%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV140^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 09:40:23 AM UTC 2026
% Result : Theorem 1.66s 1.43s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of formulae : 161 ( 43 unt; 0 typ; 8 def)
% Number of atoms : 1553 ( 147 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 5198 ( 144 ~; 194 |; 285 &;3369 @)
% ( 8 <=>; 450 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 472 ( 472 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 46 usr; 45 con; 0-2 aty)
% ( 748 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 889 ( 779 ^; 110 !; 0 ?; 889 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: a > a > $o ).
thf(func_def_19,type,
sK3: a ).
thf(func_def_20,type,
sK4: a ).
thf(func_def_21,type,
sK5: a > a > $o ).
thf(func_def_22,type,
sK6: a > a > $o ).
thf(func_def_23,type,
sK7: a ).
thf(func_def_24,type,
sK8: a ).
thf(func_def_25,type,
sK9: a ).
thf(func_def_26,type,
sK10: a ).
thf(func_def_27,type,
sK11: a ).
thf(func_def_28,type,
sK12: a ).
thf(func_def_29,type,
sK13: a ).
thf(func_def_30,type,
sK14: a ).
thf(func_def_31,type,
sK15: a ).
thf(func_def_32,type,
sK16: a ).
thf(func_def_33,type,
sK17: a ).
thf(func_def_34,type,
sK18: a ).
thf(func_def_35,type,
sK19: a ).
thf(func_def_36,type,
sK20: a ).
thf(func_def_37,type,
sK21: a ).
thf(func_def_38,type,
sK22: a ).
thf(func_def_39,type,
sK23: a ).
thf(func_def_40,type,
sK24: a ).
thf(func_def_41,type,
sK25: a ).
thf(func_def_42,type,
sK26: a ).
thf(func_def_43,type,
sK27: a ).
thf(func_def_44,type,
sK28: a ).
thf(func_def_45,type,
sK29: a ).
thf(func_def_46,type,
sK30: a ).
thf(func_def_47,type,
sK31: a ).
thf(func_def_48,type,
sK32: a ).
thf(func_def_49,type,
sK33: a ).
thf(func_def_50,type,
sK34: a ).
thf(func_def_51,type,
sK35: a ).
thf(func_def_52,type,
sK36: a ).
thf(func_def_53,type,
sK37: a ).
thf(func_def_54,type,
sK38: a ).
thf(f1416,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f108,f172,f261,f469,f665,f870,f1006,f1050,f1415]) ).
thf(f1415,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[status(thm)],[f1414]) ).
thf(f1414,plain,
( $false
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f1413]) ).
thf(f1413,plain,
( ( $false = $true )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f1412]) ).
thf(f1412,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_19 ),
inference(forward_demodulation,[status(thm)],[f1404,f1279]) ).
thf(f1279,plain,
( ( ( sK6 @ sK36 @ sK33 )
= $true )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[status(thm)],[f1251]) ).
thf(f1251,plain,
( ( $true
= ( ( sK6 @ sK36 @ sK33 )
& ( sK6 @ sK34 @ sK36 ) ) )
| ~ spl0_19 ),
inference(not_proxy_clausification,[status(thm)],[f1170]) ).
thf(f1170,plain,
( ( ( ~ ( ( sK6 @ sK36 @ sK33 )
& ( sK6 @ sK34 @ sK36 ) ) )
= $false )
| ~ spl0_19 ),
inference(beta_eta_normalization,[status(thm)],[f1169]) ).
thf(f1169,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK6 @ Y0 @ sK33 )
& ( sK6 @ sK34 @ Y0 ) )
@ sK36 ) )
| ~ spl0_19 ),
inference(sigma_clausification,[status(thm)],[f1158]) ).
thf(f1158,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK6 @ Y0 @ sK33 )
& ( sK6 @ sK34 @ Y0 ) ) ) )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f1157]) ).
thf(f1157,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK33 )
& ( sK6 @ sK34 @ Y0 ) )
=> $false ) ) )
| ~ spl0_19 ),
inference(backward_demodulation,[status(thm)],[f1138,f1156]) ).
thf(f1156,plain,
( ( $false
= ( sK6 @ sK34 @ sK33 ) )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f1155]) ).
thf(f1155,plain,
( ( $false
= ( $true
=> ( sK6 @ sK34 @ sK33 ) ) )
| ~ spl0_19 ),
inference(backward_demodulation,[status(thm)],[f1148,f1154]) ).
thf(f1154,plain,
( ( $true
= ( ( sK6 @ sK35 @ sK33 )
& ( sK6 @ sK34 @ sK35 ) ) )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[status(thm)],[f1148]) ).
thf(f1148,plain,
( ( $false
= ( ( ( sK6 @ sK35 @ sK33 )
& ( sK6 @ sK34 @ sK35 ) )
=> ( sK6 @ sK34 @ sK33 ) ) )
| ~ spl0_19 ),
inference(beta_eta_normalization,[status(thm)],[f1147]) ).
thf(f1147,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK33 )
& ( sK6 @ sK34 @ Y0 ) )
=> ( sK6 @ sK34 @ sK33 ) )
@ sK35 ) )
| ~ spl0_19 ),
inference(sigma_clausification,[status(thm)],[f1138]) ).
thf(f1138,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK33 )
& ( sK6 @ sK34 @ Y0 ) )
=> ( sK6 @ sK34 @ sK33 ) ) ) )
| ~ spl0_19 ),
inference(beta_eta_normalization,[status(thm)],[f1137]) ).
thf(f1137,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ sK33 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ sK33 ) ) )
@ sK34 ) )
| ~ spl0_19 ),
inference(sigma_clausification,[status(thm)],[f1128]) ).
thf(f1128,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ sK33 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ sK33 ) ) ) ) )
| ~ spl0_19 ),
inference(beta_eta_normalization,[status(thm)],[f1124]) ).
thf(f1124,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ sK33 ) )
| ~ spl0_19 ),
inference(sigma_clausification,[status(thm)],[f664]) ).
thf(f664,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f663]) ).
thf(f663,definition,
( spl0_19
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f1404,plain,
( ( $true
= ( ~ ( sK6 @ sK36 @ sK33 ) ) )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f1398]) ).
thf(f1398,plain,
( ( $true
= ( ( sK6 @ sK36 @ sK33 )
=> $false ) )
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f1293,f1156]) ).
thf(f1293,plain,
( ! [X0: a] :
( $true
= ( ( sK6 @ sK36 @ X0 )
=> ( sK6 @ sK34 @ X0 ) ) )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f1288]) ).
thf(f1288,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK6 @ sK36 @ X0 ) )
=> ( sK6 @ sK34 @ X0 ) ) )
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f70,f1285]) ).
thf(f1285,plain,
( ( $true
= ( sK6 @ sK34 @ sK36 ) )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f1284]) ).
thf(f1284,plain,
( ( $true
= ( $true
& ( sK6 @ sK34 @ sK36 ) ) )
| ~ spl0_19 ),
inference(backward_demodulation,[status(thm)],[f1251,f1279]) ).
thf(f70,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK6 @ X1 @ X3 )
& ( sK6 @ X3 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y0 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y0 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
=> ( sK6 @ sK4 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) )
@ sK6 ) ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f17,f19]) ).
thf(f19,plain,
( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK5 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK5 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y3 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y3 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y3 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y3 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a,X2: a,X3: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ! [X7: a > a > $o] :
( ( ! [X8: a,X9: a,X10: a] :
( ( ( X7 @ X10 @ X8 )
& ( X7 @ X9 @ X10 ) )
=> ( X7 @ X9 @ X8 ) )
& ! [X11: a,X12: a] :
( ( X0 @ X11 @ X12 )
=> ( X7 @ X11 @ X12 ) ) )
=> ( X7 @ X5 @ X6 ) )
| ! [X13: a > a > $o] :
( ( ! [X14: a,X15: a,X16: a] :
( ( ( X13 @ X15 @ X14 )
& ( X13 @ X14 @ X16 ) )
=> ( X13 @ X15 @ X16 ) )
& ! [X17: a,X18: a] :
( ( X3 @ X18 @ X17 )
=> ( X13 @ X18 @ X17 ) ) )
=> ( X13 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X19: a,X20: a,X21: a] :
( ( ( X4 @ X21 @ X20 )
& ( X4 @ X19 @ X21 ) )
=> ( X4 @ X19 @ X20 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ! [X22: a > a > $o] :
( ( ! [X23: a,X24: a,X25: a] :
( ( ( X22 @ X23 @ X24 )
& ( X22 @ X25 @ X23 ) )
=> ( X22 @ X25 @ X24 ) )
& ! [X26: a,X27: a] :
( ( ( X3 @ X27 @ X26 )
| ( X0 @ X27 @ X26 ) )
=> ( X22 @ X27 @ X26 ) ) )
=> ( X22 @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X2: a,X3: a,X1: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ! [X7: a > a > $o] :
( ( ! [X10: a,X8: a,X9: a] :
( ( ( X7 @ X9 @ X10 )
& ( X7 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X5 @ X6 ) )
| ! [X7: a > a > $o] :
( ( ! [X9: a,X8: a,X10: a] :
( ( ( X7 @ X8 @ X9 )
& ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X10: a,X6: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ! [X6: a,X10: a,X5: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X6: a,X5: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X2: a,X3: a,X1: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ! [X7: a > a > $o] :
( ( ! [X10: a,X8: a,X9: a] :
( ( ( X7 @ X9 @ X10 )
& ( X7 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X5 @ X6 ) )
| ! [X7: a > a > $o] :
( ( ! [X9: a,X8: a,X10: a] :
( ( ( X7 @ X8 @ X9 )
& ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X10: a,X6: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ! [X6: a,X10: a,X5: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X6: a,X5: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.wk03IwR8rH/DTF2THF_22134.p',cTHM250C_pme) ).
thf(f1050,plain,
~ spl0_18,
inference(avatar_contradiction_clause,[status(thm)],[f1049]) ).
thf(f1049,plain,
( $false
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f1048]) ).
thf(f1048,plain,
( ( $false = $true )
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1047]) ).
thf(f1047,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1046]) ).
thf(f1046,plain,
( ( $true
= ( ~ ( ( sK5 @ sK31 @ sK32 )
| $true ) ) )
| ~ spl0_18 ),
inference(forward_demodulation,[status(thm)],[f1045,f1033]) ).
thf(f1033,plain,
( ( $true
= ( sK2 @ sK31 @ sK32 ) )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f1031]) ).
thf(f1031,plain,
( ( $false
= ( ( sK2 @ sK31 @ sK32 )
=> ( sK6 @ sK31 @ sK32 ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f1030]) ).
thf(f1030,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ sK31 @ Y0 )
=> ( sK6 @ sK31 @ Y0 ) )
@ sK32 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[status(thm)],[f1023]) ).
thf(f1023,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK31 @ Y0 )
=> ( sK6 @ sK31 @ Y0 ) ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f1021]) ).
thf(f1021,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK31 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[status(thm)],[f661]) ).
thf(f661,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f660]) ).
thf(f660,definition,
( spl0_18
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f1045,plain,
( ( $true
= ( ~ ( ( sK5 @ sK31 @ sK32 )
| ( sK2 @ sK31 @ sK32 ) ) ) )
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1039]) ).
thf(f1039,plain,
( ( $true
= ( ( ( sK5 @ sK31 @ sK32 )
| ( sK2 @ sK31 @ sK32 ) )
=> $false ) )
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f35,f1035]) ).
thf(f1035,plain,
( ( $false
= ( sK6 @ sK31 @ sK32 ) )
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1034]) ).
thf(f1034,plain,
( ( $false
= ( $true
=> ( sK6 @ sK31 @ sK32 ) ) )
| ~ spl0_18 ),
inference(backward_demodulation,[status(thm)],[f1031,f1033]) ).
thf(f35,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK5 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f30]) ).
thf(f30,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f25,f28]) ).
thf(f1006,plain,
~ spl0_16,
inference(avatar_contradiction_clause,[status(thm)],[f1005]) ).
thf(f1005,plain,
( $false
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f1004]) ).
thf(f1004,plain,
( ( $false = $true )
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f1003]) ).
thf(f1003,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f1002]) ).
thf(f1002,plain,
( ( $true
= ( ~ ( $true
| ( sK2 @ sK30 @ sK29 ) ) ) )
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f998,f989]) ).
thf(f989,plain,
( ( $true
= ( sK5 @ sK30 @ sK29 ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f987]) ).
thf(f987,plain,
( ( $false
= ( ( sK5 @ sK30 @ sK29 )
=> ( sK6 @ sK30 @ sK29 ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f986]) ).
thf(f986,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK5 @ Y0 @ sK29 )
=> ( sK6 @ Y0 @ sK29 ) )
@ sK30 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f881]) ).
thf(f881,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ Y0 @ sK29 )
=> ( sK6 @ Y0 @ sK29 ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f879]) ).
thf(f879,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK29 ) )
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f468]) ).
thf(f468,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f467]) ).
thf(f467,definition,
( spl0_16
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f998,plain,
( ( $true
= ( ~ ( ( sK5 @ sK30 @ sK29 )
| ( sK2 @ sK30 @ sK29 ) ) ) )
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f995]) ).
thf(f995,plain,
( ( $true
= ( ( ( sK5 @ sK30 @ sK29 )
| ( sK2 @ sK30 @ sK29 ) )
=> $false ) )
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f35,f991]) ).
thf(f991,plain,
( ( $false
= ( sK6 @ sK30 @ sK29 ) )
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f990]) ).
thf(f990,plain,
( ( $false
= ( $true
=> ( sK6 @ sK30 @ sK29 ) ) )
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f987,f989]) ).
thf(f870,plain,
~ spl0_15,
inference(avatar_contradiction_clause,[status(thm)],[f869]) ).
thf(f869,plain,
( $false
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f866]) ).
thf(f866,plain,
( ( $false = $true )
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f70,f857]) ).
thf(f857,plain,
( ( $false
= ( ( ( sK6 @ sK27 @ sK26 )
& ( sK6 @ sK26 @ sK28 ) )
=> ( sK6 @ sK27 @ sK28 ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f856]) ).
thf(f856,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK27 @ sK26 )
& ( sK6 @ sK26 @ Y0 ) )
=> ( sK6 @ sK27 @ Y0 ) )
@ sK28 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f841]) ).
thf(f841,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK27 @ sK26 )
& ( sK6 @ sK26 @ Y0 ) )
=> ( sK6 @ sK27 @ Y0 ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f840]) ).
thf(f840,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ sK26 )
& ( sK6 @ sK26 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK27 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f824]) ).
thf(f824,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ sK26 )
& ( sK6 @ sK26 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f820]) ).
thf(f820,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) )
@ sK26 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f465]) ).
thf(f465,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f464]) ).
thf(f464,definition,
( spl0_15
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f665,plain,
( spl0_18
| spl0_19
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f656,f170,f106,f663,f660]) ).
thf(f106,definition,
( spl0_2
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f170,definition,
( spl0_4
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f656,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f650]) ).
thf(f650,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f556]) ).
thf(f556,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f550]) ).
thf(f550,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f544,f472]) ).
thf(f472,plain,
( ( $false
= ( sK6 @ sK8 @ sK7 ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f471]) ).
thf(f471,plain,
( ( $false
= ( $true
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f470]) ).
thf(f470,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f279,f171]) ).
thf(f171,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f170]) ).
thf(f279,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f278]) ).
thf(f278,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f272]) ).
thf(f272,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f268]) ).
thf(f268,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f106]) ).
thf(f544,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK8 @ sK7 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f543]) ).
thf(f543,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f171]) ).
thf(f469,plain,
( spl0_15
| spl0_16
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f460,f167,f106,f467,f464]) ).
thf(f167,definition,
( spl0_3
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f460,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f447]) ).
thf(f447,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f291]) ).
thf(f291,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f287]) ).
thf(f287,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f176,f282]) ).
thf(f282,plain,
( ( $false
= ( sK6 @ sK8 @ sK7 ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f281]) ).
thf(f281,plain,
( ( $false
= ( $true
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f280]) ).
thf(f280,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| $true )
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f279,f168]) ).
thf(f168,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f167]) ).
thf(f176,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y0 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK8 @ sK7 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f175]) ).
thf(f175,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f168]) ).
thf(f261,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f260]) ).
thf(f260,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f256]) ).
thf(f256,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f253,f70]) ).
thf(f253,plain,
( ( ( ( ( sK6 @ sK14 @ sK12 )
& ( sK6 @ sK12 @ sK13 ) )
=> ( sK6 @ sK14 @ sK13 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f252]) ).
thf(f252,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK12 )
& ( sK6 @ sK12 @ sK13 ) )
=> ( sK6 @ Y0 @ sK13 ) )
@ sK14 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f251]) ).
thf(f251,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK12 )
& ( sK6 @ sK12 @ sK13 ) )
=> ( sK6 @ Y0 @ sK13 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f250]) ).
thf(f250,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ sK12 )
& ( sK6 @ sK12 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK13 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f249]) ).
thf(f249,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ sK12 )
& ( sK6 @ sK12 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f245]) ).
thf(f245,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) )
@ sK12 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f103,definition,
( spl0_1
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f172,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f165,f106,f170,f167]) ).
thf(f165,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f111]) ).
thf(f111,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f107]) ).
thf(f108,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f99,f106,f103]) ).
thf(f99,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f51]) ).
thf(f51,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> $false ) ),
inference(superposition,[status(thm)],[f43,f27]) ).
thf(f27,plain,
( $false
= ( sK6 @ sK4 @ sK3 ) ),
inference(boolean_simplification,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
= ( $true
=> ( sK6 @ sK4 @ sK3 ) ) ),
inference(backward_demodulation,[status(thm)],[f23,f25]) ).
thf(f43,plain,
! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK4 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK5 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV140^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:40:25 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEV140^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Set Theory (Relations)
% 0.30/0.46 % Problem : TPS problem THM250C
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0517 [Bro09]
% 0.30/0.46 % : THM250C [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.09 v8.1.0, 0.17 v7.5.0, 0.33 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.67 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.30/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.30/0.46 % Number of connectives : 71 ( 0 ~; 2 |; 8 &; 48 @)
% 0.30/0.46 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 23 ( 23 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.30/0.46 % Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 % : Polymorphic definitions expanded.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a_type,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(cTHM250C_pme,conjecture,
% 0.30/0.46 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.30/0.46 ( ! [Xp1: a > a > $o] :
% 0.30/0.46 ( ( ! [Xx0: a,Xy0: a] :
% 0.30/0.46 ( ( ! [Xp10: a > a > $o] :
% 0.30/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.30/0.46 ( ( R @ Xx1 @ Xy1 )
% 0.30/0.46 => ( Xp10 @ Xx1 @ Xy1 ) )
% 0.30/0.46 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.30/0.46 ( ( ( Xp10 @ Xx1 @ Xy1 )
% 0.30/0.46 & ( Xp10 @ Xy1 @ Xz ) )
% 0.30/0.46 => ( Xp10 @ Xx1 @ Xz ) ) )
% 0.30/0.46 => ( Xp10 @ Xx0 @ Xy0 ) )
% 0.30/0.46 | ! [Xp10: a > a > $o] :
% 0.30/0.46 ( ( ! [Xx1: a,Xy1: a] :
% 0.30/0.46 ( ( S @ Xx1 @ Xy1 )
% 0.30/0.46 => ( Xp10 @ Xx1 @ Xy1 ) )
% 0.30/0.46 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.30/0.46 ( ( ( Xp10 @ Xx1 @ Xy1 )
% 0.30/0.46 & ( Xp10 @ Xy1 @ Xz ) )
% 0.30/0.46 => ( Xp10 @ Xx1 @ Xz ) ) )
% 0.30/0.46 => ( Xp10 @ Xx0 @ Xy0 ) ) )
% 0.30/0.46 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.30/0.46 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.30/0.46 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.30/0.46 & ( Xp1 @ Xy0 @ Xz ) )
% 0.30/0.46 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.30/0.46 => ( Xp1 @ Xx @ Xy ) )
% 0.30/0.46 => ! [Xp1: a > a > $o] :
% 0.30/0.46 ( ( ! [Xx0: a,Xy0: a] :
% 0.30/0.46 ( ( ( R @ Xx0 @ Xy0 )
% 0.30/0.46 | ( S @ Xx0 @ Xy0 ) )
% 0.30/0.46 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.30/0.46 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.30/0.46 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.30/0.46 & ( Xp1 @ Xy0 @ Xz ) )
% 0.30/0.46 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.30/0.46 => ( Xp1 @ Xx @ Xy ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.46/1.28 ---- Embedded in THF ---
% 1.46/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.28 %%% Generated on Tue Feb 24 12:40:26 EST 2026
% 1.46/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.28 %%% Logic specification used:
% 1.46/1.28 %%% thf(spec, logic, $$dhol).
% 1.46/1.28
% 1.46/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.wk03IwR8rH/DTF2DTF22134.p
% See solution above
% 1.46/1.28 ------------------------
% 1.46/1.29 ---- Cleaned THF ---
% 1.46/1.29 thf(a_type,type,
% 1.46/1.29 a: $tType ).
% 1.46/1.29
% 1.46/1.29 thf(cTHM250C_pme,conjecture,
% 1.46/1.29 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.46/1.29 ( ! [Xp1: a > a > $o] :
% 1.46/1.29 ( ( ! [Xx0: a,Xy0: a] :
% 1.46/1.29 ( ( ! [Xp10: a > a > $o] :
% 1.46/1.29 ( ( ! [Xx1: a,Xy1: a] :
% 1.46/1.29 ( ( R @ Xx1 @ Xy1 )
% 1.46/1.29 => ( Xp10 @ Xx1 @ Xy1 ) )
% 1.46/1.29 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.46/1.29 ( ( ( Xp10 @ Xx1 @ Xy1 )
% 1.46/1.29 & ( Xp10 @ Xy1 @ Xz ) )
% 1.46/1.29 => ( Xp10 @ Xx1 @ Xz ) ) )
% 1.46/1.29 => ( Xp10 @ Xx0 @ Xy0 ) )
% 1.46/1.29 | ! [Xp10: a > a > $o] :
% 1.46/1.29 ( ( ! [Xx1: a,Xy1: a] :
% 1.46/1.29 ( ( S @ Xx1 @ Xy1 )
% 1.46/1.29 => ( Xp10 @ Xx1 @ Xy1 ) )
% 1.46/1.29 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.46/1.29 ( ( ( Xp10 @ Xx1 @ Xy1 )
% 1.46/1.29 & ( Xp10 @ Xy1 @ Xz ) )
% 1.46/1.29 => ( Xp10 @ Xx1 @ Xz ) ) )
% 1.46/1.29 => ( Xp10 @ Xx0 @ Xy0 ) ) )
% 1.46/1.29 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.46/1.29 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.46/1.29 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 1.46/1.29 & ( Xp1 @ Xy0 @ Xz ) )
% 1.46/1.29 => ( Xp1 @ Xx0 @ Xz ) ) )
% 1.46/1.29 => ( Xp1 @ Xx @ Xy ) )
% 1.46/1.29 => ! [Xp1: a > a > $o] :
% 1.46/1.29 ( ( ! [Xx0: a,Xy0: a] :
% 1.46/1.29 ( ( ( R @ Xx0 @ Xy0 )
% 1.46/1.29 | ( S @ Xx0 @ Xy0 ) )
% 1.46/1.29 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.46/1.29 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.46/1.29 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 1.46/1.29 & ( Xp1 @ Xy0 @ Xz ) )
% 1.46/1.29 => ( Xp1 @ Xx0 @ Xz ) ) )
% 1.46/1.29 => ( Xp1 @ Xx @ Xy ) ) ) ).
% 1.46/1.29 ------------------------
% 1.66/1.31 % (22355)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_22134 for (2999ds/2Mi)
% 1.66/1.31 % (22353)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_22134 for (2999ds/27Mi)
% 1.66/1.31 % (22355)Instruction limit reached!
% 1.66/1.31 % (22355)------------------------------
% 1.66/1.31 % (22355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (22355)Termination reason: Unknown
% 1.66/1.31 % (22355)Termination phase: Saturation
% 1.66/1.31
% 1.66/1.31 % (22355)Memory used [KB]: 1023
% 1.66/1.31 % (22355)Time elapsed: 0.003 s
% 1.66/1.31 % (22355)Instructions burned: 4 (million)
% 1.66/1.31 % (22355)------------------------------
% 1.66/1.31 % (22355)------------------------------
% 1.66/1.32 % (22351)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/183Mi)
% 1.66/1.32 % (22352)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_22134 for (2999ds/4Mi)
% 1.66/1.32 % (22354)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/2Mi)
% 1.66/1.32 % (22356)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_22134 for (2999ds/275Mi)
% 1.66/1.32 % (22357)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/18Mi)
% 1.66/1.32 % (22354)Instruction limit reached!
% 1.66/1.32 % (22354)------------------------------
% 1.66/1.32 % (22354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (22354)Termination reason: Unknown
% 1.66/1.32 % (22354)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (22354)Memory used [KB]: 895
% 1.66/1.32 % (22354)Time elapsed: 0.003 s
% 1.66/1.32 % (22354)Instructions burned: 2 (million)
% 1.66/1.32 % (22354)------------------------------
% 1.66/1.32 % (22354)------------------------------
% 1.66/1.32 % (22352)Instruction limit reached!
% 1.66/1.32 % (22352)------------------------------
% 1.66/1.32 % (22352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (22352)Termination reason: Unknown
% 1.66/1.32 % (22352)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (22352)Memory used [KB]: 1023
% 1.66/1.32 % (22352)Time elapsed: 0.005 s
% 1.66/1.32 % (22352)Instructions burned: 5 (million)
% 1.66/1.32 % (22352)------------------------------
% 1.66/1.32 % (22352)------------------------------
% 1.66/1.32 % (22353)Instruction limit reached!
% 1.66/1.32 % (22353)------------------------------
% 1.66/1.32 % (22353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (22353)Termination reason: Unknown
% 1.66/1.32 % (22353)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (22353)Memory used [KB]: 5628
% 1.66/1.32 % (22353)Time elapsed: 0.011 s
% 1.66/1.32 % (22353)Instructions burned: 29 (million)
% 1.66/1.32 % (22353)------------------------------
% 1.66/1.32 % (22353)------------------------------
% 1.66/1.32 % (22358)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/3Mi)
% 1.66/1.32 % (22358)Instruction limit reached!
% 1.66/1.32 % (22358)------------------------------
% 1.66/1.32 % (22358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (22358)Termination reason: Unknown
% 1.66/1.32 % (22358)Termination phase: Preprocessing 3
% 1.66/1.32
% 1.66/1.32 % (22358)Memory used [KB]: 1023
% 1.66/1.32 % (22358)Time elapsed: 0.002 s
% 1.66/1.32 % (22358)Instructions burned: 3 (million)
% 1.66/1.32 % (22358)------------------------------
% 1.66/1.32 % (22358)------------------------------
% 1.66/1.33 % (22357)Instruction limit reached!
% 1.66/1.33 % (22357)------------------------------
% 1.66/1.33 % (22357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (22357)Termination reason: Unknown
% 1.66/1.33 % (22357)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (22357)Memory used [KB]: 5628
% 1.66/1.33 % (22357)Time elapsed: 0.013 s
% 1.66/1.33 % (22357)Instructions burned: 19 (million)
% 1.66/1.33 % (22357)------------------------------
% 1.66/1.33 % (22357)------------------------------
% 1.66/1.33 % (22361)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_22134 for (2999ds/3Mi)
% 1.66/1.33 % (22362)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_22134 for (2999ds/1041Mi)
% 1.66/1.33 % (22361)Instruction limit reached!
% 1.66/1.33 % (22361)------------------------------
% 1.66/1.33 % (22361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (22361)Termination reason: Unknown
% 1.66/1.33 % (22361)Termination phase: Property scanning
% 1.66/1.33
% 1.66/1.33 % (22361)Memory used [KB]: 1023
% 1.66/1.33 % (22361)Time elapsed: 0.002 s
% 1.66/1.33 % (22361)Instructions burned: 4 (million)
% 1.66/1.33 % (22361)------------------------------
% 1.66/1.33 % (22361)------------------------------
% 1.66/1.33 % (22359)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_22134 for (2999ds/37Mi)
% 1.66/1.34 % (22360)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_22134 for (2999ds/15Mi)
% 1.66/1.34 % (22364)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/16Mi)
% 1.66/1.35 % (22363)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/7Mi)
% 1.66/1.35 % (22364)Instruction limit reached!
% 1.66/1.35 % (22364)------------------------------
% 1.66/1.35 % (22364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (22364)Termination reason: Unknown
% 1.66/1.35 % (22364)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (22364)Memory used [KB]: 5628
% 1.66/1.35 % (22364)Time elapsed: 0.007 s
% 1.66/1.35 % (22364)Instructions burned: 16 (million)
% 1.66/1.35 % (22364)------------------------------
% 1.66/1.35 % (22364)------------------------------
% 1.66/1.35 % (22360)Instruction limit reached!
% 1.66/1.35 % (22360)------------------------------
% 1.66/1.35 % (22360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (22360)Termination reason: Unknown
% 1.66/1.35 % (22360)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (22360)Memory used [KB]: 5756
% 1.66/1.35 % (22360)Time elapsed: 0.012 s
% 1.66/1.35 % (22360)Instructions burned: 16 (million)
% 1.66/1.35 % (22360)------------------------------
% 1.66/1.35 % (22360)------------------------------
% 1.66/1.35 % (22363)Instruction limit reached!
% 1.66/1.35 % (22363)------------------------------
% 1.66/1.35 % (22363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (22363)Termination reason: Unknown
% 1.66/1.35 % (22363)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (22363)Memory used [KB]: 1023
% 1.66/1.35 % (22363)Time elapsed: 0.006 s
% 1.66/1.35 % (22363)Instructions burned: 7 (million)
% 1.66/1.35 % (22363)------------------------------
% 1.66/1.35 % (22363)------------------------------
% 1.66/1.35 % (22359)Instruction limit reached!
% 1.66/1.35 % (22359)------------------------------
% 1.66/1.35 % (22359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (22359)Termination reason: Unknown
% 1.66/1.35 % (22359)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (22359)Memory used [KB]: 5628
% 1.66/1.35 % (22359)Time elapsed: 0.022 s
% 1.66/1.35 % (22359)Instructions burned: 37 (million)
% 1.66/1.35 % (22359)------------------------------
% 1.66/1.35 % (22359)------------------------------
% 1.66/1.36 % (22365)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_22134 for (2999ds/3Mi)
% 1.66/1.36 % (22365)Instruction limit reached!
% 1.66/1.36 % (22365)------------------------------
% 1.66/1.36 % (22365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (22365)Termination reason: Unknown
% 1.66/1.36 % (22365)Termination phase: Property scanning
% 1.66/1.36
% 1.66/1.36 % (22365)Memory used [KB]: 1023
% 1.66/1.36 % (22365)Time elapsed: 0.003 s
% 1.66/1.36 % (22365)Instructions burned: 4 (million)
% 1.66/1.36 % (22365)------------------------------
% 1.66/1.36 % (22365)------------------------------
% 1.66/1.36 % (22366)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_22134 for (2999ds/3Mi)
% 1.66/1.37 % (22366)Instruction limit reached!
% 1.66/1.37 % (22366)------------------------------
% 1.66/1.37 % (22366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (22366)Termination reason: Unknown
% 1.66/1.37 % (22366)Termination phase: Property scanning
% 1.66/1.37
% 1.66/1.37 % (22366)Memory used [KB]: 1023
% 1.66/1.37 % (22366)Time elapsed: 0.004 s
% 1.66/1.37 % (22366)Instructions burned: 4 (million)
% 1.66/1.37 % (22366)------------------------------
% 1.66/1.37 % (22366)------------------------------
% 1.66/1.37 % (22367)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/7Mi)
% 1.66/1.37 % (22369)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/4Mi)
% 1.66/1.37 % (22369)Instruction limit reached!
% 1.66/1.37 % (22369)------------------------------
% 1.66/1.37 % (22369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (22369)Termination reason: Unknown
% 1.66/1.37 % (22369)Termination phase: Property scanning
% 1.66/1.37
% 1.66/1.37 % (22369)Memory used [KB]: 1023
% 1.66/1.37 % (22369)Time elapsed: 0.003 s
% 1.66/1.37 % (22369)Instructions burned: 4 (million)
% 1.66/1.37 % (22369)------------------------------
% 1.66/1.37 % (22369)------------------------------
% 1.66/1.37 % (22367)Instruction limit reached!
% 1.66/1.37 % (22367)------------------------------
% 1.66/1.37 % (22367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (22367)Termination reason: Unknown
% 1.66/1.37 % (22367)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (22367)Memory used [KB]: 5500
% 1.66/1.37 % (22367)Time elapsed: 0.005 s
% 1.66/1.37 % (22367)Instructions burned: 8 (million)
% 1.66/1.37 % (22367)------------------------------
% 1.66/1.37 % (22367)------------------------------
% 1.66/1.37 % (22368)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/3Mi)
% 1.66/1.37 % (22368)Instruction limit reached!
% 1.66/1.37 % (22368)------------------------------
% 1.66/1.37 % (22368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (22368)Termination reason: Unknown
% 1.66/1.37 % (22368)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (22368)Memory used [KB]: 5500
% 1.66/1.37 % (22368)Time elapsed: 0.004 s
% 1.66/1.37 % (22368)Instructions burned: 4 (million)
% 1.66/1.37 % (22368)------------------------------
% 1.66/1.37 % (22368)------------------------------
% 1.66/1.38 % (22371)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/710Mi)
% 1.66/1.38 % (22372)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/6Mi)
% 1.66/1.38 % (22372)Instruction limit reached!
% 1.66/1.38 % (22372)------------------------------
% 1.66/1.38 % (22372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (22372)Termination reason: Unknown
% 1.66/1.38 % (22372)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (22372)Memory used [KB]: 5500
% 1.66/1.38 % (22372)Time elapsed: 0.004 s
% 1.66/1.38 % (22372)Instructions burned: 7 (million)
% 1.66/1.38 % (22372)------------------------------
% 1.66/1.38 % (22372)------------------------------
% 1.66/1.38 % (22370)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/18Mi)
% 1.66/1.39 % (22373)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_22134 for (2999ds/902Mi)
% 1.66/1.39 % (22351)Instruction limit reached!
% 1.66/1.39 % (22351)------------------------------
% 1.66/1.39 % (22351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (22351)Termination reason: Unknown
% 1.66/1.39 % (22351)Termination phase: Saturation
% 1.66/1.39
% 1.66/1.39 % (22351)Memory used [KB]: 6268
% 1.66/1.39 % (22351)Time elapsed: 0.078 s
% 1.66/1.39 % (22351)Instructions burned: 185 (million)
% 1.66/1.39 % (22351)------------------------------
% 1.66/1.39 % (22351)------------------------------
% 1.66/1.39 % (22374)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_22134 for (2999ds/21Mi)
% 1.66/1.39 % (22370)Instruction limit reached!
% 1.66/1.39 % (22370)------------------------------
% 1.66/1.39 % (22370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (22370)Termination reason: Unknown
% 1.66/1.39 % (22370)Termination phase: Saturation
% 1.66/1.39
% 1.66/1.39 % (22370)Memory used [KB]: 5628
% 1.66/1.39 % (22370)Time elapsed: 0.012 s
% 1.66/1.39 % (22370)Instructions burned: 18 (million)
% 1.66/1.39 % (22370)------------------------------
% 1.66/1.39 % (22370)------------------------------
% 1.66/1.40 % (22374)Instruction limit reached!
% 1.66/1.40 % (22374)------------------------------
% 1.66/1.40 % (22374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (22374)Termination reason: Unknown
% 1.66/1.40 % (22374)Termination phase: Saturation
% 1.66/1.40
% 1.66/1.40 % (22374)Memory used [KB]: 5756
% 1.66/1.40 % (22374)Time elapsed: 0.010 s
% 1.66/1.40 % (22374)Instructions burned: 23 (million)
% 1.66/1.40 % (22374)------------------------------
% 1.66/1.40 % (22374)------------------------------
% 1.66/1.40 % (22375)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/5Mi)
% 1.66/1.40 % (22375)Instruction limit reached!
% 1.66/1.40 % (22375)------------------------------
% 1.66/1.40 % (22375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (22375)Termination reason: Unknown
% 1.66/1.40 % (22375)Termination phase: Saturation
% 1.66/1.40
% 1.66/1.40 % (22375)Memory used [KB]: 5500
% 1.66/1.40 % (22375)Time elapsed: 0.003 s
% 1.66/1.40 % (22375)Instructions burned: 5 (million)
% 1.66/1.40 % (22375)------------------------------
% 1.66/1.40 % (22375)------------------------------
% 1.66/1.41 % (22376)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_22134 for (2999ds/6Mi)
% 1.66/1.41 % (22376)Instruction limit reached!
% 1.66/1.41 % (22376)------------------------------
% 1.66/1.41 % (22376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (22376)Termination reason: Unknown
% 1.66/1.41 % (22376)Termination phase: Saturation
% 1.66/1.41
% 1.66/1.41 % (22376)Memory used [KB]: 5500
% 1.66/1.41 % (22376)Time elapsed: 0.003 s
% 1.66/1.41 % (22376)Instructions burned: 6 (million)
% 1.66/1.41 % (22376)------------------------------
% 1.66/1.41 % (22376)------------------------------
% 1.66/1.41 % (22377)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22134 for (2999ds/377Mi)
% 1.66/1.41 % (22378)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_22134 for (2999ds/779Mi)
% 1.66/1.42 % (22379)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_22134 for (2999ds/19Mi)
% 1.66/1.42 % (22362)First to succeed.
% 1.66/1.43 % (22379)Instruction limit reached!
% 1.66/1.43 % (22379)------------------------------
% 1.66/1.43 % (22379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (22379)Termination reason: Unknown
% 1.66/1.43 % (22379)Termination phase: Saturation
% 1.66/1.43
% 1.66/1.43 % (22379)Memory used [KB]: 5500
% 1.66/1.43 % (22379)Time elapsed: 0.008 s
% 1.66/1.43 % (22379)Instructions burned: 22 (million)
% 1.66/1.43 % (22379)------------------------------
% 1.66/1.43 % (22379)------------------------------
% 1.66/1.43 % (22362)Refutation found. Thanks to Tanya!
% 1.66/1.43 % SZS status Theorem for DTF2THF_22134
% 1.66/1.43 % SZS output start Proof for DTF2THF_22134
% 1.66/1.43 thf(type_def_5, type, a: $tType).
% 1.66/1.43 thf(func_def_0, type, a: $tType).
% 1.66/1.43 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.66/1.43 thf(func_def_18, type, sK2: a > a > $o).
% 1.66/1.43 thf(func_def_19, type, sK3: a).
% 1.66/1.43 thf(func_def_20, type, sK4: a).
% 1.66/1.43 thf(func_def_21, type, sK5: a > a > $o).
% 1.66/1.43 thf(func_def_22, type, sK6: a > a > $o).
% 1.66/1.43 thf(func_def_23, type, sK7: a).
% 1.66/1.43 thf(func_def_24, type, sK8: a).
% 1.66/1.43 thf(func_def_25, type, sK9: a).
% 1.66/1.43 thf(func_def_26, type, sK10: a).
% 1.66/1.43 thf(func_def_27, type, sK11: a).
% 1.66/1.43 thf(func_def_28, type, sK12: a).
% 1.66/1.43 thf(func_def_29, type, sK13: a).
% 1.66/1.43 thf(func_def_30, type, sK14: a).
% 1.66/1.43 thf(func_def_31, type, sK15: a).
% 1.66/1.43 thf(func_def_32, type, sK16: a).
% 1.66/1.43 thf(func_def_33, type, sK17: a).
% 1.66/1.43 thf(func_def_34, type, sK18: a).
% 1.66/1.43 thf(func_def_35, type, sK19: a).
% 1.66/1.43 thf(func_def_36, type, sK20: a).
% 1.66/1.43 thf(func_def_37, type, sK21: a).
% 1.66/1.43 thf(func_def_38, type, sK22: a).
% 1.66/1.43 thf(func_def_39, type, sK23: a).
% 1.66/1.43 thf(func_def_40, type, sK24: a).
% 1.66/1.43 thf(func_def_41, type, sK25: a).
% 1.66/1.43 thf(func_def_42, type, sK26: a).
% 1.66/1.43 thf(func_def_43, type, sK27: a).
% 1.66/1.43 thf(func_def_44, type, sK28: a).
% 1.66/1.43 thf(func_def_45, type, sK29: a).
% 1.66/1.43 thf(func_def_46, type, sK30: a).
% 1.66/1.43 thf(func_def_47, type, sK31: a).
% 1.66/1.43 thf(func_def_48, type, sK32: a).
% 1.66/1.43 thf(func_def_49, type, sK33: a).
% 1.66/1.43 thf(func_def_50, type, sK34: a).
% 1.66/1.43 thf(func_def_51, type, sK35: a).
% 1.66/1.43 thf(func_def_52, type, sK36: a).
% 1.66/1.43 thf(func_def_53, type, sK37: a).
% 1.66/1.43 thf(func_def_54, type, sK38: a).
% 1.66/1.43 thf(f1416,plain,(
% 1.66/1.43 $false),
% 1.66/1.43 inference(avatar_sat_refutation,[status(thm)],[f108,f172,f261,f469,f665,f870,f1006,f1050,f1415])).
% 1.66/1.43 thf(f1415,plain,(
% 1.66/1.43 ~spl0_19),
% 1.66/1.43 inference(avatar_contradiction_clause,[status(thm)],[f1414])).
% 1.66/1.43 thf(f1414,plain,(
% 1.66/1.43 $false | ~spl0_19),
% 1.66/1.43 inference(trivial_inequality_removal,[status(thm)],[f1413])).
% 1.66/1.43 thf(f1413,plain,(
% 1.66/1.43 ($false = $true) | ~spl0_19),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1412])).
% 1.66/1.43 thf(f1412,plain,(
% 1.66/1.43 ($true = (~ $true)) | ~spl0_19),
% 1.66/1.43 inference(forward_demodulation,[status(thm)],[f1404,f1279])).
% 1.66/1.43 thf(f1279,plain,(
% 1.66/1.43 ((sK6 @ sK36 @ sK33) = $true) | ~spl0_19),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f1251])).
% 1.66/1.43 thf(f1251,plain,(
% 1.66/1.43 ($true = ((sK6 @ sK36 @ sK33) & (sK6 @ sK34 @ sK36))) | ~spl0_19),
% 1.66/1.43 inference(not_proxy_clausification,[status(thm)],[f1170])).
% 1.66/1.43 thf(f1170,plain,(
% 1.66/1.43 ((~ ((sK6 @ sK36 @ sK33) & (sK6 @ sK34 @ sK36))) = $false) | ~spl0_19),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f1169])).
% 1.66/1.43 thf(f1169,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (~ ((sK6 @ Y0 @ sK33) & (sK6 @ sK34 @ Y0)))) @ sK36)) | ~spl0_19),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f1158])).
% 1.66/1.43 thf(f1158,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK6 @ Y0 @ sK33) & (sK6 @ sK34 @ Y0)))))) | ~spl0_19),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1157])).
% 1.66/1.43 thf(f1157,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0 @ sK33) & (sK6 @ sK34 @ Y0)) => $false)))) | ~spl0_19),
% 1.66/1.43 inference(backward_demodulation,[status(thm)],[f1138,f1156])).
% 1.66/1.43 thf(f1156,plain,(
% 1.66/1.43 ($false = (sK6 @ sK34 @ sK33)) | ~spl0_19),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1155])).
% 1.66/1.43 thf(f1155,plain,(
% 1.66/1.43 ($false = ($true => (sK6 @ sK34 @ sK33))) | ~spl0_19),
% 1.66/1.43 inference(backward_demodulation,[status(thm)],[f1148,f1154])).
% 1.66/1.43 thf(f1154,plain,(
% 1.66/1.43 ($true = ((sK6 @ sK35 @ sK33) & (sK6 @ sK34 @ sK35))) | ~spl0_19),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f1148])).
% 1.66/1.43 thf(f1148,plain,(
% 1.66/1.43 ($false = (((sK6 @ sK35 @ sK33) & (sK6 @ sK34 @ sK35)) => (sK6 @ sK34 @ sK33))) | ~spl0_19),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f1147])).
% 1.66/1.43 thf(f1147,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (((sK6 @ Y0 @ sK33) & (sK6 @ sK34 @ Y0)) => (sK6 @ sK34 @ sK33))) @ sK35)) | ~spl0_19),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f1138])).
% 1.66/1.43 thf(f1138,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0 @ sK33) & (sK6 @ sK34 @ Y0)) => (sK6 @ sK34 @ sK33))))) | ~spl0_19),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f1137])).
% 1.66/1.43 thf(f1137,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ sK33) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ sK33))))) @ sK34)) | ~spl0_19),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f1128])).
% 1.66/1.43 thf(f1128,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ sK33) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ sK33))))))) | ~spl0_19),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f1124])).
% 1.66/1.43 thf(f1124,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y1 @ Y0))))))) @ sK33)) | ~spl0_19),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f664])).
% 1.66/1.43 thf(f664,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y1 @ Y0))))))))) | ~spl0_19),
% 1.66/1.43 inference(avatar_component_clause,[status(thm)],[f663])).
% 1.66/1.43 thf(f663,definition,(
% 1.66/1.43 spl0_19 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y1 @ Y0)))))))))),
% 1.66/1.43 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 1.66/1.43 thf(f1404,plain,(
% 1.66/1.43 ($true = (~ (sK6 @ sK36 @ sK33))) | ~spl0_19),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1398])).
% 1.66/1.43 thf(f1398,plain,(
% 1.66/1.43 ($true = ((sK6 @ sK36 @ sK33) => $false)) | ~spl0_19),
% 1.66/1.43 inference(superposition,[status(thm)],[f1293,f1156])).
% 1.66/1.43 thf(f1293,plain,(
% 1.66/1.43 ( ! [X0 : a] : (($true = ((sK6 @ sK36 @ X0) => (sK6 @ sK34 @ X0)))) ) | ~spl0_19),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1288])).
% 1.66/1.43 thf(f1288,plain,(
% 1.66/1.43 ( ! [X0 : a] : (($true = (($true & (sK6 @ sK36 @ X0)) => (sK6 @ sK34 @ X0)))) ) | ~spl0_19),
% 1.66/1.43 inference(superposition,[status(thm)],[f70,f1285])).
% 1.66/1.43 thf(f1285,plain,(
% 1.66/1.43 ($true = (sK6 @ sK34 @ sK36)) | ~spl0_19),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1284])).
% 1.66/1.43 thf(f1284,plain,(
% 1.66/1.43 ($true = ($true & (sK6 @ sK34 @ sK36))) | ~spl0_19),
% 1.66/1.43 inference(backward_demodulation,[status(thm)],[f1251,f1279])).
% 1.66/1.43 thf(f70,plain,(
% 1.66/1.43 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK6 @ X1 @ X3) & (sK6 @ X3 @ X2)) => (sK6 @ X1 @ X2)))) )),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.66/1.43 thf(f69,plain,(
% 1.66/1.43 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK6 @ X1 @ Y0) & (sK6 @ Y0 @ X2)) => (sK6 @ X1 @ X2))) @ X3) = $true)) )),
% 1.66/1.43 inference(pi_clausification,[status(thm)],[f68])).
% 1.66/1.43 thf(f68,plain,(
% 1.66/1.43 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ X1 @ Y0) & (sK6 @ Y0 @ X2)) => (sK6 @ X1 @ X2)))) = $true)) )),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.66/1.43 thf(f67,plain,(
% 1.66/1.43 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ X1 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ X1 @ Y0))))) @ X2))) )),
% 1.66/1.43 inference(pi_clausification,[status(thm)],[f60])).
% 1.66/1.43 thf(f60,plain,(
% 1.66/1.43 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ X1 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ X1 @ Y0)))))))) )),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.66/1.43 thf(f59,plain,(
% 1.66/1.43 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y2 @ Y1)) => (sK6 @ Y0 @ Y1))))))) @ X1) = $true)) )),
% 1.66/1.43 inference(pi_clausification,[status(thm)],[f28])).
% 1.66/1.43 thf(f28,plain,(
% 1.66/1.43 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y2 @ Y1)) => (sK6 @ Y0 @ Y1)))))))))),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.66/1.43 thf(f25,plain,(
% 1.66/1.43 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y2 @ Y1)) => (sK6 @ Y0 @ Y1))))))))) = $true)),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.66/1.43 thf(f23,plain,(
% 1.66/1.43 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y2 @ Y1)) => (sK6 @ Y0 @ Y1))))))))) => (sK6 @ sK4 @ sK3)))),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.66/1.43 thf(f22,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK4 @ sK3))) @ sK6))),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f21])).
% 1.66/1.43 thf(f21,plain,(
% 1.66/1.43 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK4 @ sK3)))))),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f20])).
% 1.66/1.43 thf(f20,plain,(
% 1.66/1.43 ($false = ($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK4 @ sK3))))))),
% 1.66/1.43 inference(backward_demodulation,[status(thm)],[f17,f19])).
% 1.66/1.43 thf(f19,plain,(
% 1.66/1.43 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK5 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3)))))),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.66/1.43 thf(f17,plain,(
% 1.66/1.43 ($false = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK5 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3)))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) => (Y0 @ sK4 @ sK3))))))),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.66/1.43 thf(f16,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y3 @ Y2))))) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ sK3)))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ sK4 @ sK3)))))) @ sK5))),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f15])).
% 1.66/1.43 thf(f15,plain,(
% 1.66/1.43 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y3 @ Y2))))) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ sK3)))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3))))))))) => (Y1 @ sK4 @ sK3))))))))),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.66/1.43 thf(f14,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y7 @ Y6))))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y1 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y4 @ Y3))))) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ sK3)))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ sK3)))))))) @ sK4))),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f13])).
% 1.66/1.43 thf(f13,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y7 @ Y6))))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y1 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y4 @ Y3))))) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ sK3)))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4))))))))) => (Y2 @ Y0 @ sK3))))))))))),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.66/1.43 thf(f12,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK2 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y8 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y0)))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y1 @ Y0)))))))))) @ sK3))),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f11])).
% 1.66/1.43 thf(f11,plain,(
% 1.66/1.43 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK2 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y8 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y0)))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5))))))))) => (Y3 @ Y1 @ Y0))))))))))) = $false)),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.66/1.43 thf(f10,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y9 @ Y8))))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y3 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y8 @ Y10)) => (Y7 @ Y9 @ Y10))))))))) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y1)))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y2 @ Y1)))))))))))) @ sK2))),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f7])).
% 1.66/1.43 thf(f7,plain,(
% 1.66/1.43 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y9 @ Y8))))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y3 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y8 @ Y10)) => (Y7 @ Y9 @ Y10))))))))) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y1)))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y2 @ Y1))))))))))))))),
% 1.66/1.43 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.66/1.43 thf(f6,plain,(
% 1.66/1.43 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y9 @ Y8))))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y3 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y8 @ Y10)) => (Y7 @ Y9 @ Y10))))))))) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y1)))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y2 @ Y1)))))))))))))))),
% 1.66/1.43 inference(cnf_transformation,[status(thm)],[f5])).
% 1.66/1.43 thf(f5,plain,(
% 1.66/1.43 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y9 @ Y8))))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y3 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y8) & (Y7 @ Y8 @ Y10)) => (Y7 @ Y9 @ Y10))))))))) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y1)))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) => (Y4 @ Y2 @ Y1)))))))))))))))),
% 1.66/1.43 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.43 thf(f4,plain,(
% 1.66/1.43 ~! [X0 : a > a > $o,X1 : a,X2 : a,X3 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : ((! [X7 : a > a > $o] : ((! [X8 : a,X9 : a,X10 : a] : (((X7 @ X10 @ X8) & (X7 @ X9 @ X10)) => (X7 @ X9 @ X8)) & ! [X11 : a,X12 : a] : ((X0 @ X11 @ X12) => (X7 @ X11 @ X12))) => (X7 @ X5 @ X6)) | ! [X13 : a > a > $o] : ((! [X14 : a,X15 : a,X16 : a] : (((X13 @ X15 @ X14) & (X13 @ X14 @ X16)) => (X13 @ X15 @ X16)) & ! [X17 : a,X18 : a] : ((X3 @ X18 @ X17) => (X13 @ X18 @ X17))) => (X13 @ X5 @ X6))) => (X4 @ X5 @ X6)) & ! [X19 : a,X20 : a,X21 : a] : (((X4 @ X21 @ X20) & (X4 @ X19 @ X21)) => (X4 @ X19 @ X20))) => (X4 @ X1 @ X2)) => ! [X22 : a > a > $o] : ((! [X23 : a,X24 : a,X25 : a] : (((X22 @ X23 @ X24) & (X22 @ X25 @ X23)) => (X22 @ X25 @ X24)) & ! [X26 : a,X27 : a] : (((X3 @ X27 @ X26) | (X0 @ X27 @ X26)) => (X22 @ X27 @ X26))) => (X22 @ X1 @ X2)))),
% 1.66/1.43 inference(rectify,[status(thm)],[f2])).
% 1.66/1.43 thf(f2,negated_conjecture,(
% 1.66/1.43 ~! [X0 : a > a > $o,X2 : a,X3 : a,X1 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : ((! [X7 : a > a > $o] : ((! [X10 : a,X8 : a,X9 : a] : (((X7 @ X9 @ X10) & (X7 @ X8 @ X9)) => (X7 @ X8 @ X10)) & ! [X8 : a,X9 : a] : ((X0 @ X8 @ X9) => (X7 @ X8 @ X9))) => (X7 @ X5 @ X6)) | ! [X7 : a > a > $o] : ((! [X9 : a,X8 : a,X10 : a] : (((X7 @ X8 @ X9) & (X7 @ X9 @ X10)) => (X7 @ X8 @ X10)) & ! [X9 : a,X8 : a] : ((X1 @ X8 @ X9) => (X7 @ X8 @ X9))) => (X7 @ X5 @ X6))) => (X4 @ X5 @ X6)) & ! [X5 : a,X10 : a,X6 : a] : (((X4 @ X6 @ X10) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X10))) => (X4 @ X2 @ X3)) => ! [X4 : a > a > $o] : ((! [X6 : a,X10 : a,X5 : a] : (((X4 @ X6 @ X10) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X10)) & ! [X6 : a,X5 : a] : (((X1 @ X5 @ X6) | (X0 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)))),
% 1.66/1.43 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.43 thf(f1,conjecture,(
% 1.66/1.43 ! [X0 : a > a > $o,X2 : a,X3 : a,X1 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : ((! [X7 : a > a > $o] : ((! [X10 : a,X8 : a,X9 : a] : (((X7 @ X9 @ X10) & (X7 @ X8 @ X9)) => (X7 @ X8 @ X10)) & ! [X8 : a,X9 : a] : ((X0 @ X8 @ X9) => (X7 @ X8 @ X9))) => (X7 @ X5 @ X6)) | ! [X7 : a > a > $o] : ((! [X9 : a,X8 : a,X10 : a] : (((X7 @ X8 @ X9) & (X7 @ X9 @ X10)) => (X7 @ X8 @ X10)) & ! [X9 : a,X8 : a] : ((X1 @ X8 @ X9) => (X7 @ X8 @ X9))) => (X7 @ X5 @ X6))) => (X4 @ X5 @ X6)) & ! [X5 : a,X10 : a,X6 : a] : (((X4 @ X6 @ X10) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X10))) => (X4 @ X2 @ X3)) => ! [X4 : a > a > $o] : ((! [X6 : a,X10 : a,X5 : a] : (((X4 @ X6 @ X10) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X10)) & ! [X6 : a,X5 : a] : (((X1 @ X5 @ X6) | (X0 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)))),
% 1.66/1.43 file('/export/starexec/sandbox2/tmp/tmp.wk03IwR8rH/DTF2THF_22134.p',cTHM250C_pme)).
% 1.66/1.43 thf(f1050,plain,(
% 1.66/1.43 ~spl0_18),
% 1.66/1.43 inference(avatar_contradiction_clause,[status(thm)],[f1049])).
% 1.66/1.43 thf(f1049,plain,(
% 1.66/1.43 $false | ~spl0_18),
% 1.66/1.43 inference(trivial_inequality_removal,[status(thm)],[f1048])).
% 1.66/1.43 thf(f1048,plain,(
% 1.66/1.43 ($false = $true) | ~spl0_18),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1047])).
% 1.66/1.43 thf(f1047,plain,(
% 1.66/1.43 ($true = (~ $true)) | ~spl0_18),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1046])).
% 1.66/1.43 thf(f1046,plain,(
% 1.66/1.43 ($true = (~ ((sK5 @ sK31 @ sK32) | $true))) | ~spl0_18),
% 1.66/1.43 inference(forward_demodulation,[status(thm)],[f1045,f1033])).
% 1.66/1.43 thf(f1033,plain,(
% 1.66/1.43 ($true = (sK2 @ sK31 @ sK32)) | ~spl0_18),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f1031])).
% 1.66/1.43 thf(f1031,plain,(
% 1.66/1.43 ($false = ((sK2 @ sK31 @ sK32) => (sK6 @ sK31 @ sK32))) | ~spl0_18),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f1030])).
% 1.66/1.43 thf(f1030,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: ((sK2 @ sK31 @ Y0) => (sK6 @ sK31 @ Y0))) @ sK32)) | ~spl0_18),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f1023])).
% 1.66/1.43 thf(f1023,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK31 @ Y0) => (sK6 @ sK31 @ Y0))))) | ~spl0_18),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f1021])).
% 1.66/1.43 thf(f1021,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))) @ sK31)) | ~spl0_18),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f661])).
% 1.66/1.43 thf(f661,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))))) | ~spl0_18),
% 1.66/1.43 inference(avatar_component_clause,[status(thm)],[f660])).
% 1.66/1.43 thf(f660,definition,(
% 1.66/1.43 spl0_18 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))))),
% 1.66/1.43 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 1.66/1.43 thf(f1045,plain,(
% 1.66/1.43 ($true = (~ ((sK5 @ sK31 @ sK32) | (sK2 @ sK31 @ sK32)))) | ~spl0_18),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1039])).
% 1.66/1.43 thf(f1039,plain,(
% 1.66/1.43 ($true = (((sK5 @ sK31 @ sK32) | (sK2 @ sK31 @ sK32)) => $false)) | ~spl0_18),
% 1.66/1.43 inference(superposition,[status(thm)],[f35,f1035])).
% 1.66/1.43 thf(f1035,plain,(
% 1.66/1.43 ($false = (sK6 @ sK31 @ sK32)) | ~spl0_18),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1034])).
% 1.66/1.43 thf(f1034,plain,(
% 1.66/1.43 ($false = ($true => (sK6 @ sK31 @ sK32))) | ~spl0_18),
% 1.66/1.43 inference(backward_demodulation,[status(thm)],[f1031,f1033])).
% 1.66/1.43 thf(f35,plain,(
% 1.66/1.43 ( ! [X2 : a,X1 : a] : (($true = (((sK5 @ X1 @ X2) | (sK2 @ X1 @ X2)) => (sK6 @ X1 @ X2)))) )),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.66/1.43 thf(f34,plain,(
% 1.66/1.43 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK5 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK6 @ X1 @ Y0))) @ X2))) )),
% 1.66/1.43 inference(pi_clausification,[status(thm)],[f33])).
% 1.66/1.43 thf(f33,plain,(
% 1.66/1.43 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK5 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK6 @ X1 @ Y0)))))) )),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.66/1.43 thf(f32,plain,(
% 1.66/1.43 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))) @ X1) = $true)) )),
% 1.66/1.43 inference(pi_clausification,[status(thm)],[f31])).
% 1.66/1.43 thf(f31,plain,(
% 1.66/1.43 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))))),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f30])).
% 1.66/1.43 thf(f30,plain,(
% 1.66/1.43 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) & $true))),
% 1.66/1.43 inference(backward_demodulation,[status(thm)],[f25,f28])).
% 1.66/1.43 thf(f1006,plain,(
% 1.66/1.43 ~spl0_16),
% 1.66/1.43 inference(avatar_contradiction_clause,[status(thm)],[f1005])).
% 1.66/1.43 thf(f1005,plain,(
% 1.66/1.43 $false | ~spl0_16),
% 1.66/1.43 inference(trivial_inequality_removal,[status(thm)],[f1004])).
% 1.66/1.43 thf(f1004,plain,(
% 1.66/1.43 ($false = $true) | ~spl0_16),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1003])).
% 1.66/1.43 thf(f1003,plain,(
% 1.66/1.43 ($true = (~ $true)) | ~spl0_16),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f1002])).
% 1.66/1.43 thf(f1002,plain,(
% 1.66/1.43 ($true = (~ ($true | (sK2 @ sK30 @ sK29)))) | ~spl0_16),
% 1.66/1.43 inference(forward_demodulation,[status(thm)],[f998,f989])).
% 1.66/1.43 thf(f989,plain,(
% 1.66/1.43 ($true = (sK5 @ sK30 @ sK29)) | ~spl0_16),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f987])).
% 1.66/1.43 thf(f987,plain,(
% 1.66/1.43 ($false = ((sK5 @ sK30 @ sK29) => (sK6 @ sK30 @ sK29))) | ~spl0_16),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f986])).
% 1.66/1.43 thf(f986,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: ((sK5 @ Y0 @ sK29) => (sK6 @ Y0 @ sK29))) @ sK30)) | ~spl0_16),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f881])).
% 1.66/1.43 thf(f881,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: ((sK5 @ Y0 @ sK29) => (sK6 @ Y0 @ sK29))))) | ~spl0_16),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f879])).
% 1.66/1.43 thf(f879,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0))))) @ sK29)) | ~spl0_16),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f468])).
% 1.66/1.43 thf(f468,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0))))))) | ~spl0_16),
% 1.66/1.43 inference(avatar_component_clause,[status(thm)],[f467])).
% 1.66/1.43 thf(f467,definition,(
% 1.66/1.43 spl0_16 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0)))))))),
% 1.66/1.43 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.66/1.43 thf(f998,plain,(
% 1.66/1.43 ($true = (~ ((sK5 @ sK30 @ sK29) | (sK2 @ sK30 @ sK29)))) | ~spl0_16),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f995])).
% 1.66/1.43 thf(f995,plain,(
% 1.66/1.43 ($true = (((sK5 @ sK30 @ sK29) | (sK2 @ sK30 @ sK29)) => $false)) | ~spl0_16),
% 1.66/1.43 inference(superposition,[status(thm)],[f35,f991])).
% 1.66/1.43 thf(f991,plain,(
% 1.66/1.43 ($false = (sK6 @ sK30 @ sK29)) | ~spl0_16),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f990])).
% 1.66/1.43 thf(f990,plain,(
% 1.66/1.43 ($false = ($true => (sK6 @ sK30 @ sK29))) | ~spl0_16),
% 1.66/1.43 inference(backward_demodulation,[status(thm)],[f987,f989])).
% 1.66/1.43 thf(f870,plain,(
% 1.66/1.43 ~spl0_15),
% 1.66/1.43 inference(avatar_contradiction_clause,[status(thm)],[f869])).
% 1.66/1.43 thf(f869,plain,(
% 1.66/1.43 $false | ~spl0_15),
% 1.66/1.43 inference(trivial_inequality_removal,[status(thm)],[f866])).
% 1.66/1.43 thf(f866,plain,(
% 1.66/1.43 ($false = $true) | ~spl0_15),
% 1.66/1.43 inference(superposition,[status(thm)],[f70,f857])).
% 1.66/1.43 thf(f857,plain,(
% 1.66/1.43 ($false = (((sK6 @ sK27 @ sK26) & (sK6 @ sK26 @ sK28)) => (sK6 @ sK27 @ sK28))) | ~spl0_15),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f856])).
% 1.66/1.43 thf(f856,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (((sK6 @ sK27 @ sK26) & (sK6 @ sK26 @ Y0)) => (sK6 @ sK27 @ Y0))) @ sK28)) | ~spl0_15),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f841])).
% 1.66/1.43 thf(f841,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ sK27 @ sK26) & (sK6 @ sK26 @ Y0)) => (sK6 @ sK27 @ Y0))))) | ~spl0_15),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f840])).
% 1.66/1.43 thf(f840,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ sK26) & (sK6 @ sK26 @ Y1)) => (sK6 @ Y0 @ Y1))))) @ sK27)) | ~spl0_15),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f824])).
% 1.66/1.43 thf(f824,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ sK26) & (sK6 @ sK26 @ Y1)) => (sK6 @ Y0 @ Y1))))))) | ~spl0_15),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f820])).
% 1.66/1.43 thf(f820,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2))))))) @ sK26)) | ~spl0_15),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f465])).
% 1.66/1.43 thf(f465,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2))))))))) | ~spl0_15),
% 1.66/1.43 inference(avatar_component_clause,[status(thm)],[f464])).
% 1.66/1.43 thf(f464,definition,(
% 1.66/1.43 spl0_15 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2)))))))))),
% 1.66/1.43 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.66/1.43 thf(f665,plain,(
% 1.66/1.43 spl0_18 | spl0_19 | ~spl0_2 | ~spl0_4),
% 1.66/1.43 inference(avatar_split_clause,[status(thm)],[f656,f170,f106,f663,f660])).
% 1.66/1.43 thf(f106,definition,(
% 1.66/1.43 spl0_2 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0)))))))),
% 1.66/1.43 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.66/1.43 thf(f170,definition,(
% 1.66/1.43 spl0_4 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))))),
% 1.66/1.43 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.66/1.43 thf(f656,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y1 @ Y0))))))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1))))))) | (~spl0_2 | ~spl0_4)),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f650])).
% 1.66/1.43 thf(f650,plain,(
% 1.66/1.43 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y1 @ Y0)))))))))) | (~spl0_2 | ~spl0_4)),
% 1.66/1.43 inference(not_proxy_clausification,[status(thm)],[f556])).
% 1.66/1.43 thf(f556,plain,(
% 1.66/1.43 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y1 @ Y0))))))))))) | (~spl0_2 | ~spl0_4)),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f550])).
% 1.66/1.43 thf(f550,plain,(
% 1.66/1.43 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK6 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y1 @ Y0))))))))) => $false)) | (~spl0_2 | ~spl0_4)),
% 1.66/1.43 inference(superposition,[status(thm)],[f544,f472])).
% 1.66/1.43 thf(f472,plain,(
% 1.66/1.43 ($false = (sK6 @ sK8 @ sK7)) | (~spl0_2 | ~spl0_4)),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f471])).
% 1.66/1.43 thf(f471,plain,(
% 1.66/1.43 ($false = ($true => (sK6 @ sK8 @ sK7))) | (~spl0_2 | ~spl0_4)),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f470])).
% 1.66/1.43 thf(f470,plain,(
% 1.66/1.43 ($false = (($true | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK7))))) => (sK6 @ sK8 @ sK7))) | (~spl0_2 | ~spl0_4)),
% 1.66/1.43 inference(forward_demodulation,[status(thm)],[f279,f171])).
% 1.66/1.43 thf(f171,plain,(
% 1.66/1.43 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))))) | ~spl0_4),
% 1.66/1.43 inference(avatar_component_clause,[status(thm)],[f170])).
% 1.66/1.43 thf(f279,plain,(
% 1.66/1.43 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK7))))) => (sK6 @ sK8 @ sK7))) | ~spl0_2),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f278])).
% 1.66/1.43 thf(f278,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ Y0 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK5 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK7))))) => (sK6 @ Y0 @ sK7))) @ sK8)) | ~spl0_2),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f272])).
% 1.66/1.43 thf(f272,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ Y0 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK5 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK7))))) => (sK6 @ Y0 @ sK7))))) | ~spl0_2),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f268])).
% 1.66/1.43 thf(f268,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))) @ sK7)) | ~spl0_2),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f107])).
% 1.66/1.43 thf(f107,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))))) | ~spl0_2),
% 1.66/1.43 inference(avatar_component_clause,[status(thm)],[f106])).
% 1.66/1.43 thf(f544,plain,(
% 1.66/1.43 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y2 @ Y0) & (X1 @ Y1 @ Y2)) => (X1 @ Y1 @ Y0))))))))) => (X1 @ sK8 @ sK7)))) ) | ~spl0_4),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f543])).
% 1.66/1.43 thf(f543,plain,(
% 1.66/1.43 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))) @ X1))) ) | ~spl0_4),
% 1.66/1.43 inference(pi_clausification,[status(thm)],[f171])).
% 1.66/1.43 thf(f469,plain,(
% 1.66/1.43 spl0_15 | spl0_16 | ~spl0_2 | ~spl0_3),
% 1.66/1.43 inference(avatar_split_clause,[status(thm)],[f460,f167,f106,f467,f464])).
% 1.66/1.43 thf(f167,definition,(
% 1.66/1.43 spl0_3 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK7)))))),
% 1.66/1.43 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.66/1.43 thf(f460,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0))))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2))))))))) | (~spl0_2 | ~spl0_3)),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f447])).
% 1.66/1.43 thf(f447,plain,(
% 1.66/1.43 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2))))))))) = $false) | (~spl0_2 | ~spl0_3)),
% 1.66/1.43 inference(not_proxy_clausification,[status(thm)],[f291])).
% 1.66/1.43 thf(f291,plain,(
% 1.66/1.43 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2))))))))))) | (~spl0_2 | ~spl0_3)),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f287])).
% 1.66/1.43 thf(f287,plain,(
% 1.66/1.43 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ Y2)) => (sK6 @ Y1 @ Y2))))))))) => $false)) | (~spl0_2 | ~spl0_3)),
% 1.66/1.43 inference(superposition,[status(thm)],[f176,f282])).
% 1.66/1.43 thf(f282,plain,(
% 1.66/1.43 ($false = (sK6 @ sK8 @ sK7)) | (~spl0_2 | ~spl0_3)),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f281])).
% 1.66/1.43 thf(f281,plain,(
% 1.66/1.43 ($false = ($true => (sK6 @ sK8 @ sK7))) | (~spl0_2 | ~spl0_3)),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f280])).
% 1.66/1.43 thf(f280,plain,(
% 1.66/1.43 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) | $true) => (sK6 @ sK8 @ sK7))) | (~spl0_2 | ~spl0_3)),
% 1.66/1.43 inference(forward_demodulation,[status(thm)],[f279,f168])).
% 1.66/1.43 thf(f168,plain,(
% 1.66/1.43 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK7))))) | ~spl0_3),
% 1.66/1.43 inference(avatar_component_clause,[status(thm)],[f167])).
% 1.66/1.43 thf(f176,plain,(
% 1.66/1.43 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK5 @ Y1 @ Y0) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y0) & (X1 @ Y0 @ Y2)) => (X1 @ Y1 @ Y2))))))))) => (X1 @ sK8 @ sK7)))) ) | ~spl0_3),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f175])).
% 1.66/1.43 thf(f175,plain,(
% 1.66/1.43 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK7))) @ X1))) ) | ~spl0_3),
% 1.66/1.43 inference(pi_clausification,[status(thm)],[f168])).
% 1.66/1.43 thf(f261,plain,(
% 1.66/1.43 ~spl0_1),
% 1.66/1.43 inference(avatar_contradiction_clause,[status(thm)],[f260])).
% 1.66/1.43 thf(f260,plain,(
% 1.66/1.43 $false | ~spl0_1),
% 1.66/1.43 inference(trivial_inequality_removal,[status(thm)],[f256])).
% 1.66/1.43 thf(f256,plain,(
% 1.66/1.43 ($false = $true) | ~spl0_1),
% 1.66/1.43 inference(superposition,[status(thm)],[f253,f70])).
% 1.66/1.43 thf(f253,plain,(
% 1.66/1.43 ((((sK6 @ sK14 @ sK12) & (sK6 @ sK12 @ sK13)) => (sK6 @ sK14 @ sK13)) = $false) | ~spl0_1),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f252])).
% 1.66/1.43 thf(f252,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (((sK6 @ Y0 @ sK12) & (sK6 @ sK12 @ sK13)) => (sK6 @ Y0 @ sK13))) @ sK14)) | ~spl0_1),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f251])).
% 1.66/1.43 thf(f251,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0 @ sK12) & (sK6 @ sK12 @ sK13)) => (sK6 @ Y0 @ sK13))))) | ~spl0_1),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f250])).
% 1.66/1.43 thf(f250,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ sK12) & (sK6 @ sK12 @ Y0)) => (sK6 @ Y1 @ Y0))))) @ sK13)) | ~spl0_1),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f249])).
% 1.66/1.43 thf(f249,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ sK12) & (sK6 @ sK12 @ Y0)) => (sK6 @ Y1 @ Y0))))))) | ~spl0_1),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f245])).
% 1.66/1.43 thf(f245,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1))))))) @ sK12)) | ~spl0_1),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f104])).
% 1.66/1.43 thf(f104,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1))))))))) | ~spl0_1),
% 1.66/1.43 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.66/1.43 thf(f103,definition,(
% 1.66/1.43 spl0_1 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))))),
% 1.66/1.43 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.66/1.43 thf(f172,plain,(
% 1.66/1.43 spl0_3 | spl0_4 | ~spl0_2),
% 1.66/1.43 inference(avatar_split_clause,[status(thm)],[f165,f106,f170,f167])).
% 1.66/1.43 thf(f165,plain,(
% 1.66/1.43 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK7))))) | ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7))))) | ~spl0_2),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.66/1.43 thf(f119,plain,(
% 1.66/1.43 ($true = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK7)))))) | ~spl0_2),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.66/1.43 thf(f117,plain,(
% 1.66/1.43 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK5 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK8 @ sK7))))) => (sK6 @ sK8 @ sK7))) | ~spl0_2),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.66/1.43 thf(f116,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ Y0 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK5 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK7))))) => (sK6 @ Y0 @ sK7))) @ sK8)) | ~spl0_2),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f115])).
% 1.66/1.43 thf(f115,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ Y0 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK5 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK7))))) => (sK6 @ Y0 @ sK7))))) | ~spl0_2),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f111])).
% 1.66/1.43 thf(f111,plain,(
% 1.66/1.43 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))) @ sK7)) | ~spl0_2),
% 1.66/1.43 inference(sigma_clausification,[status(thm)],[f107])).
% 1.66/1.43 thf(f108,plain,(
% 1.66/1.43 spl0_1 | spl0_2),
% 1.66/1.43 inference(avatar_split_clause,[status(thm)],[f99,f106,f103])).
% 1.66/1.43 thf(f99,plain,(
% 1.66/1.43 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))))),
% 1.66/1.43 inference(binary_proxy_clausification,[status(thm)],[f89])).
% 1.66/1.43 thf(f89,plain,(
% 1.66/1.43 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))))))),
% 1.66/1.43 inference(not_proxy_clausification,[status(thm)],[f52])).
% 1.66/1.43 thf(f52,plain,(
% 1.66/1.43 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0)))))))))),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f51])).
% 1.66/1.43 thf(f51,plain,(
% 1.66/1.43 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))))) => $false))),
% 1.66/1.43 inference(superposition,[status(thm)],[f43,f27])).
% 1.66/1.43 thf(f27,plain,(
% 1.66/1.43 ($false = (sK6 @ sK4 @ sK3))),
% 1.66/1.43 inference(boolean_simplification,[status(thm)],[f26])).
% 1.66/1.43 thf(f26,plain,(
% 1.66/1.43 ($false = ($true => (sK6 @ sK4 @ sK3)))),
% 1.66/1.43 inference(backward_demodulation,[status(thm)],[f23,f25])).
% 1.66/1.43 thf(f43,plain,(
% 1.66/1.43 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y2 @ Y0) & (X1 @ Y0 @ Y1)) => (X1 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK5 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK4 @ sK3)))) )),
% 1.66/1.43 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.66/1.43 thf(f42,plain,(
% 1.66/1.43 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK5 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3))) @ X1))) )),
% 1.66/1.43 inference(pi_clausification,[status(thm)],[f19])).
% 1.66/1.43 % SZS output end Proof for DTF2THF_22134
% 1.66/1.43 % (22362)------------------------------
% 1.66/1.43 % (22362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (22362)Termination reason: Refutation
% 1.66/1.43
% 1.66/1.43 % (22362)Memory used [KB]: 6652
% 1.66/1.43 % (22362)Time elapsed: 0.098 s
% 1.66/1.43 % (22362)Instructions burned: 283 (million)
% 1.66/1.43 % (22362)------------------------------
% 1.66/1.43 % (22362)------------------------------
% 1.66/1.43 % (22350)Success in time 0.116 s
%------------------------------------------------------------------------------