 @ sK32) & (sK3 @ sK32 @ Y0)) => (sK17 @ Y0))) @ sK33) = $false) | ~spl0_64),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f3255])).
% 1.67/1.55 thf(f3255,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (((sK17 @ sK32) & (sK3 @ sK32 @ Y0)) => (sK17 @ Y0)))) = $false) | ~spl0_64),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f3253])).
% 1.67/1.55 thf(f3253,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK17 @ Y1))))) @ sK32)) | ~spl0_64),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f3229])).
% 1.67/1.55 thf(f3229,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK17 @ Y1)))))) = $false) | ~spl0_64),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f3228])).
% 1.67/1.55 thf(f3228,definition,(
% 1.67/1.55 spl0_64 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK17 @ Y1)))))) = $false)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_64])],[avatar_definition])).
% 1.67/1.55 thf(f3329,plain,(
% 1.67/1.55 ($true = (sK17 @ sK33)) | (~spl0_11 | ~spl0_17 | ~spl0_64)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f3328])).
% 1.67/1.55 thf(f3328,plain,(
% 1.67/1.55 (($true => (sK17 @ sK33)) = $true) | (~spl0_11 | ~spl0_17 | ~spl0_64)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f3327,f3313])).
% 1.67/1.55 thf(f3313,plain,(
% 1.67/1.55 ((sK17 @ sK32) = $true) | ~spl0_64),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f3278])).
% 1.67/1.55 thf(f3327,plain,(
% 1.67/1.55 ($true = ((sK17 @ sK32) => (sK17 @ sK33))) | (~spl0_11 | ~spl0_17 | ~spl0_64)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f3326])).
% 1.67/1.55 thf(f3326,plain,(
% 1.67/1.55 ((((sK17 @ sK32) & $true) => (sK17 @ sK33)) = $true) | (~spl0_11 | ~spl0_17 | ~spl0_64)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f3322])).
% 1.67/1.55 thf(f3322,plain,(
% 1.67/1.55 ($true = (((sK17 @ sK32) & ($true | (sK4 @ sK32 @ sK33))) => (sK17 @ sK33))) | (~spl0_11 | ~spl0_17 | ~spl0_64)),
% 1.67/1.55 inference(superposition,[status(thm)],[f3048,f3315])).
% 1.67/1.55 thf(f3315,plain,(
% 1.67/1.55 ((sK3 @ sK32 @ sK33) = $true) | ~spl0_64),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f3314])).
% 1.67/1.55 thf(f3314,plain,(
% 1.67/1.55 ($true = ($true & (sK3 @ sK32 @ sK33))) | ~spl0_64),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f3278,f3313])).
% 1.67/1.55 thf(f3048,plain,(
% 1.67/1.55 ( ! [X2 : a,X1 : a] : (($true = (((sK17 @ X2) & ((sK3 @ X2 @ X1) | (sK4 @ X2 @ X1))) => (sK17 @ X1)))) ) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f3047])).
% 1.67/1.55 thf(f3047,plain,(
% 1.67/1.55 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK17 @ Y0) & ((sK3 @ Y0 @ X1) | (sK4 @ Y0 @ X1))) => (sK17 @ X1))) @ X2) = $true)) ) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(pi_clausification,[status(thm)],[f3034])).
% 1.67/1.55 thf(f3034,plain,(
% 1.67/1.55 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK17 @ Y0) & ((sK3 @ Y0 @ X1) | (sK4 @ Y0 @ X1))) => (sK17 @ X1)))) = $true)) ) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f3033])).
% 1.67/1.55 thf(f3033,plain,(
% 1.67/1.55 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK17 @ Y0))))) @ X1) = $true)) ) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(pi_clausification,[status(thm)],[f2965])).
% 1.67/1.55 thf(f3233,plain,(
% 1.67/1.55 spl0_64 | spl0_65 | ~spl0_11 | ~spl0_17),
% 1.67/1.55 inference(avatar_split_clause,[status(thm)],[f3224,f638,f419,f3231,f3228])).
% 1.67/1.55 thf(f3224,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK16 @ Y0) => (sK17 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK17 @ Y1)))))) = $false) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f3214])).
% 1.67/1.55 thf(f3214,plain,(
% 1.67/1.55 ($false = ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK16 @ Y0) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK17 @ Y1)))))))) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(not_proxy_clausification,[status(thm)],[f2957])).
% 1.67/1.55 thf(f2957,plain,(
% 1.67/1.55 ($true = (~ ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK16 @ Y0) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK17 @ Y1))))))))) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2953])).
% 1.67/1.55 thf(f2953,plain,(
% 1.67/1.55 ((((!! @ a @ (^[Y0 : a]: ((sK3 @ sK16 @ Y0) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK17 @ Y1))))))) => $false) = $true) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(superposition,[status(thm)],[f2936,f2929])).
% 1.67/1.55 thf(f2929,plain,(
% 1.67/1.55 ($false = (sK17 @ sK15)) | (~spl0_11 | ~spl0_17)),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f2921])).
% 1.67/1.55 thf(f2936,plain,(
% 1.67/1.55 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: ((sK3 @ sK16 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & (sK3 @ Y0 @ Y1)) => (X1 @ Y1))))))) => (X1 @ sK15)) = $true)) ) | ~spl0_17),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2935])).
% 1.67/1.55 thf(f2935,plain,(
% 1.67/1.55 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK15))) @ X1) = $true)) ) | ~spl0_17),
% 1.67/1.55 inference(pi_clausification,[status(thm)],[f639])).
% 1.67/1.55 thf(f2876,plain,(
% 1.67/1.55 ~spl0_20 | ~spl0_31 | ~spl0_56),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f2875])).
% 1.67/1.55 thf(f2875,plain,(
% 1.67/1.55 $false | (~spl0_20 | ~spl0_31 | ~spl0_56)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f2874])).
% 1.67/1.55 thf(f2874,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_20 | ~spl0_31 | ~spl0_56)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2873])).
% 1.67/1.55 thf(f2873,plain,(
% 1.67/1.55 (((sK6 @ sK22) => $true) = $false) | (~spl0_20 | ~spl0_31 | ~spl0_56)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2872,f2097])).
% 1.67/1.55 thf(f2097,plain,(
% 1.67/1.55 ((sK6 @ sK23) = $true) | ~spl0_56),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f2096])).
% 1.67/1.55 thf(f2096,definition,(
% 1.67/1.55 spl0_56 <=> ((sK6 @ sK23) = $true)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_56])],[avatar_definition])).
% 1.67/1.55 thf(f2872,plain,(
% 1.67/1.55 ($false = ((sK6 @ sK22) => (sK6 @ sK23))) | (~spl0_20 | ~spl0_31)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2871])).
% 1.67/1.55 thf(f2871,plain,(
% 1.67/1.55 ((((sK6 @ sK22) & $true) => (sK6 @ sK23)) = $false) | (~spl0_20 | ~spl0_31)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2870])).
% 1.67/1.55 thf(f2870,plain,(
% 1.67/1.55 ((((sK6 @ sK22) & ($true | (sK3 @ sK22 @ sK23))) => (sK6 @ sK23)) = $false) | (~spl0_20 | ~spl0_31)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2862,f957])).
% 1.67/1.55 thf(f957,plain,(
% 1.67/1.55 ((sK4 @ sK22 @ sK23) = $true) | ~spl0_31),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f956])).
% 1.67/1.55 thf(f956,definition,(
% 1.67/1.55 spl0_31 <=> ((sK4 @ sK22 @ sK23) = $true)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition])).
% 1.67/1.55 thf(f2862,plain,(
% 1.67/1.55 ((((sK6 @ sK22) & ((sK4 @ sK22 @ sK23) | (sK3 @ sK22 @ sK23))) => (sK6 @ sK23)) = $false) | ~spl0_20),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2861])).
% 1.67/1.55 thf(f2861,plain,(
% 1.67/1.55 (((^[Y0 : a]: (((sK6 @ sK22) & ((sK4 @ sK22 @ Y0) | (sK3 @ sK22 @ Y0))) => (sK6 @ Y0))) @ sK23) = $false) | ~spl0_20),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2848])).
% 1.67/1.55 thf(f2848,plain,(
% 1.67/1.55 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK22) & ((sK4 @ sK22 @ Y0) | (sK3 @ sK22 @ Y0))) => (sK6 @ Y0))))) | ~spl0_20),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2844])).
% 1.67/1.55 thf(f2844,plain,(
% 1.67/1.55 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK6 @ Y1))))) @ sK22) = $false) | ~spl0_20),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f673])).
% 1.67/1.55 thf(f673,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK6 @ Y1)))))) = $false) | ~spl0_20),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f672])).
% 1.67/1.55 thf(f672,definition,(
% 1.67/1.55 spl0_20 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK6 @ Y1)))))) = $false)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])).
% 1.67/1.55 thf(f2867,plain,(
% 1.67/1.55 ~spl0_20 | ~spl0_57),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f2866])).
% 1.67/1.55 thf(f2866,plain,(
% 1.67/1.55 $false | (~spl0_20 | ~spl0_57)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f2865])).
% 1.67/1.55 thf(f2865,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_20 | ~spl0_57)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2864])).
% 1.67/1.55 thf(f2864,plain,(
% 1.67/1.55 ($false = ($false => (sK6 @ sK23))) | (~spl0_20 | ~spl0_57)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2863])).
% 1.67/1.55 thf(f2863,plain,(
% 1.67/1.55 ((($false & ((sK4 @ sK22 @ sK23) | (sK3 @ sK22 @ sK23))) => (sK6 @ sK23)) = $false) | (~spl0_20 | ~spl0_57)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2862,f2100])).
% 1.67/1.55 thf(f2100,plain,(
% 1.67/1.55 ($false = (sK6 @ sK22)) | ~spl0_57),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f2099])).
% 1.67/1.55 thf(f2099,definition,(
% 1.67/1.55 spl0_57 <=> ($false = (sK6 @ sK22))),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_57])],[avatar_definition])).
% 1.67/1.55 thf(f2760,plain,(
% 1.67/1.55 ~spl0_2 | ~spl0_16 | ~spl0_25),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f2759])).
% 1.67/1.55 thf(f2759,plain,(
% 1.67/1.55 $false | (~spl0_2 | ~spl0_16 | ~spl0_25)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f2758])).
% 1.67/1.55 thf(f2758,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_2 | ~spl0_16 | ~spl0_25)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2757,f2751])).
% 1.67/1.55 thf(f2751,plain,(
% 1.67/1.55 ($false = ((sK10 @ sK19) => (sK10 @ sK20))) | (~spl0_16 | ~spl0_25)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2750])).
% 1.67/1.55 thf(f2750,plain,(
% 1.67/1.55 ((((sK10 @ sK19) & $true) => (sK10 @ sK20)) = $false) | (~spl0_16 | ~spl0_25)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2749])).
% 1.67/1.55 thf(f2749,plain,(
% 1.67/1.55 ($false = (((sK10 @ sK19) & ($true | (sK4 @ sK19 @ sK20))) => (sK10 @ sK20))) | (~spl0_16 | ~spl0_25)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2743,f775])).
% 1.67/1.55 thf(f775,plain,(
% 1.67/1.55 ($true = (sK3 @ sK19 @ sK20)) | ~spl0_25),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f774])).
% 1.67/1.55 thf(f774,definition,(
% 1.67/1.55 spl0_25 <=> ($true = (sK3 @ sK19 @ sK20))),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition])).
% 1.67/1.55 thf(f2743,plain,(
% 1.67/1.55 ($false = (((sK10 @ sK19) & ((sK3 @ sK19 @ sK20) | (sK4 @ sK19 @ sK20))) => (sK10 @ sK20))) | ~spl0_16),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2742])).
% 1.67/1.55 thf(f2742,plain,(
% 1.67/1.55 (((^[Y0 : a]: (((sK10 @ sK19) & ((sK3 @ sK19 @ Y0) | (sK4 @ sK19 @ Y0))) => (sK10 @ Y0))) @ sK20) = $false) | ~spl0_16),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2731])).
% 1.67/1.55 thf(f2731,plain,(
% 1.67/1.55 ($false = (!! @ a @ (^[Y0 : a]: (((sK10 @ sK19) & ((sK3 @ sK19 @ Y0) | (sK4 @ sK19 @ Y0))) => (sK10 @ Y0))))) | ~spl0_16),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2727])).
% 1.67/1.55 thf(f2727,plain,(
% 1.67/1.55 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK10 @ Y1))))) @ sK19) = $false) | ~spl0_16),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f612])).
% 1.67/1.55 thf(f612,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK10 @ Y1)))))) = $false) | ~spl0_16),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f611])).
% 1.67/1.55 thf(f611,definition,(
% 1.67/1.55 spl0_16 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK10 @ Y1)))))) = $false)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.67/1.55 thf(f2757,plain,(
% 1.67/1.55 ($true = ((sK10 @ sK19) => (sK10 @ sK20))) | (~spl0_2 | ~spl0_25)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2756])).
% 1.67/1.55 thf(f2756,plain,(
% 1.67/1.55 ((((sK10 @ sK19) & $true) => (sK10 @ sK20)) = $true) | (~spl0_2 | ~spl0_25)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2752])).
% 1.67/1.55 thf(f2752,plain,(
% 1.67/1.55 ($true = (((sK10 @ sK19) & ((sK4 @ sK19 @ sK20) | $true)) => (sK10 @ sK20))) | (~spl0_2 | ~spl0_25)),
% 1.67/1.55 inference(superposition,[status(thm)],[f2277,f775])).
% 1.67/1.55 thf(f2277,plain,(
% 1.67/1.55 ( ! [X2 : a,X1 : a] : (((((sK10 @ X1) & ((sK4 @ X1 @ X2) | (sK3 @ X1 @ X2))) => (sK10 @ X2)) = $true)) ) | ~spl0_2),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2276])).
% 1.67/1.55 thf(f2276,plain,(
% 1.67/1.55 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK10 @ X1) & ((sK4 @ X1 @ Y0) | (sK3 @ X1 @ Y0))) => (sK10 @ Y0))) @ X2) = $true)) ) | ~spl0_2),
% 1.67/1.55 inference(pi_clausification,[status(thm)],[f2261])).
% 1.67/1.55 thf(f2261,plain,(
% 1.67/1.55 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK10 @ X1) & ((sK4 @ X1 @ Y0) | (sK3 @ X1 @ Y0))) => (sK10 @ Y0)))) = $true)) ) | ~spl0_2),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2260])).
% 1.67/1.55 thf(f2260,plain,(
% 1.67/1.55 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))) @ X1) = $true)) ) | ~spl0_2),
% 1.67/1.55 inference(pi_clausification,[status(thm)],[f2249])).
% 1.67/1.55 thf(f2249,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1)))))) = $true) | ~spl0_2),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2248])).
% 1.67/1.55 thf(f2248,plain,(
% 1.67/1.55 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) = $true) | ~spl0_2),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f2185,f2247])).
% 1.67/1.55 thf(f2247,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (sK10 @ Y0)))) = $true) | ~spl0_2),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f2185])).
% 1.67/1.55 thf(f2185,plain,(
% 1.67/1.55 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1)))))))) | ~spl0_2),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f2173])).
% 1.67/1.55 thf(f2173,plain,(
% 1.67/1.55 ($false = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) => (sK10 @ sK8))) | ~spl0_2),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2172])).
% 1.67/1.55 thf(f2172,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8))) @ sK10)) | ~spl0_2),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2157])).
% 1.67/1.55 thf(f2157,plain,(
% 1.67/1.55 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) = $false) | ~spl0_2),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f2141])).
% 1.67/1.55 thf(f2141,plain,(
% 1.67/1.55 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))))) | ~spl0_2),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2140])).
% 1.67/1.55 thf(f2140,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK8)))))) @ sK9)) | ~spl0_2),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2129])).
% 1.67/1.55 thf(f2129,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK8))))))) = $false) | ~spl0_2),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2128])).
% 1.67/1.55 thf(f2128,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y0)))))))) @ sK8)) | ~spl0_2),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2124])).
% 1.67/1.55 thf(f2124,plain,(
% 1.67/1.55 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y0)))))))))) | ~spl0_2),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2123])).
% 1.67/1.55 thf(f2123,plain,(
% 1.67/1.55 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y1)))))))))) @ sK7) = $false) | ~spl0_2),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f43])).
% 1.67/1.55 thf(f43,plain,(
% 1.67/1.55 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y1)))))))))))) | ~spl0_2),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.67/1.55 thf(f42,definition,(
% 1.67/1.55 spl0_2 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y1))))))))))))),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.67/1.55 thf(f2748,plain,(
% 1.67/1.55 ~spl0_16 | ~spl0_40),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f2747])).
% 1.67/1.55 thf(f2747,plain,(
% 1.67/1.55 $false | (~spl0_16 | ~spl0_40)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f2746])).
% 1.67/1.55 thf(f2746,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_16 | ~spl0_40)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2745])).
% 1.67/1.55 thf(f2745,plain,(
% 1.67/1.55 (($false => (sK10 @ sK20)) = $false) | (~spl0_16 | ~spl0_40)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2744])).
% 1.67/1.55 thf(f2744,plain,(
% 1.67/1.55 ((($false & ((sK3 @ sK19 @ sK20) | (sK4 @ sK19 @ sK20))) => (sK10 @ sK20)) = $false) | (~spl0_16 | ~spl0_40)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2743,f1506])).
% 1.67/1.55 thf(f1506,plain,(
% 1.67/1.55 ((sK10 @ sK19) = $false) | ~spl0_40),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f1505])).
% 1.67/1.55 thf(f1505,definition,(
% 1.67/1.55 spl0_40 <=> ((sK10 @ sK19) = $false)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_40])],[avatar_definition])).
% 1.67/1.55 thf(f2696,plain,(
% 1.67/1.55 ~spl0_2 | ~spl0_3 | ~spl0_9),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f2695])).
% 1.67/1.55 thf(f2695,plain,(
% 1.67/1.55 $false | (~spl0_2 | ~spl0_3 | ~spl0_9)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f2694])).
% 1.67/1.55 thf(f2694,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_2 | ~spl0_3 | ~spl0_9)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2693,f2643])).
% 1.67/1.55 thf(f2643,plain,(
% 1.67/1.55 ($false = (sK10 @ sK12)) | ~spl0_3),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f2625])).
% 1.67/1.55 thf(f2625,plain,(
% 1.67/1.55 ($false = ((((sK3 @ sK13 @ sK12) | (sK4 @ sK13 @ sK12)) & (sK10 @ sK13)) => (sK10 @ sK12))) | ~spl0_3),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2624])).
% 1.67/1.55 thf(f2624,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a]: ((((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)) => (sK10 @ sK12))) @ sK13)) | ~spl0_3),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2579])).
% 1.67/1.55 thf(f2579,plain,(
% 1.67/1.55 ($false = (!! @ a @ (^[Y0 : a]: ((((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)) => (sK10 @ sK12))))) | ~spl0_3),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2577])).
% 1.67/1.55 thf(f2577,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) & (sK10 @ Y1)) => (sK10 @ Y0))))) @ sK12)) | ~spl0_3),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f241])).
% 1.67/1.55 thf(f241,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) & (sK10 @ Y1)) => (sK10 @ Y0)))))) = $false) | ~spl0_3),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f240])).
% 1.67/1.55 thf(f240,definition,(
% 1.67/1.55 spl0_3 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) & (sK10 @ Y1)) => (sK10 @ Y0)))))) = $false)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.67/1.55 thf(f2693,plain,(
% 1.67/1.55 ((sK10 @ sK12) = $true) | (~spl0_2 | ~spl0_3 | ~spl0_9)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2692])).
% 1.67/1.55 thf(f2692,plain,(
% 1.67/1.55 ($true = ($true => (sK10 @ sK12))) | (~spl0_2 | ~spl0_3 | ~spl0_9)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2687,f2673])).
% 1.67/1.55 thf(f2673,plain,(
% 1.67/1.55 ((sK10 @ sK14) = $true) | (~spl0_3 | ~spl0_9)),
% 1.67/1.55 inference(not_proxy_clausification,[status(thm)],[f2672])).
% 1.67/1.55 thf(f2672,plain,(
% 1.67/1.55 ((~ (sK10 @ sK14)) = $false) | (~spl0_3 | ~spl0_9)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2671])).
% 1.67/1.55 thf(f2671,plain,(
% 1.67/1.55 ((~ ($true & (sK10 @ sK14))) = $false) | (~spl0_3 | ~spl0_9)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2670])).
% 1.67/1.55 thf(f2670,plain,(
% 1.67/1.55 ($false = (~ (((sK3 @ sK14 @ sK12) | $true) & (sK10 @ sK14)))) | (~spl0_3 | ~spl0_9)),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f2663,f410])).
% 1.67/1.55 thf(f410,plain,(
% 1.67/1.55 ((sK4 @ sK14 @ sK12) = $true) | ~spl0_9),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f409])).
% 1.67/1.55 thf(f409,definition,(
% 1.67/1.55 spl0_9 <=> ((sK4 @ sK14 @ sK12) = $true)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.67/1.55 thf(f2663,plain,(
% 1.67/1.55 ((~ (((sK3 @ sK14 @ sK12) | (sK4 @ sK14 @ sK12)) & (sK10 @ sK14))) = $false) | ~spl0_3),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2662])).
% 1.67/1.55 thf(f2662,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a]: (~ (((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)))) @ sK14)) | ~spl0_3),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2650])).
% 1.67/1.55 thf(f2650,plain,(
% 1.67/1.55 ($false = (!! @ a @ (^[Y0 : a]: (~ (((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)))))) | ~spl0_3),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2646])).
% 1.67/1.55 thf(f2646,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: ((((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)) => $false))) = $false) | ~spl0_3),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f2579,f2643])).
% 1.67/1.55 thf(f2687,plain,(
% 1.67/1.55 ($true = ((sK10 @ sK14) => (sK10 @ sK12))) | (~spl0_2 | ~spl0_9)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2686])).
% 1.67/1.55 thf(f2686,plain,(
% 1.67/1.55 ($true = (((sK10 @ sK14) & $true) => (sK10 @ sK12))) | (~spl0_2 | ~spl0_9)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2684])).
% 1.67/1.55 thf(f2684,plain,(
% 1.67/1.55 ($true = (((sK10 @ sK14) & ($true | (sK3 @ sK14 @ sK12))) => (sK10 @ sK12))) | (~spl0_2 | ~spl0_9)),
% 1.67/1.55 inference(superposition,[status(thm)],[f2277,f410])).
% 1.67/1.55 thf(f2669,plain,(
% 1.67/1.55 ~spl0_2 | ~spl0_3 | ~spl0_10),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f2668])).
% 1.67/1.55 thf(f2668,plain,(
% 1.67/1.55 $false | (~spl0_2 | ~spl0_3 | ~spl0_10)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f2667])).
% 1.67/1.55 thf(f2667,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_2 | ~spl0_3 | ~spl0_10)),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f2649,f2666])).
% 1.67/1.55 thf(f2666,plain,(
% 1.67/1.55 ((~ (sK10 @ sK14)) = $false) | (~spl0_3 | ~spl0_10)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2665])).
% 1.67/1.55 thf(f2665,plain,(
% 1.67/1.55 ((~ ($true & (sK10 @ sK14))) = $false) | (~spl0_3 | ~spl0_10)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2664])).
% 1.67/1.55 thf(f2664,plain,(
% 1.67/1.55 ($false = (~ (($true | (sK4 @ sK14 @ sK12)) & (sK10 @ sK14)))) | (~spl0_3 | ~spl0_10)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2663,f413])).
% 1.67/1.55 thf(f413,plain,(
% 1.67/1.55 ($true = (sK3 @ sK14 @ sK12)) | ~spl0_10),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f412])).
% 1.67/1.55 thf(f412,definition,(
% 1.67/1.55 spl0_10 <=> ($true = (sK3 @ sK14 @ sK12))),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.67/1.55 thf(f2649,plain,(
% 1.67/1.55 ((~ (sK10 @ sK14)) = $true) | (~spl0_2 | ~spl0_3 | ~spl0_10)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2647])).
% 1.67/1.55 thf(f2647,plain,(
% 1.67/1.55 (((sK10 @ sK14) => $false) = $true) | (~spl0_2 | ~spl0_3 | ~spl0_10)),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f2546,f2643])).
% 1.67/1.55 thf(f2546,plain,(
% 1.67/1.55 ($true = ((sK10 @ sK14) => (sK10 @ sK12))) | (~spl0_2 | ~spl0_10)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2545])).
% 1.67/1.55 thf(f2545,plain,(
% 1.67/1.55 ($true = (((sK10 @ sK14) & $true) => (sK10 @ sK12))) | (~spl0_2 | ~spl0_10)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2543])).
% 1.67/1.55 thf(f2543,plain,(
% 1.67/1.55 ($true = (((sK10 @ sK14) & ((sK4 @ sK14 @ sK12) | $true)) => (sK10 @ sK12))) | (~spl0_2 | ~spl0_10)),
% 1.67/1.55 inference(superposition,[status(thm)],[f2277,f413])).
% 1.67/1.55 thf(f2403,plain,(
% 1.67/1.55 ~spl0_2 | ~spl0_4 | ~spl0_15 | ~spl0_22),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f2402])).
% 1.67/1.55 thf(f2402,plain,(
% 1.67/1.55 $false | (~spl0_2 | ~spl0_4 | ~spl0_15 | ~spl0_22)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f2401])).
% 1.67/1.55 thf(f2401,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_2 | ~spl0_4 | ~spl0_15 | ~spl0_22)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2400,f2120])).
% 1.67/1.55 thf(f2120,plain,(
% 1.67/1.55 ($false = (sK10 @ sK18)) | (~spl0_15 | ~spl0_22)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2119])).
% 1.67/1.55 thf(f2119,plain,(
% 1.67/1.55 (($true => (sK10 @ sK18)) = $false) | (~spl0_15 | ~spl0_22)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2118])).
% 1.67/1.55 thf(f2118,plain,(
% 1.67/1.55 ((($true | (sK4 @ sK7 @ sK18)) => (sK10 @ sK18)) = $false) | (~spl0_15 | ~spl0_22)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2035,f703])).
% 1.67/1.55 thf(f703,plain,(
% 1.67/1.55 ((sK3 @ sK7 @ sK18) = $true) | ~spl0_22),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f702])).
% 1.67/1.55 thf(f702,definition,(
% 1.67/1.55 spl0_22 <=> ((sK3 @ sK7 @ sK18) = $true)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition])).
% 1.67/1.55 thf(f2035,plain,(
% 1.67/1.55 ((((sK3 @ sK7 @ sK18) | (sK4 @ sK7 @ sK18)) => (sK10 @ sK18)) = $false) | ~spl0_15),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2031])).
% 1.67/1.55 thf(f2031,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0))) @ sK18)) | ~spl0_15),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f609])).
% 1.67/1.55 thf(f609,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0)))) = $false) | ~spl0_15),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f608])).
% 1.67/1.55 thf(f608,definition,(
% 1.67/1.55 spl0_15 <=> ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0)))) = $false)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.67/1.55 thf(f2400,plain,(
% 1.67/1.55 ($true = (sK10 @ sK18)) | (~spl0_2 | ~spl0_4 | ~spl0_22)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2399])).
% 1.67/1.55 thf(f2399,plain,(
% 1.67/1.55 (($true => (sK10 @ sK18)) = $true) | (~spl0_2 | ~spl0_4 | ~spl0_22)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2328,f244])).
% 1.67/1.55 thf(f244,plain,(
% 1.67/1.55 ((sK10 @ sK7) = $true) | ~spl0_4),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f243])).
% 1.67/1.55 thf(f243,definition,(
% 1.67/1.55 spl0_4 <=> ((sK10 @ sK7) = $true)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.67/1.55 thf(f2328,plain,(
% 1.67/1.55 ($true = ((sK10 @ sK7) => (sK10 @ sK18))) | (~spl0_2 | ~spl0_22)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2327])).
% 1.67/1.55 thf(f2327,plain,(
% 1.67/1.55 ((((sK10 @ sK7) & $true) => (sK10 @ sK18)) = $true) | (~spl0_2 | ~spl0_22)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2297])).
% 1.67/1.55 thf(f2297,plain,(
% 1.67/1.55 ((((sK10 @ sK7) & ((sK4 @ sK7 @ sK18) | $true)) => (sK10 @ sK18)) = $true) | (~spl0_2 | ~spl0_22)),
% 1.67/1.55 inference(superposition,[status(thm)],[f2277,f703])).
% 1.67/1.55 thf(f2117,plain,(
% 1.67/1.55 ~spl0_20 | ~spl0_30),
% 1.67/1.55 inference(avatar_contradiction_clause,[status(thm)],[f2116])).
% 1.67/1.55 thf(f2116,plain,(
% 1.67/1.55 $false | (~spl0_20 | ~spl0_30)),
% 1.67/1.55 inference(trivial_inequality_removal,[status(thm)],[f2115])).
% 1.67/1.55 thf(f2115,plain,(
% 1.67/1.55 ($false = $true) | (~spl0_20 | ~spl0_30)),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f2109,f2114])).
% 1.67/1.55 thf(f2114,plain,(
% 1.67/1.55 ($false = ((sK6 @ sK22) => (sK6 @ sK23))) | (~spl0_20 | ~spl0_30)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2113])).
% 1.67/1.55 thf(f2113,plain,(
% 1.67/1.55 ((((sK6 @ sK22) & $true) => (sK6 @ sK23)) = $false) | (~spl0_20 | ~spl0_30)),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2112])).
% 1.67/1.55 thf(f2112,plain,(
% 1.67/1.55 ($false = (((sK6 @ sK22) & ((sK4 @ sK22 @ sK23) | $true)) => (sK6 @ sK23))) | (~spl0_20 | ~spl0_30)),
% 1.67/1.55 inference(forward_demodulation,[status(thm)],[f2111,f954])).
% 1.67/1.55 thf(f954,plain,(
% 1.67/1.55 ((sK3 @ sK22 @ sK23) = $true) | ~spl0_30),
% 1.67/1.55 inference(avatar_component_clause,[status(thm)],[f953])).
% 1.67/1.55 thf(f953,definition,(
% 1.67/1.55 spl0_30 <=> ((sK3 @ sK22 @ sK23) = $true)),
% 1.67/1.55 introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition])).
% 1.67/1.55 thf(f2111,plain,(
% 1.67/1.55 ((((sK6 @ sK22) & ((sK4 @ sK22 @ sK23) | (sK3 @ sK22 @ sK23))) => (sK6 @ sK23)) = $false) | ~spl0_20),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2110])).
% 1.67/1.55 thf(f2110,plain,(
% 1.67/1.55 (((^[Y0 : a]: (((sK6 @ sK22) & ((sK4 @ sK22 @ Y0) | (sK3 @ sK22 @ Y0))) => (sK6 @ Y0))) @ sK23) = $false) | ~spl0_20),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f2106])).
% 1.67/1.55 thf(f2106,plain,(
% 1.67/1.55 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK22) & ((sK4 @ sK22 @ Y0) | (sK3 @ sK22 @ Y0))) => (sK6 @ Y0))))) | ~spl0_20),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f2102])).
% 1.67/1.55 thf(f2102,plain,(
% 1.67/1.55 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK6 @ Y1))))) @ sK22) = $false) | ~spl0_20),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f673])).
% 1.67/1.55 thf(f2109,plain,(
% 1.67/1.55 ($true = ((sK6 @ sK22) => (sK6 @ sK23))) | ~spl0_30),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2108])).
% 1.67/1.55 thf(f2108,plain,(
% 1.67/1.55 ((((sK6 @ sK22) & $true) => (sK6 @ sK23)) = $true) | ~spl0_30),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f2107])).
% 1.67/1.55 thf(f2107,plain,(
% 1.67/1.55 ((((sK6 @ sK22) & ($true | (sK4 @ sK22 @ sK23))) => (sK6 @ sK23)) = $true) | ~spl0_30),
% 1.67/1.55 inference(superposition,[status(thm)],[f79,f954])).
% 1.67/1.55 thf(f79,plain,(
% 1.67/1.55 ( ! [X2 : a,X1 : a] : (($true = (((sK6 @ X1) & ((sK3 @ X1 @ X2) | (sK4 @ X1 @ X2))) => (sK6 @ X2)))) )),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.67/1.55 thf(f78,plain,(
% 1.67/1.55 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK6 @ X1) & ((sK3 @ X1 @ Y0) | (sK4 @ X1 @ Y0))) => (sK6 @ Y0))) @ X2))) )),
% 1.67/1.55 inference(pi_clausification,[status(thm)],[f75])).
% 1.67/1.55 thf(f75,plain,(
% 1.67/1.55 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ X1) & ((sK3 @ X1 @ Y0) | (sK4 @ X1 @ Y0))) => (sK6 @ Y0)))) = $true)) )),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.67/1.55 thf(f74,plain,(
% 1.67/1.55 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK6 @ Y1))))) @ X1))) )),
% 1.67/1.55 inference(pi_clausification,[status(thm)],[f29])).
% 1.67/1.55 thf(f29,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK6 @ Y1)))))) = $true)),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.67/1.55 thf(f25,plain,(
% 1.67/1.55 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK4 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0))))))),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.67/1.55 thf(f23,plain,(
% 1.67/1.55 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK4 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0))))) => (sK6 @ sK2)))),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.67/1.55 thf(f22,plain,(
% 1.67/1.55 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK2))) @ sK6) = $false)),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f21])).
% 1.67/1.55 thf(f21,plain,(
% 1.67/1.55 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK2)))))),
% 1.67/1.55 inference(boolean_simplification,[status(thm)],[f20])).
% 1.67/1.55 thf(f20,plain,(
% 1.67/1.55 ($false = ($false | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK2))))))),
% 1.67/1.55 inference(backward_demodulation,[status(thm)],[f17,f19])).
% 1.67/1.55 thf(f19,plain,(
% 1.67/1.55 ((((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y1)))))))))))) = $false)),
% 1.67/1.55 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.67/1.55 thf(f17,plain,(
% 1.67/1.55 (((((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y1)))))))))))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK2))))) = $false)),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.67/1.55 thf(f16,plain,(
% 1.67/1.55 (((^[Y0 : a]: ((((~ (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK4 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK2))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK3 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y1)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK4 @ Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4))))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK3 @ Y5 @ Y6) | (sK4 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y1 @ Y5) | (sK4 @ Y1 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y2)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((sK3 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5)) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((sK4 @ Y3 @ Y5) | (sK3 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK4 @ Y3 @ Y5) | (sK3 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK4 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y2)))))))))))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK2)))))) @ sK5) = $false)),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f15])).
% 1.67/1.55 thf(f15,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: ((((~ (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK4 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK2))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK3 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y1)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK4 @ Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4))))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y1)))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK3 @ Y5 @ Y6) | (sK4 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y1 @ Y5) | (sK4 @ Y1 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y2)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((sK3 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5)) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((sK4 @ Y3 @ Y5) | (sK3 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK4 @ Y3 @ Y5) | (sK3 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK4 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y2)))))))))))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK2))))))) = $false)),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.67/1.55 thf(f14,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: ((((~ (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (Y0 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((Y0 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK2))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK3 @ Y3 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (sK3 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y2)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y3 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5))))))) => (Y4 @ Y2))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y3 @ Y5) | (sK3 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((sK3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK3 @ Y6 @ Y7) | (Y0 @ Y6 @ Y7))) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y2 @ Y6) | (Y0 @ Y2 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y3)))) & (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((((sK3 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (((Y0 @ Y4 @ Y6) | (sK3 @ Y4 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y2))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y0 @ Y4 @ Y6) | (sK3 @ Y4 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((Y0 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y3)))))))))))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (Y0 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK2)))))))) @ sK4))),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f13])).
% 1.67/1.55 thf(f13,plain,(
% 1.67/1.55 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: ((((~ (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (Y0 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((Y0 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK2))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK3 @ Y3 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (sK3 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y2)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y3 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5))))))) => (Y4 @ Y2))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y3 @ Y5) | (sK3 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((sK3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2)))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK3 @ Y6 @ Y7) | (Y0 @ Y6 @ Y7))) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y2 @ Y6) | (Y0 @ Y2 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y3)))) & (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((((sK3 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (((Y0 @ Y4 @ Y6) | (sK3 @ Y4 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y2))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y0 @ Y4 @ Y6) | (sK3 @ Y4 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((Y0 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y3)))))))))))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (Y0 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK2))))))))))),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.67/1.55 thf(f12,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: ((((~ (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y4) | (Y1 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((Y1 @ Y4 @ Y5) | (Y0 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ sK2))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y0 @ Y4 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y0 @ Y6 @ Y7)) => (Y5 @ Y7))))))) => (Y5 @ Y3)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y1 @ Y4 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y1 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6))))))) => (Y5 @ Y3))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y1 @ Y4 @ Y6) | (Y0 @ Y4 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & ((Y0 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6))) => (Y5 @ Y6))))))) => (Y5 @ Y3)))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y0 @ Y7 @ Y8) | (Y1 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y3 @ Y7) | (Y1 @ Y3 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4)))) & (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (((Y1 @ Y5 @ Y7) | (Y0 @ Y5 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y3))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y1 @ Y5 @ Y7) | (Y0 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y1 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y4)))))))))))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((Y0 @ Y4 @ Y5) | (Y1 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) | (Y0 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ sK2)))))))))) @ sK3))),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f11])).
% 1.67/1.55 thf(f11,plain,(
% 1.67/1.55 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: ((((~ (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y4) | (Y1 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((Y1 @ Y4 @ Y5) | (Y0 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ sK2))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y0 @ Y4 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y0 @ Y6 @ Y7)) => (Y5 @ Y7))))))) => (Y5 @ Y3)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y1 @ Y4 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y1 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6))))))) => (Y5 @ Y3))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y1 @ Y4 @ Y6) | (Y0 @ Y4 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & ((Y0 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6))) => (Y5 @ Y6))))))) => (Y5 @ Y3)))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y0 @ Y7 @ Y8) | (Y1 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y3 @ Y7) | (Y1 @ Y3 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4)))) & (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (((Y1 @ Y5 @ Y7) | (Y0 @ Y5 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y3))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y1 @ Y5 @ Y7) | (Y0 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y1 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y4)))))))))))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((Y0 @ Y4 @ Y5) | (Y1 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) | (Y0 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ sK2))))))))))) = $false)),
% 1.67/1.55 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.67/1.55 thf(f10,plain,(
% 1.67/1.55 ($false = ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((~ (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y2 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y2 @ Y5 @ Y6) | (Y1 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y0))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y2 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y5 @ Y7) | (Y1 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & ((Y1 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7))) => (Y6 @ Y7))))))) => (Y6 @ Y4)))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y2 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y2 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y2 @ Y6 @ Y8) | (Y1 @ Y6 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y4))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y2 @ Y6 @ Y8) | (Y1 @ Y6 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y2 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y5)))))))))))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y1 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) | (Y1 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y0)))))))))))) @ sK2))),
% 1.67/1.55 inference(sigma_clausification,[status(thm)],[f7])).
% 1.67/1.55 thf(f7,plain,(
% 1.67/1.55 ((!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((~ (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y2 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y2 @ Y5 @ Y6) | (Y1 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y0))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y2 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y5 @ Y7) | (Y1 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & ((Y1 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7))) => (Y6 @ Y7))))))) => (Y6 @ Y4)))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y2 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y2 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y2 @ Y6 @ Y8) | (Y1 @ Y6 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y4))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y2 @ Y6 @ Y8) | (Y1 @ Y6 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y2 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y5)))))))))))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y1 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) | (Y1 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y0))))))))))))) = $false)),
% 1.67/1.55 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.67/1.55 thf(f6,plain,(
% 1.67/1.55 ((~ (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((~ (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y2 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y2 @ Y5 @ Y6) | (Y1 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y0))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y2 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y5 @ Y7) | (Y1 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & ((Y1 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7))) => (Y6 @ Y7))))))) => (Y6 @ Y4)))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y2 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y2 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y2 @ Y6 @ Y8) | (Y1 @ Y6 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y4))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y2 @ Y6 @ Y8) | (Y1 @ Y6 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y2 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y5)))))))))))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y1 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) | (Y1 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y0)))))))))))))) = $true)),
% 1.67/1.55 inference(cnf_transformation,[status(thm)],[f5])).
% 1.67/1.55 thf(f5,plain,(
% 1.67/1.55 ((~ (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((~ (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y2 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y2 @ Y5 @ Y6) | (Y1 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y0))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y2 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y5 @ Y7) | (Y1 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & ((Y1 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7))) => (Y6 @ Y7))))))) => (Y6 @ Y4)))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y2 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y2 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y2 @ Y6 @ Y8) | (Y1 @ Y6 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y4))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y2 @ Y6 @ Y8) | (Y1 @ Y6 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y2 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y5)))))))))))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y1 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) | (Y1 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y0)))))))))))))) = $true)),
% 1.67/1.55 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.55 thf(f4,plain,(
% 1.67/1.55 ~! [X0 : a,X1 : a > a > $o,X2 : a > a > $o,X3 : a] : (! [X4 : a > $o] : ((! [X5 : a] : (((X2 @ X0 @ X5) | (X1 @ X0 @ X5)) => (X4 @ X5)) & ! [X6 : a,X7 : a] : ((((X1 @ X7 @ X6) | (X2 @ X7 @ X6)) & (X4 @ X7)) => (X4 @ X6))) => (X4 @ X3)) | (! [X8 : a,X9 : a,X10 : a] : ((! [X11 : a > $o] : ((! [X12 : a] : (((X2 @ X8 @ X12) | (X1 @ X8 @ X12)) => (X11 @ X12)) & ! [X13 : a,X14 : a] : (((X11 @ X13) & ((X1 @ X13 @ X14) | (X2 @ X13 @ X14))) => (X11 @ X14))) => (X11 @ X10)) & ! [X15 : a > $o] : ((! [X16 : a] : (((X1 @ X10 @ X16) | (X2 @ X10 @ X16)) => (X15 @ X16)) & ! [X17 : a,X18 : a] : ((((X1 @ X18 @ X17) | (X2 @ X18 @ X17)) & (X15 @ X18)) => (X15 @ X17))) => (X15 @ X9))) => ! [X19 : a > $o] : ((! [X20 : a,X21 : a] : ((((X2 @ X21 @ X20) | (X1 @ X21 @ X20)) & (X19 @ X21)) => (X19 @ X20)) & ! [X22 : a] : (((X2 @ X8 @ X22) | (X1 @ X8 @ X22)) => (X19 @ X22))) => (X19 @ X9))) & ! [X23 : a,X24 : a] : ((! [X25 : a > $o] : ((! [X26 : a,X27 : a] : (((X25 @ X26) & (X1 @ X26 @ X27)) => (X25 @ X27)) & ! [X28 : a] : ((X1 @ X23 @ X28) => (X25 @ X28))) => (X25 @ X24)) | ! [X29 : a > $o] : ((! [X30 : a,X31 : a] : (((X2 @ X31 @ X30) & (X29 @ X31)) => (X29 @ X30)) & ! [X32 : a] : ((X2 @ X23 @ X32) => (X29 @ X32))) => (X29 @ X24))) => ! [X33 : a > $o] : ((! [X34 : a,X35 : a] : ((((X1 @ X34 @ X35) | (X2 @ X34 @ X35)) & (X33 @ X34)) => (X33 @ X35)) & ! [X36 : a] : (((X2 @ X23 @ X36) | (X1 @ X23 @ X36)) => (X33 @ X36))) => (X33 @ X24))) & ~! [X37 : a > $o] : ((! [X38 : a,X39 : a] : ((((X2 @ X39 @ X38) | (X1 @ X39 @ X38)) & (X37 @ X39)) => (X37 @ X38)) & ! [X40 : a] : (((X1 @ X0 @ X40) | (X2 @ X0 @ X40)) => (X37 @ X40))) => (X37 @ X3))))),
% 1.67/1.55 inference(rectify,[status(thm)],[f2])).
% 1.67/1.55 thf(f2,negated_conjecture,(
% 1.67/1.55 ~! [X2 : a,X0 : a > a > $o,X1 : a > a > $o,X3 : a] : (! [X4 : a > $o] : ((! [X5 : a] : (((X1 @ X2 @ X5) | (X0 @ X2 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X3)) | (! [X8 : a,X10 : a,X9 : a] : ((! [X4 : a > $o] : ((! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5)) & ! [X6 : a,X7 : a] : (((X4 @ X6) & ((X0 @ X6 @ X7) | (X1 @ X6 @ X7))) => (X4 @ X7))) => (X4 @ X9)) & ! [X4 : a > $o] : ((! [X5 : a] : (((X0 @ X9 @ X5) | (X1 @ X9 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X10))) => ! [X4 : a > $o] : ((! [X7 : a,X6 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5))) => (X4 @ X10))) & ! [X8 : a,X9 : a] : ((! [X4 : a > $o] : ((! [X6 : a,X7 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X8 @ X5) => (X4 @ X5))) => (X4 @ X9)) | ! [X4 : a > $o] : ((! [X7 : a,X6 : a] : (((X1 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X1 @ X8 @ X5) => (X4 @ X5))) => (X4 @ X9))) => ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5))) => (X4 @ X9))) & ~! [X4 : a > $o] : ((! [X7 : a,X6 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X0 @ X2 @ X5) | (X1 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3))))),
% 1.67/1.56 inference(negated_conjecture,[status(cth)],[f1])).
% 1.67/1.56 thf(f1,conjecture,(
% 1.67/1.56 ! [X2 : a,X0 : a > a > $o,X1 : a > a > $o,X3 : a] : (! [X4 : a > $o] : ((! [X5 : a] : (((X1 @ X2 @ X5) | (X0 @ X2 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X3)) | (! [X8 : a,X10 : a,X9 : a] : ((! [X4 : a > $o] : ((! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5)) & ! [X6 : a,X7 : a] : (((X4 @ X6) & ((X0 @ X6 @ X7) | (X1 @ X6 @ X7))) => (X4 @ X7))) => (X4 @ X9)) & ! [X4 : a > $o] : ((! [X5 : a] : (((X0 @ X9 @ X5) | (X1 @ X9 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X10))) => ! [X4 : a > $o] : ((! [X7 : a,X6 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5))) => (X4 @ X10))) & ! [X8 : a,X9 : a] : ((! [X4 : a > $o] : ((! [X6 : a,X7 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X8 @ X5) => (X4 @ X5))) => (X4 @ X9)) | ! [X4 : a > $o] : ((! [X7 : a,X6 : a] : (((X1 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((X1 @ X8 @ X5) => (X4 @ X5))) => (X4 @ X9))) => ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5))) => (X4 @ X9))) & ~! [X4 : a > $o] : ((! [X7 : a,X6 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X0 @ X2 @ X5) | (X1 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3))))),
% 1.67/1.56 file('/export/starexec/sandbox/tmp/tmp.WPOE9q203G/DTF2THF_6844.p',cTHM251H_pme)).
% 1.67/1.56 thf(f2101,plain,(
% 1.67/1.56 spl0_56 | spl0_57 | ~spl0_31),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f2094,f956,f2099,f2096])).
% 1.67/1.56 thf(f2094,plain,(
% 1.67/1.56 ($false = (sK6 @ sK22)) | ((sK6 @ sK23) = $true) | ~spl0_31),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f2051])).
% 1.67/1.56 thf(f2051,plain,(
% 1.67/1.56 ($true = ((sK6 @ sK22) => (sK6 @ sK23))) | ~spl0_31),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2050])).
% 1.67/1.56 thf(f2050,plain,(
% 1.67/1.56 ((((sK6 @ sK22) & $true) => (sK6 @ sK23)) = $true) | ~spl0_31),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2049])).
% 1.67/1.56 thf(f2049,plain,(
% 1.67/1.56 ((((sK6 @ sK22) & ((sK3 @ sK22 @ sK23) | $true)) => (sK6 @ sK23)) = $true) | ~spl0_31),
% 1.67/1.56 inference(superposition,[status(thm)],[f79,f957])).
% 1.67/1.56 thf(f2041,plain,(
% 1.67/1.56 ~spl0_2 | ~spl0_4 | ~spl0_15 | ~spl0_21),
% 1.67/1.56 inference(avatar_contradiction_clause,[status(thm)],[f2040])).
% 1.67/1.56 thf(f2040,plain,(
% 1.67/1.56 $false | (~spl0_2 | ~spl0_4 | ~spl0_15 | ~spl0_21)),
% 1.67/1.56 inference(trivial_inequality_removal,[status(thm)],[f2039])).
% 1.67/1.56 thf(f2039,plain,(
% 1.67/1.56 ($false = $true) | (~spl0_2 | ~spl0_4 | ~spl0_15 | ~spl0_21)),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f2030,f2038])).
% 1.67/1.56 thf(f2038,plain,(
% 1.67/1.56 ($false = (sK10 @ sK18)) | (~spl0_15 | ~spl0_21)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2037])).
% 1.67/1.56 thf(f2037,plain,(
% 1.67/1.56 (($true => (sK10 @ sK18)) = $false) | (~spl0_15 | ~spl0_21)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2036])).
% 1.67/1.56 thf(f2036,plain,(
% 1.67/1.56 ((((sK3 @ sK7 @ sK18) | $true) => (sK10 @ sK18)) = $false) | (~spl0_15 | ~spl0_21)),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f2035,f700])).
% 1.67/1.56 thf(f700,plain,(
% 1.67/1.56 ((sK4 @ sK7 @ sK18) = $true) | ~spl0_21),
% 1.67/1.56 inference(avatar_component_clause,[status(thm)],[f699])).
% 1.67/1.56 thf(f699,definition,(
% 1.67/1.56 spl0_21 <=> ((sK4 @ sK7 @ sK18) = $true)),
% 1.67/1.56 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 1.67/1.56 thf(f2030,plain,(
% 1.67/1.56 ($true = (sK10 @ sK18)) | (~spl0_2 | ~spl0_4 | ~spl0_21)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2029])).
% 1.67/1.56 thf(f2029,plain,(
% 1.67/1.56 (($true => (sK10 @ sK18)) = $true) | (~spl0_2 | ~spl0_4 | ~spl0_21)),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f2026,f244])).
% 1.67/1.56 thf(f2026,plain,(
% 1.67/1.56 ($true = ((sK10 @ sK7) => (sK10 @ sK18))) | (~spl0_2 | ~spl0_21)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2025])).
% 1.67/1.56 thf(f2025,plain,(
% 1.67/1.56 ((((sK10 @ sK7) & $true) => (sK10 @ sK18)) = $true) | (~spl0_2 | ~spl0_21)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2021])).
% 1.67/1.56 thf(f2021,plain,(
% 1.67/1.56 ($true = (((sK10 @ sK7) & ($true | (sK3 @ sK7 @ sK18))) => (sK10 @ sK18))) | (~spl0_2 | ~spl0_21)),
% 1.67/1.56 inference(superposition,[status(thm)],[f1408,f700])).
% 1.67/1.56 thf(f1408,plain,(
% 1.67/1.56 ( ! [X2 : a,X1 : a] : (((((sK10 @ X1) & ((sK4 @ X1 @ X2) | (sK3 @ X1 @ X2))) => (sK10 @ X2)) = $true)) ) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1407])).
% 1.67/1.56 thf(f1407,plain,(
% 1.67/1.56 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK10 @ X1) & ((sK4 @ X1 @ Y0) | (sK3 @ X1 @ Y0))) => (sK10 @ Y0))) @ X2) = $true)) ) | ~spl0_2),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f1397])).
% 1.67/1.56 thf(f1397,plain,(
% 1.67/1.56 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK10 @ X1) & ((sK4 @ X1 @ Y0) | (sK3 @ X1 @ Y0))) => (sK10 @ Y0)))) = $true)) ) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1396])).
% 1.67/1.56 thf(f1396,plain,(
% 1.67/1.56 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))) @ X1) = $true)) ) | ~spl0_2),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f1336])).
% 1.67/1.56 thf(f1336,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1)))))) = $true) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f1333])).
% 1.67/1.56 thf(f1333,plain,(
% 1.67/1.56 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1)))))))) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f1321])).
% 1.67/1.56 thf(f1321,plain,(
% 1.67/1.56 ($false = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) => (sK10 @ sK8))) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1320])).
% 1.67/1.56 thf(f1320,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8))) @ sK10)) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f1310])).
% 1.67/1.56 thf(f1310,plain,(
% 1.67/1.56 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) = $false) | ~spl0_2),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1309])).
% 1.67/1.56 thf(f1309,plain,(
% 1.67/1.56 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))))) | ~spl0_2),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f1294,f1308])).
% 1.67/1.56 thf(f1308,plain,(
% 1.67/1.56 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) = $true) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f1294])).
% 1.67/1.56 thf(f1294,plain,(
% 1.67/1.56 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))))) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1293])).
% 1.67/1.56 thf(f1293,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK8)))))) @ sK9)) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f1282])).
% 1.67/1.56 thf(f1282,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK8))))))) = $false) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1281])).
% 1.67/1.56 thf(f1281,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y0)))))))) @ sK8)) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f1277])).
% 1.67/1.56 thf(f1277,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y0)))))))))) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1276])).
% 1.67/1.56 thf(f1276,plain,(
% 1.67/1.56 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y1)))))))))) @ sK7) = $false) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f43])).
% 1.67/1.56 thf(f2009,plain,(
% 1.67/1.56 ~spl0_16 | ~spl0_26 | ~spl0_39),
% 1.67/1.56 inference(avatar_contradiction_clause,[status(thm)],[f2008])).
% 1.67/1.56 thf(f2008,plain,(
% 1.67/1.56 $false | (~spl0_16 | ~spl0_26 | ~spl0_39)),
% 1.67/1.56 inference(trivial_inequality_removal,[status(thm)],[f2007])).
% 1.67/1.56 thf(f2007,plain,(
% 1.67/1.56 ($false = $true) | (~spl0_16 | ~spl0_26 | ~spl0_39)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2006])).
% 1.67/1.56 thf(f2006,plain,(
% 1.67/1.56 ($false = ((sK10 @ sK19) => $true)) | (~spl0_16 | ~spl0_26 | ~spl0_39)),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f2005,f1503])).
% 1.67/1.56 thf(f1503,plain,(
% 1.67/1.56 ($true = (sK10 @ sK20)) | ~spl0_39),
% 1.67/1.56 inference(avatar_component_clause,[status(thm)],[f1502])).
% 1.67/1.56 thf(f1502,definition,(
% 1.67/1.56 spl0_39 <=> ($true = (sK10 @ sK20))),
% 1.67/1.56 introduced(definition,[new_symbols(naming,[spl0_39])],[avatar_definition])).
% 1.67/1.56 thf(f2005,plain,(
% 1.67/1.56 ($false = ((sK10 @ sK19) => (sK10 @ sK20))) | (~spl0_16 | ~spl0_26)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2004])).
% 1.67/1.56 thf(f2004,plain,(
% 1.67/1.56 ((((sK10 @ sK19) & $true) => (sK10 @ sK20)) = $false) | (~spl0_16 | ~spl0_26)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f2003])).
% 1.67/1.56 thf(f2003,plain,(
% 1.67/1.56 ((((sK10 @ sK19) & ((sK3 @ sK19 @ sK20) | $true)) => (sK10 @ sK20)) = $false) | (~spl0_16 | ~spl0_26)),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f2002,f778])).
% 1.67/1.56 thf(f778,plain,(
% 1.67/1.56 ((sK4 @ sK19 @ sK20) = $true) | ~spl0_26),
% 1.67/1.56 inference(avatar_component_clause,[status(thm)],[f777])).
% 1.67/1.56 thf(f777,definition,(
% 1.67/1.56 spl0_26 <=> ((sK4 @ sK19 @ sK20) = $true)),
% 1.67/1.56 introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition])).
% 1.67/1.56 thf(f2002,plain,(
% 1.67/1.56 ($false = (((sK10 @ sK19) & ((sK3 @ sK19 @ sK20) | (sK4 @ sK19 @ sK20))) => (sK10 @ sK20))) | ~spl0_16),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f2001])).
% 1.67/1.56 thf(f2001,plain,(
% 1.67/1.56 (((^[Y0 : a]: (((sK10 @ sK19) & ((sK3 @ sK19 @ Y0) | (sK4 @ sK19 @ Y0))) => (sK10 @ Y0))) @ sK20) = $false) | ~spl0_16),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f1985])).
% 1.67/1.56 thf(f1985,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (((sK10 @ sK19) & ((sK3 @ sK19 @ Y0) | (sK4 @ sK19 @ Y0))) => (sK10 @ Y0))))) | ~spl0_16),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1981])).
% 1.67/1.56 thf(f1981,plain,(
% 1.67/1.56 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK10 @ Y1))))) @ sK19) = $false) | ~spl0_16),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f612])).
% 1.67/1.56 thf(f1507,plain,(
% 1.67/1.56 spl0_39 | spl0_40 | ~spl0_2 | ~spl0_26),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f1500,f777,f42,f1505,f1502])).
% 1.67/1.56 thf(f1500,plain,(
% 1.67/1.56 ($true = (sK10 @ sK20)) | ((sK10 @ sK19) = $false) | (~spl0_2 | ~spl0_26)),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f1463])).
% 1.67/1.56 thf(f1463,plain,(
% 1.67/1.56 ($true = ((sK10 @ sK19) => (sK10 @ sK20))) | (~spl0_2 | ~spl0_26)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1462])).
% 1.67/1.56 thf(f1462,plain,(
% 1.67/1.56 ((((sK10 @ sK19) & $true) => (sK10 @ sK20)) = $true) | (~spl0_2 | ~spl0_26)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1445])).
% 1.67/1.56 thf(f1445,plain,(
% 1.67/1.56 ((((sK10 @ sK19) & ($true | (sK3 @ sK19 @ sK20))) => (sK10 @ sK20)) = $true) | (~spl0_2 | ~spl0_26)),
% 1.67/1.56 inference(superposition,[status(thm)],[f1408,f778])).
% 1.67/1.56 thf(f1273,plain,(
% 1.67/1.56 ~spl0_11 | ~spl0_18 | ~spl0_34),
% 1.67/1.56 inference(avatar_contradiction_clause,[status(thm)],[f1272])).
% 1.67/1.56 thf(f1272,plain,(
% 1.67/1.56 $false | (~spl0_11 | ~spl0_18 | ~spl0_34)),
% 1.67/1.56 inference(trivial_inequality_removal,[status(thm)],[f1271])).
% 1.67/1.56 thf(f1271,plain,(
% 1.67/1.56 ($false = $true) | (~spl0_11 | ~spl0_18 | ~spl0_34)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1270])).
% 1.67/1.56 thf(f1270,plain,(
% 1.67/1.56 ((~ $true) = $true) | (~spl0_11 | ~spl0_18 | ~spl0_34)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1269])).
% 1.67/1.56 thf(f1269,plain,(
% 1.67/1.56 ((~ ($true | (sK3 @ sK16 @ sK27))) = $true) | (~spl0_11 | ~spl0_18 | ~spl0_34)),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f1268,f1257])).
% 1.67/1.56 thf(f1257,plain,(
% 1.67/1.56 ($true = (sK4 @ sK16 @ sK27)) | ~spl0_34),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f1255])).
% 1.67/1.56 thf(f1255,plain,(
% 1.67/1.56 (((sK4 @ sK16 @ sK27) => (sK17 @ sK27)) = $false) | ~spl0_34),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1251])).
% 1.67/1.56 thf(f1251,plain,(
% 1.67/1.56 (((^[Y0 : a]: ((sK4 @ sK16 @ Y0) => (sK17 @ Y0))) @ sK27) = $false) | ~spl0_34),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f1179])).
% 1.67/1.56 thf(f1179,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: ((sK4 @ sK16 @ Y0) => (sK17 @ Y0))))) | ~spl0_34),
% 1.67/1.56 inference(avatar_component_clause,[status(thm)],[f1178])).
% 1.67/1.56 thf(f1178,definition,(
% 1.67/1.56 spl0_34 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK4 @ sK16 @ Y0) => (sK17 @ Y0)))))),
% 1.67/1.56 introduced(definition,[new_symbols(naming,[spl0_34])],[avatar_definition])).
% 1.67/1.56 thf(f1268,plain,(
% 1.67/1.56 ((~ ((sK4 @ sK16 @ sK27) | (sK3 @ sK16 @ sK27))) = $true) | (~spl0_11 | ~spl0_18 | ~spl0_34)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1263])).
% 1.67/1.56 thf(f1263,plain,(
% 1.67/1.56 ((((sK4 @ sK16 @ sK27) | (sK3 @ sK16 @ sK27)) => $false) = $true) | (~spl0_11 | ~spl0_18 | ~spl0_34)),
% 1.67/1.56 inference(superposition,[status(thm)],[f1062,f1259])).
% 1.67/1.56 thf(f1259,plain,(
% 1.67/1.56 ($false = (sK17 @ sK27)) | ~spl0_34),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1258])).
% 1.67/1.56 thf(f1258,plain,(
% 1.67/1.56 (($true => (sK17 @ sK27)) = $false) | ~spl0_34),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f1255,f1257])).
% 1.67/1.56 thf(f1062,plain,(
% 1.67/1.56 ( ! [X1 : a] : (((((sK4 @ sK16 @ X1) | (sK3 @ sK16 @ X1)) => (sK17 @ X1)) = $true)) ) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1061])).
% 1.67/1.56 thf(f1061,plain,(
% 1.67/1.56 ( ! [X1 : a] : ((((^[Y0 : a]: (((sK4 @ sK16 @ Y0) | (sK3 @ sK16 @ Y0)) => (sK17 @ Y0))) @ X1) = $true)) ) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f1037])).
% 1.67/1.56 thf(f1037,plain,(
% 1.67/1.56 ($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ sK16 @ Y0) | (sK3 @ sK16 @ Y0)) => (sK17 @ Y0))))) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f1004])).
% 1.67/1.56 thf(f1004,plain,(
% 1.67/1.56 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK16 @ Y0) | (sK3 @ sK16 @ Y0)) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK17 @ Y0)))))))) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f993])).
% 1.67/1.56 thf(f993,plain,(
% 1.67/1.56 ($false = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK16 @ Y0) | (sK3 @ sK16 @ Y0)) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK17 @ Y0))))))) => (sK17 @ sK15))) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f992])).
% 1.67/1.56 thf(f992,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15))) @ sK17)) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f981])).
% 1.67/1.56 thf(f981,plain,(
% 1.67/1.56 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15)))) = $false) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f980])).
% 1.67/1.56 thf(f980,plain,(
% 1.67/1.56 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15)))))) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f979])).
% 1.67/1.56 thf(f979,plain,(
% 1.67/1.56 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) | $true) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15))))) = $false) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f978,f642])).
% 1.67/1.56 thf(f642,plain,(
% 1.67/1.56 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK15)))) = $true) | ~spl0_18),
% 1.67/1.56 inference(avatar_component_clause,[status(thm)],[f641])).
% 1.67/1.56 thf(f641,definition,(
% 1.67/1.56 spl0_18 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK15)))) = $true)),
% 1.67/1.56 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 1.67/1.56 thf(f978,plain,(
% 1.67/1.56 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK15))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15)))))) | ~spl0_11),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f977])).
% 1.67/1.56 thf(f977,plain,(
% 1.67/1.56 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK15))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK15)))))) @ sK16) = $false) | ~spl0_11),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f968])).
% 1.67/1.56 thf(f968,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK15))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK15))))))) = $false) | ~spl0_11),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f967])).
% 1.67/1.56 thf(f967,plain,(
% 1.67/1.56 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))) @ sK15) = $false) | ~spl0_11),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f420])).
% 1.67/1.56 thf(f1248,plain,(
% 1.67/1.56 ~spl0_11 | ~spl0_18 | ~spl0_35),
% 1.67/1.56 inference(avatar_contradiction_clause,[status(thm)],[f1247])).
% 1.67/1.56 thf(f1247,plain,(
% 1.67/1.56 $false | (~spl0_11 | ~spl0_18 | ~spl0_35)),
% 1.67/1.56 inference(trivial_inequality_removal,[status(thm)],[f1246])).
% 1.67/1.56 thf(f1246,plain,(
% 1.67/1.56 ($false = $true) | (~spl0_11 | ~spl0_18 | ~spl0_35)),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f1245,f1193])).
% 1.67/1.56 thf(f1193,plain,(
% 1.67/1.56 ((sK17 @ sK24) = $false) | ~spl0_35),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f1192])).
% 1.67/1.56 thf(f1192,plain,(
% 1.67/1.56 ($false = (((sK4 @ sK25 @ sK24) & (sK17 @ sK25)) => (sK17 @ sK24))) | ~spl0_35),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1191])).
% 1.67/1.56 thf(f1191,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (((sK4 @ Y0 @ sK24) & (sK17 @ Y0)) => (sK17 @ sK24))) @ sK25)) | ~spl0_35),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f1190])).
% 1.67/1.56 thf(f1190,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (((sK4 @ Y0 @ sK24) & (sK17 @ Y0)) => (sK17 @ sK24))))) | ~spl0_35),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1186])).
% 1.67/1.56 thf(f1186,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) & (sK17 @ Y1)) => (sK17 @ Y0))))) @ sK24)) | ~spl0_35),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f1182])).
% 1.67/1.56 thf(f1182,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) & (sK17 @ Y1)) => (sK17 @ Y0))))))) | ~spl0_35),
% 1.67/1.56 inference(avatar_component_clause,[status(thm)],[f1181])).
% 1.67/1.56 thf(f1181,definition,(
% 1.67/1.56 spl0_35 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) & (sK17 @ Y1)) => (sK17 @ Y0)))))))),
% 1.67/1.56 introduced(definition,[new_symbols(naming,[spl0_35])],[avatar_definition])).
% 1.67/1.56 thf(f1245,plain,(
% 1.67/1.56 ((sK17 @ sK24) = $true) | (~spl0_11 | ~spl0_18 | ~spl0_35)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1244])).
% 1.67/1.56 thf(f1244,plain,(
% 1.67/1.56 (($true => (sK17 @ sK24)) = $true) | (~spl0_11 | ~spl0_18 | ~spl0_35)),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f1243,f1215])).
% 1.67/1.56 thf(f1215,plain,(
% 1.67/1.56 ($true = (sK17 @ sK26)) | ~spl0_35),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f1212])).
% 1.67/1.56 thf(f1212,plain,(
% 1.67/1.56 (((sK4 @ sK26 @ sK24) & (sK17 @ sK26)) = $true) | ~spl0_35),
% 1.67/1.56 inference(not_proxy_clausification,[status(thm)],[f1202])).
% 1.67/1.56 thf(f1202,plain,(
% 1.67/1.56 ((~ ((sK4 @ sK26 @ sK24) & (sK17 @ sK26))) = $false) | ~spl0_35),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1201])).
% 1.67/1.56 thf(f1201,plain,(
% 1.67/1.56 (((^[Y0 : a]: (~ ((sK4 @ Y0 @ sK24) & (sK17 @ Y0)))) @ sK26) = $false) | ~spl0_35),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f1197])).
% 1.67/1.56 thf(f1197,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (~ ((sK4 @ Y0 @ sK24) & (sK17 @ Y0))))) = $false) | ~spl0_35),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1196])).
% 1.67/1.56 thf(f1196,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (((sK4 @ Y0 @ sK24) & (sK17 @ Y0)) => $false)))) | ~spl0_35),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f1190,f1193])).
% 1.67/1.56 thf(f1243,plain,(
% 1.67/1.56 (((sK17 @ sK26) => (sK17 @ sK24)) = $true) | (~spl0_11 | ~spl0_18 | ~spl0_35)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1242])).
% 1.67/1.56 thf(f1242,plain,(
% 1.67/1.56 ($true = (((sK17 @ sK26) & $true) => (sK17 @ sK24))) | (~spl0_11 | ~spl0_18 | ~spl0_35)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1238])).
% 1.67/1.56 thf(f1238,plain,(
% 1.67/1.56 ($true = (((sK17 @ sK26) & ((sK3 @ sK26 @ sK24) | $true)) => (sK17 @ sK24))) | (~spl0_11 | ~spl0_18 | ~spl0_35)),
% 1.67/1.56 inference(superposition,[status(thm)],[f1064,f1218])).
% 1.67/1.56 thf(f1218,plain,(
% 1.67/1.56 ((sK4 @ sK26 @ sK24) = $true) | ~spl0_35),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1217])).
% 1.67/1.56 thf(f1217,plain,(
% 1.67/1.56 ($true = ((sK4 @ sK26 @ sK24) & $true)) | ~spl0_35),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f1212,f1215])).
% 1.67/1.56 thf(f1064,plain,(
% 1.67/1.56 ( ! [X2 : a,X1 : a] : (($true = (((sK17 @ X2) & ((sK3 @ X2 @ X1) | (sK4 @ X2 @ X1))) => (sK17 @ X1)))) ) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1063])).
% 1.67/1.56 thf(f1063,plain,(
% 1.67/1.56 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK17 @ Y0) & ((sK3 @ Y0 @ X1) | (sK4 @ Y0 @ X1))) => (sK17 @ X1))) @ X2) = $true)) ) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f1060])).
% 1.67/1.56 thf(f1060,plain,(
% 1.67/1.56 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK17 @ Y0) & ((sK3 @ Y0 @ X1) | (sK4 @ Y0 @ X1))) => (sK17 @ X1)))) = $true)) ) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1059])).
% 1.67/1.56 thf(f1059,plain,(
% 1.67/1.56 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK17 @ Y0))))) @ X1) = $true)) ) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f1039])).
% 1.67/1.56 thf(f1039,plain,(
% 1.67/1.56 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK17 @ Y0))))))) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1038])).
% 1.67/1.56 thf(f1038,plain,(
% 1.67/1.56 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK17 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK17 @ Y0))))))) = $true) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f1004,f1037])).
% 1.67/1.56 thf(f1183,plain,(
% 1.67/1.56 spl0_34 | spl0_35 | ~spl0_11 | ~spl0_18),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f1174,f641,f419,f1181,f1178])).
% 1.67/1.56 thf(f1174,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) & (sK17 @ Y1)) => (sK17 @ Y0))))))) | ($false = (!! @ a @ (^[Y0 : a]: ((sK4 @ sK16 @ Y0) => (sK17 @ Y0))))) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f1150])).
% 1.67/1.56 thf(f1150,plain,(
% 1.67/1.56 ($false = ((!! @ a @ (^[Y0 : a]: ((sK4 @ sK16 @ Y0) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) & (sK17 @ Y1)) => (sK17 @ Y0)))))))) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(not_proxy_clausification,[status(thm)],[f1024])).
% 1.67/1.56 thf(f1024,plain,(
% 1.67/1.56 ((~ ((!! @ a @ (^[Y0 : a]: ((sK4 @ sK16 @ Y0) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) & (sK17 @ Y1)) => (sK17 @ Y0)))))))) = $true) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1022])).
% 1.67/1.56 thf(f1022,plain,(
% 1.67/1.56 ((((!! @ a @ (^[Y0 : a]: ((sK4 @ sK16 @ Y0) => (sK17 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) & (sK17 @ Y1)) => (sK17 @ Y0))))))) => $false) = $true) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(superposition,[status(thm)],[f1008,f1006])).
% 1.67/1.56 thf(f1006,plain,(
% 1.67/1.56 ($false = (sK17 @ sK15)) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f1005])).
% 1.67/1.56 thf(f1005,plain,(
% 1.67/1.56 (($true => (sK17 @ sK15)) = $false) | (~spl0_11 | ~spl0_18)),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f993,f1004])).
% 1.67/1.56 thf(f1008,plain,(
% 1.67/1.56 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: ((sK4 @ sK16 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ Y0) & (X1 @ Y1)) => (X1 @ Y0))))))) => (X1 @ sK15)) = $true)) ) | ~spl0_18),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f1007])).
% 1.67/1.56 thf(f1007,plain,(
% 1.67/1.56 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK15))) @ X1))) ) | ~spl0_18),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f642])).
% 1.67/1.56 thf(f958,plain,(
% 1.67/1.56 spl0_30 | spl0_31 | ~spl0_20),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f951,f672,f956,f953])).
% 1.67/1.56 thf(f951,plain,(
% 1.67/1.56 ((sK3 @ sK22 @ sK23) = $true) | ((sK4 @ sK22 @ sK23) = $true) | ~spl0_20),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f940])).
% 1.67/1.56 thf(f940,plain,(
% 1.67/1.56 ($true = ((sK4 @ sK22 @ sK23) | (sK3 @ sK22 @ sK23))) | ~spl0_20),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f939])).
% 1.67/1.56 thf(f939,plain,(
% 1.67/1.56 (($true & ((sK4 @ sK22 @ sK23) | (sK3 @ sK22 @ sK23))) = $true) | ~spl0_20),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f893,f938])).
% 1.67/1.56 thf(f938,plain,(
% 1.67/1.56 ($true = (sK6 @ sK22)) | ~spl0_20),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f893])).
% 1.67/1.56 thf(f893,plain,(
% 1.67/1.56 ($true = ((sK6 @ sK22) & ((sK4 @ sK22 @ sK23) | (sK3 @ sK22 @ sK23)))) | ~spl0_20),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f891])).
% 1.67/1.56 thf(f891,plain,(
% 1.67/1.56 ((((sK6 @ sK22) & ((sK4 @ sK22 @ sK23) | (sK3 @ sK22 @ sK23))) => (sK6 @ sK23)) = $false) | ~spl0_20),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f890])).
% 1.67/1.56 thf(f890,plain,(
% 1.67/1.56 (((^[Y0 : a]: (((sK6 @ sK22) & ((sK4 @ sK22 @ Y0) | (sK3 @ sK22 @ Y0))) => (sK6 @ Y0))) @ sK23) = $false) | ~spl0_20),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f887])).
% 1.67/1.56 thf(f887,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK22) & ((sK4 @ sK22 @ Y0) | (sK3 @ sK22 @ Y0))) => (sK6 @ Y0))))) | ~spl0_20),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f885])).
% 1.67/1.56 thf(f885,plain,(
% 1.67/1.56 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK6 @ Y1))))) @ sK22) = $false) | ~spl0_20),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f673])).
% 1.67/1.56 thf(f879,plain,(
% 1.67/1.56 ~spl0_19),
% 1.67/1.56 inference(avatar_contradiction_clause,[status(thm)],[f878])).
% 1.67/1.56 thf(f878,plain,(
% 1.67/1.56 $false | ~spl0_19),
% 1.67/1.56 inference(trivial_inequality_removal,[status(thm)],[f877])).
% 1.67/1.56 thf(f877,plain,(
% 1.67/1.56 ($false = $true) | ~spl0_19),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f876])).
% 1.67/1.56 thf(f876,plain,(
% 1.67/1.56 ((~ $true) = $true) | ~spl0_19),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f873])).
% 1.67/1.56 thf(f873,plain,(
% 1.67/1.56 ($true = (~ ($true | (sK3 @ sK5 @ sK21)))) | ~spl0_19),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f866,f872])).
% 1.67/1.56 thf(f872,plain,(
% 1.67/1.56 ((sK4 @ sK5 @ sK21) = $true) | ~spl0_19),
% 1.67/1.56 inference(not_proxy_clausification,[status(thm)],[f839])).
% 1.67/1.56 thf(f839,plain,(
% 1.67/1.56 ((~ (sK4 @ sK5 @ sK21)) = $false) | ~spl0_19),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f838])).
% 1.67/1.56 thf(f838,plain,(
% 1.67/1.56 (((sK4 @ sK5 @ sK21) => $false) = $false) | ~spl0_19),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f837,f828])).
% 1.67/1.56 thf(f828,plain,(
% 1.67/1.56 ($false = (sK6 @ sK21)) | ~spl0_19),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f825])).
% 1.67/1.56 thf(f825,plain,(
% 1.67/1.56 ((((sK3 @ sK5 @ sK21) | (sK4 @ sK5 @ sK21)) => (sK6 @ sK21)) = $false) | ~spl0_19),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f824])).
% 1.67/1.56 thf(f824,plain,(
% 1.67/1.56 (((^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK4 @ sK5 @ Y0)) => (sK6 @ Y0))) @ sK21) = $false) | ~spl0_19),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f670])).
% 1.67/1.56 thf(f670,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK4 @ sK5 @ Y0)) => (sK6 @ Y0)))) = $false) | ~spl0_19),
% 1.67/1.56 inference(avatar_component_clause,[status(thm)],[f669])).
% 1.67/1.56 thf(f669,definition,(
% 1.67/1.56 spl0_19 <=> ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK4 @ sK5 @ Y0)) => (sK6 @ Y0)))) = $false)),
% 1.67/1.56 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 1.67/1.56 thf(f837,plain,(
% 1.67/1.56 ($false = ((sK4 @ sK5 @ sK21) => (sK6 @ sK21))) | ~spl0_19),
% 1.67/1.56 inference(trivial_inequality_removal,[status(thm)],[f836])).
% 1.67/1.56 thf(f836,plain,(
% 1.67/1.56 ($false = ((sK4 @ sK5 @ sK21) => (sK6 @ sK21))) | ($false = $true) | ~spl0_19),
% 1.67/1.56 inference(forward_demodulation,[status(thm)],[f831,f828])).
% 1.67/1.56 thf(f831,plain,(
% 1.67/1.56 ($true = (sK6 @ sK21)) | ($false = ((sK4 @ sK5 @ sK21) => (sK6 @ sK21))) | ~spl0_19),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f830])).
% 1.67/1.56 thf(f830,plain,(
% 1.67/1.56 ($true = (sK6 @ sK21)) | ((($false | (sK4 @ sK5 @ sK21)) => (sK6 @ sK21)) = $false) | ~spl0_19),
% 1.67/1.56 inference(superposition,[status(thm)],[f825,f392])).
% 1.67/1.56 thf(f392,plain,(
% 1.67/1.56 ( ! [X1 : a] : (((sK3 @ sK5 @ X1) = $false) | ((sK6 @ X1) = $true)) )),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.67/1.56 thf(f34,plain,(
% 1.67/1.56 ( ! [X1 : a] : (($false = ((sK4 @ sK5 @ X1) | (sK3 @ sK5 @ X1))) | ((sK6 @ X1) = $true)) )),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.67/1.56 thf(f33,plain,(
% 1.67/1.56 ( ! [X1 : a] : (((((sK4 @ sK5 @ X1) | (sK3 @ sK5 @ X1)) => (sK6 @ X1)) = $true)) )),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.67/1.56 thf(f32,plain,(
% 1.67/1.56 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (((sK4 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0))) @ X1))) )),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f31])).
% 1.67/1.56 thf(f31,plain,(
% 1.67/1.56 ($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0)))))),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f30])).
% 1.67/1.56 thf(f30,plain,(
% 1.67/1.56 (($true & (!! @ a @ (^[Y0 : a]: (((sK4 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0))))) = $true)),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f25,f29])).
% 1.67/1.56 thf(f866,plain,(
% 1.67/1.56 ((~ ((sK4 @ sK5 @ sK21) | (sK3 @ sK5 @ sK21))) = $true) | ~spl0_19),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f865])).
% 1.67/1.56 thf(f865,plain,(
% 1.67/1.56 ((((sK4 @ sK5 @ sK21) | (sK3 @ sK5 @ sK21)) => $false) = $true) | ~spl0_19),
% 1.67/1.56 inference(superposition,[status(thm)],[f33,f828])).
% 1.67/1.56 thf(f779,plain,(
% 1.67/1.56 spl0_25 | spl0_26 | ~spl0_16),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f770,f611,f777,f774])).
% 1.67/1.56 thf(f770,plain,(
% 1.67/1.56 ((sK4 @ sK19 @ sK20) = $true) | ($true = (sK3 @ sK19 @ sK20)) | ~spl0_16),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f732])).
% 1.67/1.56 thf(f732,plain,(
% 1.67/1.56 (((sK3 @ sK19 @ sK20) | (sK4 @ sK19 @ sK20)) = $true) | ~spl0_16),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f722])).
% 1.67/1.56 thf(f722,plain,(
% 1.67/1.56 ($true = ((sK10 @ sK19) & ((sK3 @ sK19 @ sK20) | (sK4 @ sK19 @ sK20)))) | ~spl0_16),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f718])).
% 1.67/1.56 thf(f718,plain,(
% 1.67/1.56 ($false = (((sK10 @ sK19) & ((sK3 @ sK19 @ sK20) | (sK4 @ sK19 @ sK20))) => (sK10 @ sK20))) | ~spl0_16),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f717])).
% 1.67/1.56 thf(f717,plain,(
% 1.67/1.56 (((^[Y0 : a]: (((sK10 @ sK19) & ((sK3 @ sK19 @ Y0) | (sK4 @ sK19 @ Y0))) => (sK10 @ Y0))) @ sK20) = $false) | ~spl0_16),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f708])).
% 1.67/1.56 thf(f708,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (((sK10 @ sK19) & ((sK3 @ sK19 @ Y0) | (sK4 @ sK19 @ Y0))) => (sK10 @ Y0))))) | ~spl0_16),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f707])).
% 1.67/1.56 thf(f707,plain,(
% 1.67/1.56 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK10 @ Y1))))) @ sK19) = $false) | ~spl0_16),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f612])).
% 1.67/1.56 thf(f704,plain,(
% 1.67/1.56 spl0_21 | spl0_22 | ~spl0_15),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f695,f608,f702,f699])).
% 1.67/1.56 thf(f695,plain,(
% 1.67/1.56 ((sK4 @ sK7 @ sK18) = $true) | ((sK3 @ sK7 @ sK18) = $true) | ~spl0_15),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f684])).
% 1.67/1.56 thf(f684,plain,(
% 1.67/1.56 (((sK3 @ sK7 @ sK18) | (sK4 @ sK7 @ sK18)) = $true) | ~spl0_15),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f680])).
% 1.67/1.56 thf(f680,plain,(
% 1.67/1.56 ((((sK3 @ sK7 @ sK18) | (sK4 @ sK7 @ sK18)) => (sK10 @ sK18)) = $false) | ~spl0_15),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f679])).
% 1.67/1.56 thf(f679,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0))) @ sK18)) | ~spl0_15),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f609])).
% 1.67/1.56 thf(f674,plain,(
% 1.67/1.56 spl0_19 | spl0_20 | ~spl0_12),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f665,f422,f672,f669])).
% 1.67/1.56 thf(f422,definition,(
% 1.67/1.56 spl0_12 <=> ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2))))) = $false)),
% 1.67/1.56 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.67/1.56 thf(f665,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK4 @ sK5 @ Y0)) => (sK6 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK6 @ Y1)))))) = $false) | ~spl0_12),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f662])).
% 1.67/1.56 thf(f662,plain,(
% 1.67/1.56 ($false = ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK4 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK6 @ Y1)))))))) | ~spl0_12),
% 1.67/1.56 inference(not_proxy_clausification,[status(thm)],[f661])).
% 1.67/1.56 thf(f661,plain,(
% 1.67/1.56 ((~ ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK4 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK6 @ Y1)))))))) = $true) | ~spl0_12),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f652])).
% 1.67/1.56 thf(f652,plain,(
% 1.67/1.56 ($true = (((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK4 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK6 @ Y1))))))) => $false)) | ~spl0_12),
% 1.67/1.56 inference(superposition,[status(thm)],[f650,f27])).
% 1.67/1.56 thf(f27,plain,(
% 1.67/1.56 ($false = (sK6 @ sK2))),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f26])).
% 1.67/1.56 thf(f26,plain,(
% 1.67/1.56 ($false = ($true => (sK6 @ sK2)))),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f23,f25])).
% 1.67/1.56 thf(f650,plain,(
% 1.67/1.56 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK4 @ sK5 @ Y0)) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (X1 @ Y1))))))) => (X1 @ sK2)) = $true)) ) | ~spl0_12),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f649])).
% 1.67/1.56 thf(f649,plain,(
% 1.67/1.56 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2))) @ X1))) ) | ~spl0_12),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f646])).
% 1.67/1.56 thf(f646,plain,(
% 1.67/1.56 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2)))) = $true) | ~spl0_12),
% 1.67/1.56 inference(not_proxy_clausification,[status(thm)],[f423])).
% 1.67/1.56 thf(f423,plain,(
% 1.67/1.56 ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2))))) = $false) | ~spl0_12),
% 1.67/1.56 inference(avatar_component_clause,[status(thm)],[f422])).
% 1.67/1.56 thf(f643,plain,(
% 1.67/1.56 spl0_17 | spl0_18 | ~spl0_11),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f636,f419,f641,f638])).
% 1.67/1.56 thf(f636,plain,(
% 1.67/1.56 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) = $true) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK15)))) = $true) | ~spl0_11),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f623])).
% 1.67/1.56 thf(f623,plain,(
% 1.67/1.56 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK15))))) = $true) | ~spl0_11),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f621])).
% 1.67/1.56 thf(f621,plain,(
% 1.67/1.56 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK16 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK15))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK16 @ Y1) | (sK3 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK15)))))) | ~spl0_11),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f620])).
% 1.67/1.56 thf(f620,plain,(
% 1.67/1.56 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK15))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK15)))))) @ sK16) = $false) | ~spl0_11),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f619])).
% 1.67/1.56 thf(f619,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK15))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK15))))))) = $false) | ~spl0_11),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f618])).
% 1.67/1.56 thf(f618,plain,(
% 1.67/1.56 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))) @ sK15) = $false) | ~spl0_11),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f420])).
% 1.67/1.56 thf(f613,plain,(
% 1.67/1.56 spl0_15 | spl0_16 | ~spl0_2),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f604,f42,f611,f608])).
% 1.67/1.56 thf(f604,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK10 @ Y1)))))) = $false) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f598])).
% 1.67/1.56 thf(f598,plain,(
% 1.67/1.56 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0)))))) | ~spl0_2),
% 1.67/1.56 inference(not_proxy_clausification,[status(thm)],[f496])).
% 1.67/1.56 thf(f496,plain,(
% 1.67/1.56 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0))))))) | ~spl0_2),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f494])).
% 1.67/1.56 thf(f494,plain,(
% 1.67/1.56 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0))))) => $false) = $true) | ~spl0_2),
% 1.67/1.56 inference(superposition,[status(thm)],[f489,f474])).
% 1.67/1.56 thf(f474,plain,(
% 1.67/1.56 ($false = (sK10 @ sK8)) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f456])).
% 1.67/1.56 thf(f456,plain,(
% 1.67/1.56 ($false = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) => (sK10 @ sK8))) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f455])).
% 1.67/1.56 thf(f455,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8))) @ sK10)) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f449])).
% 1.67/1.56 thf(f449,plain,(
% 1.67/1.56 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) = $false) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f446])).
% 1.67/1.56 thf(f446,plain,(
% 1.67/1.56 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))))) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f445])).
% 1.67/1.56 thf(f445,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK8)))))) @ sK9)) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f441])).
% 1.67/1.56 thf(f441,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK8))))))) = $false) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f440])).
% 1.67/1.56 thf(f440,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y0)))))))) @ sK8)) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f431])).
% 1.67/1.56 thf(f431,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y0)))))))))) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f430])).
% 1.67/1.56 thf(f430,plain,(
% 1.67/1.56 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y1)))))))))) @ sK7) = $false) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f43])).
% 1.67/1.56 thf(f489,plain,(
% 1.67/1.56 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1))) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (X1 @ Y0))))) => (X1 @ sK8)))) ) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f488])).
% 1.67/1.56 thf(f488,plain,(
% 1.67/1.56 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))) @ X1) = $true)) ) | ~spl0_2),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f483])).
% 1.67/1.56 thf(f483,plain,(
% 1.67/1.56 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true) | ~spl0_2),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f482])).
% 1.67/1.56 thf(f482,plain,(
% 1.67/1.56 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) & $true) = $true) | ~spl0_2),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f450,f480])).
% 1.67/1.56 thf(f480,plain,(
% 1.67/1.56 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f450])).
% 1.67/1.56 thf(f450,plain,(
% 1.67/1.56 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) = $true) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f446])).
% 1.67/1.56 thf(f424,plain,(
% 1.67/1.56 spl0_11 | spl0_12 | ~spl0_1),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f417,f39,f422,f419])).
% 1.67/1.56 thf(f39,definition,(
% 1.67/1.56 spl0_1 <=> ($false = ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))))))),
% 1.67/1.56 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.67/1.56 thf(f417,plain,(
% 1.67/1.56 ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2))))) = $false) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))))) | ~spl0_1),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.67/1.56 thf(f40,plain,(
% 1.67/1.56 ($false = ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0))))))))))) | ~spl0_1),
% 1.67/1.56 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.67/1.56 thf(f414,plain,(
% 1.67/1.56 spl0_9 | spl0_10 | ~spl0_3),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f405,f240,f412,f409])).
% 1.67/1.56 thf(f405,plain,(
% 1.67/1.56 ((sK4 @ sK14 @ sK12) = $true) | ($true = (sK3 @ sK14 @ sK12)) | ~spl0_3),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f378])).
% 1.67/1.56 thf(f378,plain,(
% 1.67/1.56 (((sK3 @ sK14 @ sK12) | (sK4 @ sK14 @ sK12)) = $true) | ~spl0_3),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f359])).
% 1.67/1.56 thf(f359,plain,(
% 1.67/1.56 ($true = (((sK3 @ sK14 @ sK12) | (sK4 @ sK14 @ sK12)) & (sK10 @ sK14))) | ~spl0_3),
% 1.67/1.56 inference(not_proxy_clausification,[status(thm)],[f343])).
% 1.67/1.56 thf(f343,plain,(
% 1.67/1.56 ((~ (((sK3 @ sK14 @ sK12) | (sK4 @ sK14 @ sK12)) & (sK10 @ sK14))) = $false) | ~spl0_3),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f342])).
% 1.67/1.56 thf(f342,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (~ (((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)))) @ sK14)) | ~spl0_3),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f332])).
% 1.67/1.56 thf(f332,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (~ (((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)))))) | ~spl0_3),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f331])).
% 1.67/1.56 thf(f331,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: ((((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)) => $false))) = $false) | ~spl0_3),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f282,f330])).
% 1.67/1.56 thf(f330,plain,(
% 1.67/1.56 ($false = (sK10 @ sK12)) | ~spl0_3),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f329])).
% 1.67/1.56 thf(f329,plain,(
% 1.67/1.56 ($false = ($true => (sK10 @ sK12))) | ~spl0_3),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f293,f328])).
% 1.67/1.56 thf(f328,plain,(
% 1.67/1.56 ($true = (((sK3 @ sK13 @ sK12) | (sK4 @ sK13 @ sK12)) & (sK10 @ sK13))) | ~spl0_3),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f293])).
% 1.67/1.56 thf(f293,plain,(
% 1.67/1.56 ($false = ((((sK3 @ sK13 @ sK12) | (sK4 @ sK13 @ sK12)) & (sK10 @ sK13)) => (sK10 @ sK12))) | ~spl0_3),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f292])).
% 1.67/1.56 thf(f292,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: ((((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)) => (sK10 @ sK12))) @ sK13)) | ~spl0_3),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f282])).
% 1.67/1.56 thf(f282,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: ((((sK3 @ Y0 @ sK12) | (sK4 @ Y0 @ sK12)) & (sK10 @ Y0)) => (sK10 @ sK12))))) | ~spl0_3),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f278])).
% 1.67/1.56 thf(f278,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) & (sK10 @ Y1)) => (sK10 @ Y0))))) @ sK12)) | ~spl0_3),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f241])).
% 1.67/1.56 thf(f245,plain,(
% 1.67/1.56 spl0_3 | spl0_4 | ~spl0_2),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f238,f42,f243,f240])).
% 1.67/1.56 thf(f238,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) & (sK10 @ Y1)) => (sK10 @ Y0)))))) = $false) | ((sK10 @ sK7) = $true) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f192])).
% 1.67/1.56 thf(f192,plain,(
% 1.67/1.56 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) & (sK10 @ Y1)) => (sK10 @ Y0)))))) => (sK10 @ sK7))) | ~spl0_2),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f191])).
% 1.67/1.56 thf(f191,plain,(
% 1.67/1.56 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) & (sK10 @ Y1)) => (sK10 @ Y0)))))) & $true) => (sK10 @ sK7)) = $true) | ~spl0_2),
% 1.67/1.56 inference(superposition,[status(thm)],[f175,f117])).
% 1.67/1.56 thf(f117,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (sK10 @ Y0)))) = $true) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.67/1.56 thf(f81,plain,(
% 1.67/1.56 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1)))))))) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.67/1.56 thf(f77,plain,(
% 1.67/1.56 ($false = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) => (sK10 @ sK8))) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.67/1.56 thf(f76,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8))) @ sK10)) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f73])).
% 1.67/1.56 thf(f73,plain,(
% 1.67/1.56 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))) = $false) | ~spl0_2),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f72])).
% 1.67/1.56 thf(f72,plain,(
% 1.67/1.56 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))))) | ~spl0_2),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f65,f71])).
% 1.67/1.56 thf(f71,plain,(
% 1.67/1.56 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) = $true) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.67/1.56 thf(f65,plain,(
% 1.67/1.56 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK8)))))) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.67/1.56 thf(f64,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK8)))))) @ sK9)) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f59])).
% 1.67/1.56 thf(f59,plain,(
% 1.67/1.56 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK8))))))) = $false) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.67/1.56 thf(f58,plain,(
% 1.67/1.56 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y0)))))))) @ sK8)) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f51])).
% 1.67/1.56 thf(f51,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK4 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y0)))))))))) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.67/1.56 thf(f50,plain,(
% 1.67/1.56 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y1)))))))))) @ sK7) = $false) | ~spl0_2),
% 1.67/1.56 inference(sigma_clausification,[status(thm)],[f43])).
% 1.67/1.56 thf(f175,plain,(
% 1.67/1.56 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) & (X1 @ Y1)) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK4 @ sK9 @ Y0) | (sK3 @ sK9 @ Y0)) => (X1 @ Y0))))) => (X1 @ sK7)))) ) | ~spl0_2),
% 1.67/1.56 inference(beta_eta_normalization,[status(thm)],[f174])).
% 1.67/1.56 thf(f174,plain,(
% 1.67/1.56 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))) @ X1))) ) | ~spl0_2),
% 1.67/1.56 inference(pi_clausification,[status(thm)],[f164])).
% 1.67/1.56 thf(f164,plain,(
% 1.67/1.56 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) | ~spl0_2),
% 1.67/1.56 inference(boolean_simplification,[status(thm)],[f163])).
% 1.67/1.56 thf(f163,plain,(
% 1.67/1.56 (($true & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK4 @ sK9 @ Y1) | (sK3 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) = $true) | ~spl0_2),
% 1.67/1.56 inference(backward_demodulation,[status(thm)],[f71,f162])).
% 1.67/1.56 thf(f162,plain,(
% 1.67/1.56 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true) | ~spl0_2),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.67/1.56 thf(f44,plain,(
% 1.67/1.56 spl0_1 | spl0_2),
% 1.67/1.56 inference(avatar_split_clause,[status(thm)],[f37,f42,f39])).
% 1.67/1.56 thf(f37,plain,(
% 1.67/1.56 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK4 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y1)))))))))))) | ($false = ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK4 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK2))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))))))),
% 1.67/1.56 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.67/1.56 % SZS output end Proof for DTF2THF_6844
% 1.67/1.56 % (6955)------------------------------
% 1.67/1.56 % (6955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.56 % (6955)Termination reason: Refutation
% 1.67/1.56
% 1.67/1.56 % (6955)Memory used [KB]: 7419
% 1.67/1.56 % (6955)Time elapsed: 0.213 s
% 1.67/1.56 % (6955)Instructions burned: 625 (million)
% 1.67/1.56 % (6955)------------------------------
% 1.67/1.56 % (6955)------------------------------
% 1.67/1.56 % (6943)Success in time 0.244 s
%------------------------------------------------------------------------------