%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV155^5 : 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 : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:25 AM UTC 2026
% Result : Theorem 1.65s 1.50s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 18
% Syntax : Number of formulae : 320 ( 32 unt; 0 typ; 17 def)
% Number of atoms : 3797 ( 298 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 13005 ( 421 ~; 699 |; 698 &;8294 @)
% ( 17 <=>;1068 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 1020 (1020 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 50 con; 0-2 aty)
% (1808 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2132 (1874 ^; 258 !; 0 ?;2132 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a > a > $o ).
thf(func_def_22,type,
sK3: a ).
thf(func_def_23,type,
sK4: a > a > $o ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a > a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a > a > $o ).
thf(func_def_29,type,
sK10: a ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a > a > $o ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a ).
thf(func_def_50,type,
sK31: a ).
thf(func_def_51,type,
sK32: a ).
thf(func_def_52,type,
sK33: a ).
thf(func_def_53,type,
sK34: a ).
thf(func_def_54,type,
sK35: a ).
thf(func_def_55,type,
sK36: a ).
thf(f1556,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f56,f75,f118,f249,f285,f401,f427,f444,f463,f578,f595,f623,f901,f956,f992,f1306,f1316,f1555]) ).
thf(f1555,plain,
( ~ spl0_4
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f1554]) ).
thf(f1554,plain,
( $false
| ~ spl0_4
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1553]) ).
thf(f1553,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f1546,f1462]) ).
thf(f1462,plain,
( ( $false
= ( sK13 @ sK33 @ sK34 ) )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1461]) ).
thf(f1461,plain,
( ( ( $true
=> ( sK13 @ sK33 @ sK34 ) )
= $false )
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f1450,f1460]) ).
thf(f1460,plain,
( ( $true
= ( ( sK13 @ sK33 @ sK35 )
& ( sK13 @ sK35 @ sK34 ) ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f1450]) ).
thf(f1450,plain,
( ( $false
= ( ( ( sK13 @ sK33 @ sK35 )
& ( sK13 @ sK35 @ sK34 ) )
=> ( sK13 @ sK33 @ sK34 ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f1449]) ).
thf(f1449,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK13 @ sK33 @ Y0 )
& ( sK13 @ Y0 @ sK34 ) )
=> ( sK13 @ sK33 @ sK34 ) )
@ sK35 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f1445]) ).
thf(f1445,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ sK33 @ Y0 )
& ( sK13 @ Y0 @ sK34 ) )
=> ( sK13 @ sK33 @ sK34 ) ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f1444]) ).
thf(f1444,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ sK33 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ sK33 @ Y0 ) ) )
@ sK34 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f1432]) ).
thf(f1432,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ sK33 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ sK33 @ Y0 ) ) ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f1430]) ).
thf(f1430,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y2 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) )
@ sK33 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f400]) ).
thf(f400,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y2 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f399]) ).
thf(f399,definition,
( spl0_11
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y2 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f1546,plain,
( ( $true
= ( sK13 @ sK33 @ sK34 ) )
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1544]) ).
thf(f1544,plain,
( ( $true
= ( $true
=> ( sK13 @ sK33 @ sK34 ) ) )
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f1508,f1500]) ).
thf(f1500,plain,
( ( $true
= ( sK13 @ sK36 @ sK34 ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f1487]) ).
thf(f1487,plain,
( ( $true
= ( ( sK13 @ sK33 @ sK36 )
& ( sK13 @ sK36 @ sK34 ) ) )
| ~ spl0_11 ),
inference(not_proxy_clausification,[status(thm)],[f1476]) ).
thf(f1476,plain,
( ( $false
= ( ~ ( ( sK13 @ sK33 @ sK36 )
& ( sK13 @ sK36 @ sK34 ) ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f1475]) ).
thf(f1475,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK13 @ sK33 @ Y0 )
& ( sK13 @ Y0 @ sK34 ) )
@ sK36 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f1464]) ).
thf(f1464,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK13 @ sK33 @ Y0 )
& ( sK13 @ Y0 @ sK34 ) ) )
= $false )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1463]) ).
thf(f1463,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ sK33 @ Y0 )
& ( sK13 @ Y0 @ sK34 ) )
=> $false ) )
= $false )
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f1445,f1462]) ).
thf(f1508,plain,
( ! [X0: a] :
( $true
= ( ( sK13 @ sK36 @ X0 )
=> ( sK13 @ sK33 @ X0 ) ) )
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1505]) ).
thf(f1505,plain,
( ! [X0: a] :
( $true
= ( ( ( sK13 @ sK36 @ X0 )
& $true )
=> ( sK13 @ sK33 @ X0 ) ) )
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f1342,f1503]) ).
thf(f1503,plain,
( ( $true
= ( sK13 @ sK33 @ sK36 ) )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1502]) ).
thf(f1502,plain,
( ( $true
= ( ( sK13 @ sK33 @ sK36 )
& $true ) )
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f1487,f1500]) ).
thf(f1342,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK13 @ X1 @ X2 )
& ( sK13 @ X3 @ X1 ) )
=> ( sK13 @ X3 @ X2 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1341]) ).
thf(f1341,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK13 @ X1 @ X2 )
& ( sK13 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X2 ) )
@ X3 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f1332]) ).
thf(f1332,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ X1 @ X2 )
& ( sK13 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X2 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1331]) ).
thf(f1331,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ X1 @ Y0 )
& ( sK13 @ Y1 @ X1 ) )
=> ( sK13 @ Y1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f1320]) ).
thf(f1320,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ X1 @ Y0 )
& ( sK13 @ Y1 @ X1 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1317]) ).
thf(f1317,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f1111]) ).
thf(f1111,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f1053]) ).
thf(f1053,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f1046]) ).
thf(f1046,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK13 @ sK10 @ sK12 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1045]) ).
thf(f1045,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK12 ) )
@ sK13 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f1025]) ).
thf(f1025,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f1021]) ).
thf(f1021,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK12 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1020]) ).
thf(f1020,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ sK11 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f1015]) ).
thf(f1015,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ sK11 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1014]) ).
thf(f1014,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ sK10 @ Y1 ) ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f1001]) ).
thf(f1001,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ sK10 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1000]) ).
thf(f1000,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) )
@ sK10 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f73,definition,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1316,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f1315]) ).
thf(f1315,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1314]) ).
thf(f1314,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1313]) ).
thf(f1313,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1312]) ).
thf(f1312,plain,
( ( $true
= ( ~ ( $true
| ( sK4 @ sK14 @ sK15 ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f1311,f284]) ).
thf(f284,plain,
( ( $true
= ( sK2 @ sK14 @ sK15 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f283]) ).
thf(f283,definition,
( spl0_10
<=> ( $true
= ( sK2 @ sK14 @ sK15 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f1311,plain,
( ( $true
= ( ~ ( ( sK2 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1310]) ).
thf(f1310,plain,
( ( $true
= ( ( ( sK2 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f1156,f1309]) ).
thf(f1309,plain,
( ( ( sK13 @ sK14 @ sK15 )
= $false )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1308]) ).
thf(f1308,plain,
( ( $false
= ( $true
=> ( sK13 @ sK14 @ sK15 ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1307]) ).
thf(f1307,plain,
( ( $false
= ( ( ( sK4 @ sK14 @ sK15 )
| $true )
=> ( sK13 @ sK14 @ sK15 ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f1300,f284]) ).
thf(f1300,plain,
( ( ( ( ( sK4 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) )
=> ( sK13 @ sK14 @ sK15 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1299]) ).
thf(f1299,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK14 @ Y0 )
| ( sK2 @ sK14 @ Y0 ) )
=> ( sK13 @ sK14 @ Y0 ) )
@ sK15 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f1295]) ).
thf(f1295,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK14 @ Y0 )
| ( sK2 @ sK14 @ Y0 ) )
=> ( sK13 @ sK14 @ Y0 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1288]) ).
thf(f1288,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) )
@ sK14 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f245]) ).
thf(f245,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f244]) ).
thf(f244,definition,
( spl0_7
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f1156,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK2 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) )
=> ( sK13 @ X2 @ X1 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1155]) ).
thf(f1155,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f1139]) ).
thf(f1139,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1138]) ).
thf(f1138,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f1114]) ).
thf(f1114,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1113]) ).
thf(f1113,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f1053,f1111]) ).
thf(f1306,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f1305]) ).
thf(f1305,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1304]) ).
thf(f1304,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f1170,f1303]) ).
thf(f1303,plain,
( ( ( sK13 @ sK14 @ sK15 )
= $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1302]) ).
thf(f1302,plain,
( ( $false
= ( $true
=> ( sK13 @ sK14 @ sK15 ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1301]) ).
thf(f1301,plain,
( ( ( ( $true
| ( sK2 @ sK14 @ sK15 ) )
=> ( sK13 @ sK14 @ sK15 ) )
= $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f1300,f281]) ).
thf(f281,plain,
( ( $true
= ( sK4 @ sK14 @ sK15 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f280]) ).
thf(f280,definition,
( spl0_9
<=> ( $true
= ( sK4 @ sK14 @ sK15 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f1170,plain,
( ( $true
= ( sK13 @ sK14 @ sK15 ) )
| ~ spl0_4
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1169]) ).
thf(f1169,plain,
( ( $true
= ( $true
=> ( sK13 @ sK14 @ sK15 ) ) )
| ~ spl0_4
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1165]) ).
thf(f1165,plain,
( ( $true
= ( ( ( sK2 @ sK14 @ sK15 )
| $true )
=> ( sK13 @ sK14 @ sK15 ) ) )
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f1156,f281]) ).
thf(f992,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f991]) ).
thf(f991,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(trivial_inequality_removal,[status(thm)],[f987]) ).
thf(f987,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(superposition,[status(thm)],[f976,f672]) ).
thf(f672,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK9 @ X1 @ X2 )
& ( sK9 @ X2 @ X3 ) )
=> ( sK9 @ X1 @ X3 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f671]) ).
thf(f671,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK9 @ X1 @ X2 )
& ( sK9 @ X2 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) )
@ X3 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f656]) ).
thf(f656,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ X1 @ X2 )
& ( sK9 @ X2 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f655]) ).
thf(f655,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ X1 @ Y0 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f651]) ).
thf(f651,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ X1 @ Y0 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f650]) ).
thf(f650,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f641]) ).
thf(f641,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f640]) ).
thf(f640,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f633,f639]) ).
thf(f639,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f633]) ).
thf(f633,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f628]) ).
thf(f628,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK9 @ sK8 @ sK7 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f627]) ).
thf(f627,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK9 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f626]) ).
thf(f626,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f625]) ).
thf(f625,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f624]) ).
thf(f624,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f473,f117]) ).
thf(f117,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f116]) ).
thf(f116,definition,
( spl0_6
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f473,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f472]) ).
thf(f472,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f469]) ).
thf(f469,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f468]) ).
thf(f468,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK7 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f976,plain,
( ( $false
= ( ( ( sK9 @ sK32 @ sK31 )
& ( sK9 @ sK31 @ sK30 ) )
=> ( sK9 @ sK32 @ sK30 ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f975]) ).
thf(f975,plain,
( ( ( ^ [Y0: a] :
( ( ( sK9 @ Y0 @ sK31 )
& ( sK9 @ sK31 @ sK30 ) )
=> ( sK9 @ Y0 @ sK30 ) )
@ sK32 )
= $false )
| ~ spl0_22 ),
inference(sigma_clausification,[status(thm)],[f968]) ).
thf(f968,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ Y0 @ sK31 )
& ( sK9 @ sK31 @ sK30 ) )
=> ( sK9 @ Y0 @ sK30 ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f967]) ).
thf(f967,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ sK30 ) )
=> ( sK9 @ Y1 @ sK30 ) ) )
@ sK31 ) )
| ~ spl0_22 ),
inference(sigma_clausification,[status(thm)],[f963]) ).
thf(f963,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ sK30 ) )
=> ( sK9 @ Y1 @ sK30 ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[status(thm)],[f959]) ).
thf(f959,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) )
@ sK30 )
= $false )
| ~ spl0_22 ),
inference(sigma_clausification,[status(thm)],[f897]) ).
thf(f897,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_22 ),
inference(avatar_component_clause,[status(thm)],[f896]) ).
thf(f896,definition,
( spl0_22
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition]) ).
thf(f956,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f955]) ).
thf(f955,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f954]) ).
thf(f954,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f953]) ).
thf(f953,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f952]) ).
thf(f952,plain,
( ( $true
= ( ~ ( ( sK4 @ sK29 @ sK28 )
| $true ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f951,f939]) ).
thf(f939,plain,
( ( $true
= ( sK2 @ sK29 @ sK28 ) )
| ~ spl0_23 ),
inference(binary_proxy_clausification,[status(thm)],[f927]) ).
thf(f927,plain,
( ( ( ( sK2 @ sK29 @ sK28 )
=> ( sK9 @ sK29 @ sK28 ) )
= $false )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f926]) ).
thf(f926,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK28 )
=> ( sK9 @ Y0 @ sK28 ) )
@ sK29 ) )
| ~ spl0_23 ),
inference(sigma_clausification,[status(thm)],[f914]) ).
thf(f914,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK28 )
=> ( sK9 @ Y0 @ sK28 ) ) )
= $false )
| ~ spl0_23 ),
inference(beta_eta_normalization,[status(thm)],[f910]) ).
thf(f910,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) )
@ sK28 ) )
| ~ spl0_23 ),
inference(sigma_clausification,[status(thm)],[f900]) ).
thf(f900,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[status(thm)],[f899]) ).
thf(f899,definition,
( spl0_23
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition]) ).
thf(f951,plain,
( ( $true
= ( ~ ( ( sK4 @ sK29 @ sK28 )
| ( sK2 @ sK29 @ sK28 ) ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f942]) ).
thf(f942,plain,
( ( $true
= ( ( ( sK4 @ sK29 @ sK28 )
| ( sK2 @ sK29 @ sK28 ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f840,f941]) ).
thf(f941,plain,
( ( ( sK9 @ sK29 @ sK28 )
= $false )
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f940]) ).
thf(f940,plain,
( ( $false
= ( $true
=> ( sK9 @ sK29 @ sK28 ) ) )
| ~ spl0_23 ),
inference(backward_demodulation,[status(thm)],[f927,f939]) ).
thf(f840,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK4 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
=> ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f839]) ).
thf(f839,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f824]) ).
thf(f824,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f823]) ).
thf(f823,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f639]) ).
thf(f901,plain,
( spl0_22
| spl0_23
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f892,f116,f70,f899,f896]) ).
thf(f892,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f886]) ).
thf(f886,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(not_proxy_clausification,[status(thm)],[f743]) ).
thf(f743,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f740]) ).
thf(f740,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f729,f632]) ).
thf(f632,plain,
( ( ( sK9 @ sK8 @ sK7 )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f628]) ).
thf(f729,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK8 @ sK7 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f728]) ).
thf(f728,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 ) )
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f117]) ).
thf(f623,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f622]) ).
thf(f622,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f621]) ).
thf(f621,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f620]) ).
thf(f620,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f619]) ).
thf(f619,plain,
( ( $true
= ( ~ ( $true
| ( sK2 @ sK25 @ sK24 ) ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[status(thm)],[f617,f606]) ).
thf(f606,plain,
( ( $true
= ( sK4 @ sK25 @ sK24 ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f604]) ).
thf(f604,plain,
( ( ( ( sK4 @ sK25 @ sK24 )
=> ( sK9 @ sK25 @ sK24 ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f603]) ).
thf(f603,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK4 @ Y0 @ sK24 )
=> ( sK9 @ Y0 @ sK24 ) )
@ sK25 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f602]) ).
thf(f602,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 @ sK24 )
=> ( sK9 @ Y0 @ sK24 ) ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f598]) ).
thf(f598,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) )
@ sK24 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f577]) ).
thf(f577,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f576]) ).
thf(f576,definition,
( spl0_15
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f617,plain,
( ( $true
= ( ~ ( ( sK4 @ sK25 @ sK24 )
| ( sK2 @ sK25 @ sK24 ) ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f612]) ).
thf(f612,plain,
( ( $true
= ( ( ( sK4 @ sK25 @ sK24 )
| ( sK2 @ sK25 @ sK24 ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f498,f608]) ).
thf(f608,plain,
( ( $false
= ( sK9 @ sK25 @ sK24 ) )
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f607]) ).
thf(f607,plain,
( ( ( $true
=> ( sK9 @ sK25 @ sK24 ) )
= $false )
| ~ spl0_15 ),
inference(backward_demodulation,[status(thm)],[f604,f606]) ).
thf(f498,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK4 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
=> ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f497]) ).
thf(f497,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f494]) ).
thf(f494,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f493]) ).
thf(f493,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f490]) ).
thf(f490,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f481]) ).
thf(f481,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f479]) ).
thf(f479,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK9 @ sK8 @ sK7 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f478]) ).
thf(f478,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK9 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f476]) ).
thf(f476,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f475]) ).
thf(f475,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f474]) ).
thf(f474,plain,
( ( ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f473,f114]) ).
thf(f114,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f113,definition,
( spl0_5
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f595,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f594]) ).
thf(f594,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f590]) ).
thf(f590,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f500,f587]) ).
thf(f587,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ sK22 @ sK21 )
& ( sK9 @ sK21 @ Y0 ) )
=> ( sK9 @ sK22 @ Y0 ) ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f586]) ).
thf(f586,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y0 @ sK21 )
& ( sK9 @ sK21 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ sK22 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[status(thm)],[f583]) ).
thf(f583,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y0 @ sK21 )
& ( sK9 @ sK21 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f581]) ).
thf(f581,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
@ sK21 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[status(thm)],[f574]) ).
thf(f574,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f573]) ).
thf(f573,definition,
( spl0_14
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f500,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ X1 @ X2 )
& ( sK9 @ X2 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f499]) ).
thf(f499,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ X1 @ Y0 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f496]) ).
thf(f496,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ X1 @ Y0 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f495]) ).
thf(f495,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f492]) ).
thf(f492,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f491]) ).
thf(f491,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f481,f490]) ).
thf(f578,plain,
( spl0_14
| spl0_15
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f569,f113,f70,f576,f573]) ).
thf(f569,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f486]) ).
thf(f486,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(not_proxy_clausification,[status(thm)],[f485]) ).
thf(f485,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f484]) ).
thf(f484,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ Y2 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f471,f483]) ).
thf(f483,plain,
( ( ( sK9 @ sK8 @ sK7 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f482]) ).
thf(f482,plain,
( ( $false
= ( $true
=> ( sK9 @ sK8 @ sK7 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f479,f481]) ).
thf(f471,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y0 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK8 @ sK7 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f470]) ).
thf(f470,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 ) )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f114]) ).
thf(f463,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[status(thm)],[f462]) ).
thf(f462,plain,
( $false
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f457]) ).
thf(f457,plain,
( ( $true = $false )
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f455,f37]) ).
thf(f37,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ X2 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f25,f30]) ).
thf(f30,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK5 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f17,f19]) ).
thf(f19,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK3 ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK3 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( Y0 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ sK3 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( Y0 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ sK3 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a,X3: a > a > $o] :
( ( ( ! [X4: a,X5: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X3 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X9: a,X10: a,X11: a] :
( ( ( X6 @ X10 @ X11 )
& ( X6 @ X9 @ X10 ) )
=> ( X6 @ X9 @ X11 ) ) )
=> ( X6 @ X4 @ X5 ) )
| ! [X12: a > a > $o] :
( ( ! [X13: a,X14: a] :
( ( X1 @ X13 @ X14 )
=> ( X12 @ X13 @ X14 ) )
& ! [X15: a,X16: a,X17: a] :
( ( ( X12 @ X17 @ X15 )
& ( X12 @ X16 @ X17 ) )
=> ( X12 @ X16 @ X15 ) ) )
=> ( X12 @ X4 @ X5 ) ) )
=> ! [X18: a > a > $o] :
( ( ! [X19: a,X20: a,X21: a] :
( ( ( X18 @ X20 @ X19 )
& ( X18 @ X21 @ X20 ) )
=> ( X18 @ X21 @ X19 ) )
& ! [X22: a,X23: a] :
( ( ( X3 @ X23 @ X22 )
| ( X1 @ X23 @ X22 ) )
=> ( X18 @ X23 @ X22 ) ) )
=> ( X18 @ X4 @ X5 ) ) )
& ! [X24: a,X25: a,X26: a] :
( ( ! [X27: a > a > $o] :
( ( ! [X28: a,X29: a,X30: a] :
( ( ( X27 @ X28 @ X30 )
& ( X27 @ X30 @ X29 ) )
=> ( X27 @ X28 @ X29 ) )
& ! [X31: a,X32: a] :
( ( ( X3 @ X32 @ X31 )
| ( X1 @ X32 @ X31 ) )
=> ( X27 @ X32 @ X31 ) ) )
=> ( X27 @ X25 @ X24 ) )
& ! [X33: a > a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( X3 @ X35 @ X34 )
| ( X1 @ X35 @ X34 ) )
=> ( X33 @ X35 @ X34 ) )
& ! [X36: a,X37: a,X38: a] :
( ( ( X33 @ X36 @ X37 )
& ( X33 @ X38 @ X36 ) )
=> ( X33 @ X38 @ X37 ) ) )
=> ( X33 @ X26 @ X25 ) ) )
=> ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a,X42: a] :
( ( ( X39 @ X40 @ X42 )
& ( X39 @ X42 @ X41 ) )
=> ( X39 @ X40 @ X41 ) )
& ! [X43: a,X44: a] :
( ( ( X1 @ X43 @ X44 )
| ( X3 @ X43 @ X44 ) )
=> ( X39 @ X43 @ X44 ) ) )
=> ( X39 @ X26 @ X24 ) ) ) )
=> ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a,X48: a] :
( ( ( X45 @ X48 @ X47 )
& ( X45 @ X46 @ X48 ) )
=> ( X45 @ X46 @ X47 ) )
& ! [X49: a,X50: a] :
( ( ( X1 @ X49 @ X50 )
| ( X3 @ X49 @ X50 ) )
=> ( X45 @ X49 @ X50 ) ) )
=> ( X45 @ X0 @ X2 ) ) )
=> ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a] :
( ( ( X1 @ X53 @ X52 )
| ( X3 @ X53 @ X52 ) )
=> ( X51 @ X53 @ X52 ) )
& ! [X54: a,X55: a,X56: a] :
( ( ( X51 @ X55 @ X56 )
& ( X51 @ X54 @ X55 ) )
=> ( X51 @ X54 @ X56 ) ) )
=> ( X51 @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X1: a > a > $o,X3: a,X0: a > a > $o] :
( ( ( ! [X4: a,X5: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
| ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X9: a,X7: a,X8: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X9: a,X8: a,X7: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) )
& ! [X8: a,X7: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
& ! [X9: a,X5: a,X4: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X10: a,X8: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X8: a,X7: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X5 @ X9 ) )
& ! [X6: a > a > $o] :
( ( ! [X8: a,X7: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
& ! [X8: a,X10: a,X7: a] :
( ( ( X6 @ X8 @ X10 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X10 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X7: a,X10: a,X8: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X7: a,X8: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X9 ) ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X4: a,X9: a,X5: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) )
& ! [X4: a,X5: a] :
( ( ( X1 @ X4 @ X5 )
| ( X0 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X6 @ X2 @ X3 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X1 @ X4 @ X5 )
| ( X0 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) )
& ! [X4: a,X5: a,X9: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) ) )
=> ( X6 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a,X1: a > a > $o,X3: a,X0: a > a > $o] :
( ( ( ! [X4: a,X5: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
| ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X9: a,X7: a,X8: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X9: a,X8: a,X7: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) )
& ! [X8: a,X7: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
& ! [X9: a,X5: a,X4: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X10: a,X8: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X8: a,X7: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X5 @ X9 ) )
& ! [X6: a > a > $o] :
( ( ! [X8: a,X7: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
& ! [X8: a,X10: a,X7: a] :
( ( ( X6 @ X8 @ X10 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X10 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X7: a,X10: a,X8: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X7: a,X8: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X9 ) ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X4: a,X9: a,X5: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) )
& ! [X4: a,X5: a] :
( ( ( X1 @ X4 @ X5 )
| ( X0 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X6 @ X2 @ X3 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X1 @ X4 @ X5 )
| ( X0 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) )
& ! [X4: a,X5: a,X9: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) ) )
=> ( X6 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QkaXZIWX9l/DTF2THF_29067.p',cTHM250D_pme) ).
thf(f455,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK18 )
& ( sK6 @ sK18 @ sK19 ) )
=> ( sK6 @ Y0 @ sK19 ) ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f454]) ).
thf(f454,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ sK18 )
& ( sK6 @ sK18 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK19 )
= $false )
| ~ spl0_13 ),
inference(sigma_clausification,[status(thm)],[f453]) ).
thf(f453,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ sK18 )
& ( sK6 @ sK18 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f449]) ).
thf(f449,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) )
@ sK18 )
= $false )
| ~ spl0_13 ),
inference(sigma_clausification,[status(thm)],[f426]) ).
thf(f426,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f425]) ).
thf(f425,definition,
( spl0_13
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f444,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[status(thm)],[f443]) ).
thf(f443,plain,
( $false
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f440]) ).
thf(f440,plain,
( ( $true = $false )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f92,f436]) ).
thf(f436,plain,
( ( $false
= ( ( ( sK2 @ sK17 @ sK16 )
| ( sK4 @ sK17 @ sK16 ) )
=> ( sK6 @ sK17 @ sK16 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f435]) ).
thf(f435,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK16 )
| ( sK4 @ Y0 @ sK16 ) )
=> ( sK6 @ Y0 @ sK16 ) )
@ sK17 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f432]) ).
thf(f432,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK16 )
| ( sK4 @ Y0 @ sK16 ) )
=> ( sK6 @ Y0 @ sK16 ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f430]) ).
thf(f430,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK16 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f423]) ).
thf(f423,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f422]) ).
thf(f422,definition,
( spl0_12
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f92,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X1 @ X2 )
| ( sK4 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f427,plain,
( spl0_12
| spl0_13
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f418,f51,f425,f422]) ).
thf(f51,definition,
( spl0_1
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f418,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f415]) ).
thf(f415,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f414]) ).
thf(f414,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f408]) ).
thf(f408,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f405,f24]) ).
thf(f24,plain,
( $false
= ( sK6 @ sK5 @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f405,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK5 @ sK3 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f404]) ).
thf(f404,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f401,plain,
( spl0_11
| spl0_7
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f395,f247,f73,f244,f399]) ).
thf(f247,definition,
( spl0_8
<=> ( $true
= ( sK13 @ sK11 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f395,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y2 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f392]) ).
thf(f392,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y2 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[status(thm)],[f321]) ).
thf(f321,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y2 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f319]) ).
thf(f319,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y2 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f224,f296]) ).
thf(f296,plain,
( ( ( sK13 @ sK10 @ sK11 )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f288]) ).
thf(f288,plain,
( ( $false
= ( $true
& ( sK13 @ sK10 @ sK11 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f225,f248]) ).
thf(f248,plain,
( ( $true
= ( sK13 @ sK11 @ sK12 ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f247]) ).
thf(f225,plain,
( ! [X0: a] :
( $false
= ( ( sK13 @ X0 @ sK12 )
& ( sK13 @ sK10 @ X0 ) ) )
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f214]) ).
thf(f214,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK13 @ X0 @ sK12 )
& ( sK13 @ sK10 @ X0 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f207]) ).
thf(f207,plain,
( ! [X0: a] :
( $true
= ( ( ( sK13 @ X0 @ sK12 )
& ( sK13 @ sK10 @ X0 ) )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f197,f152]) ).
thf(f152,plain,
( ( ( sK13 @ sK10 @ sK12 )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f151]) ).
thf(f151,plain,
( ( $false
= ( $true
=> ( sK13 @ sK10 @ sK12 ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f148,f150]) ).
thf(f150,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK13 @ sK10 @ sK12 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f147]) ).
thf(f147,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK12 ) )
@ sK13 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK12 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f139]) ).
thf(f139,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ sK11 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ sK11 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f133]) ).
thf(f133,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ sK10 @ Y1 ) ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ sK10 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) )
@ sK10 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f74]) ).
thf(f197,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK13 @ X1 @ X2 )
& ( sK13 @ X3 @ X1 ) )
=> ( sK13 @ X3 @ X2 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f196]) ).
thf(f196,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK13 @ X1 @ X2 )
& ( sK13 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X2 ) )
@ X3 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ X1 @ X2 )
& ( sK13 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X2 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f186]) ).
thf(f186,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ X1 @ Y0 )
& ( sK13 @ Y1 @ X1 ) )
=> ( sK13 @ Y1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ X1 @ Y0 )
& ( sK13 @ Y1 @ X1 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f179]) ).
thf(f179,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f155]) ).
thf(f155,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f150,f154]) ).
thf(f154,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f150]) ).
thf(f224,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK10 @ sK11 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f223]) ).
thf(f223,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f285,plain,
( spl0_9
| spl0_10
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f278,f244,f283,f280]) ).
thf(f278,plain,
( ( $true
= ( sK4 @ sK14 @ sK15 ) )
| ( $true
= ( sK2 @ sK14 @ sK15 ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f263]) ).
thf(f263,plain,
( ( $true
= ( ( sK4 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f261]) ).
thf(f261,plain,
( ( ( ( ( sK4 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) )
=> ( sK13 @ sK14 @ sK15 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f260]) ).
thf(f260,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK14 @ Y0 )
| ( sK2 @ sK14 @ Y0 ) )
=> ( sK13 @ sK14 @ Y0 ) )
@ sK15 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f257]) ).
thf(f257,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK14 @ Y0 )
| ( sK2 @ sK14 @ Y0 ) )
=> ( sK13 @ sK14 @ Y0 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f252]) ).
thf(f252,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) )
@ sK14 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f245]) ).
thf(f249,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f242,f73,f247,f244]) ).
thf(f242,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( sK13 @ sK11 @ sK12 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f181]) ).
thf(f181,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) )
=> ( sK13 @ sK11 @ sK12 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f180]) ).
thf(f180,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) )
& $true )
=> ( sK13 @ sK11 @ sK12 ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f164,f156]) ).
thf(f164,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK11 @ sK12 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f163]) ).
thf(f163,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f160]) ).
thf(f160,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f159]) ).
thf(f159,plain,
( ( $true
= ( $true
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f142,f158]) ).
thf(f118,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f111,f70,f116,f113]) ).
thf(f111,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK7 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f71]) ).
thf(f75,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f68,f54,f73,f70]) ).
thf(f54,definition,
( spl0_2
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f68,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f56,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f49,f54,f51]) ).
thf(f49,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK3 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV155^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.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 12:42:03 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
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEV155^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.47 % Domain : Set Theory (Relations)
% 0.28/0.47 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : tps_1232 [Bro09]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.42 v9.1.0, 0.50 v9.0.0, 0.42 v8.2.0, 0.27 v8.1.0, 0.42 v7.5.0, 0.58 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 1.00 v4.0.0
% 0.28/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.28/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.28/0.47 % Number of connectives : 161 ( 0 ~; 7 |; 18 &; 108 @)
% 0.28/0.47 % ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 23 ( 23 avg)
% 0.28/0.47 % Number of types : 2 ( 1 usr)
% 0.28/0.47 % Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.28/0.47 % Number of variables : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% 0.28/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(a_type,type,
% 0.28/0.47 a: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(cTHM250D_pme,conjecture,
% 0.28/0.47 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.28/0.47 ( ( ( ! [Xx0: a,Xy0: a] :
% 0.28/0.47 ( ( ! [Xp1: a > a > $o] :
% 0.28/0.47 ( ( ! [Xx1: a,Xy1: a] :
% 0.28/0.47 ( ( R @ Xx1 @ Xy1 )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.28/0.47 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.28/0.47 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.28/0.47 & ( Xp1 @ Xy1 @ Xz ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.28/0.47 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.28/0.47 | ! [Xp1: a > a > $o] :
% 0.28/0.47 ( ( ! [Xx1: a,Xy1: a] :
% 0.28/0.47 ( ( S @ Xx1 @ Xy1 )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.28/0.47 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.28/0.47 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.28/0.47 & ( Xp1 @ Xy1 @ Xz ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.28/0.47 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 0.28/0.47 => ! [Xp1: a > a > $o] :
% 0.28/0.47 ( ( ! [Xx1: a,Xy1: a] :
% 0.28/0.47 ( ( ( R @ Xx1 @ Xy1 )
% 0.28/0.47 | ( S @ Xx1 @ Xy1 ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.28/0.47 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.28/0.47 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.28/0.47 & ( Xp1 @ Xy1 @ Xz ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.28/0.47 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 0.28/0.47 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.28/0.47 ( ( ! [Xp1: a > a > $o] :
% 0.28/0.47 ( ( ! [Xx1: a,Xy1: a] :
% 0.28/0.47 ( ( ( R @ Xx1 @ Xy1 )
% 0.28/0.47 | ( S @ Xx1 @ Xy1 ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.28/0.47 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.28/0.47 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.28/0.47 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.28/0.47 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.28/0.47 & ! [Xp1: a > a > $o] :
% 0.28/0.47 ( ( ! [Xx1: a,Xy1: a] :
% 0.28/0.47 ( ( ( R @ Xx1 @ Xy1 )
% 0.28/0.47 | ( S @ Xx1 @ Xy1 ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.28/0.47 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.28/0.47 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.28/0.47 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.28/0.47 => ( Xp1 @ Xy0 @ Xz ) ) )
% 0.28/0.47 => ! [Xp1: a > a > $o] :
% 0.28/0.47 ( ( ! [Xx1: a,Xy1: a] :
% 0.28/0.47 ( ( ( R @ Xx1 @ Xy1 )
% 0.28/0.47 | ( S @ Xx1 @ Xy1 ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.28/0.47 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.28/0.47 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.28/0.47 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.28/0.47 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.28/0.47 => ( Xp1 @ Xx0 @ Xz ) ) ) )
% 0.28/0.47 => ! [Xp1: a > a > $o] :
% 0.28/0.47 ( ( ! [Xx0: a,Xy0: a] :
% 0.28/0.47 ( ( ( R @ Xx0 @ Xy0 )
% 0.28/0.47 | ( S @ Xx0 @ Xy0 ) )
% 0.28/0.47 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.28/0.47 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.28/0.47 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.28/0.47 & ( Xp1 @ Xy0 @ Xz ) )
% 0.28/0.47 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.28/0.47 => ( Xp1 @ Xx @ Xy ) ) )
% 0.28/0.47 => ! [Xp1: a > a > $o] :
% 0.28/0.47 ( ( ! [Xx0: a,Xy0: a] :
% 0.28/0.47 ( ( ( R @ Xx0 @ Xy0 )
% 0.28/0.47 | ( S @ Xx0 @ Xy0 ) )
% 0.28/0.47 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.28/0.47 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.28/0.47 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.28/0.47 & ( Xp1 @ Xy0 @ Xz ) )
% 0.28/0.47 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.28/0.47 => ( Xp1 @ Xx @ Xy ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.50/1.27 ---- Embedded in THF ---
% 1.50/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.27 %%% Generated on Tue Feb 24 12:42:04 EST 2026
% 1.50/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.27 %%% Logic specification used:
% 1.50/1.27 %%% thf(spec, logic, $$dhol).
% 1.50/1.27
% 1.50/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.QkaXZIWX9l/DTF2DTF29067.p
% See solution above
% 1.50/1.27 ------------------------
% 1.50/1.29 ---- Cleaned THF ---
% 1.50/1.29 thf(a_type,type,
% 1.50/1.29 a: $tType ).
% 1.50/1.29
% 1.50/1.29 thf(cTHM250D_pme,conjecture,
% 1.50/1.29 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.50/1.29 ( ( ( ! [Xx0: a,Xy0: a] :
% 1.50/1.29 ( ( ! [Xp1: a > a > $o] :
% 1.50/1.29 ( ( ! [Xx1: a,Xy1: a] :
% 1.50/1.29 ( ( R @ Xx1 @ Xy1 )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.50/1.29 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.50/1.29 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.50/1.29 & ( Xp1 @ Xy1 @ Xz ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xz ) ) )
% 1.50/1.29 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.50/1.29 | ! [Xp1: a > a > $o] :
% 1.50/1.29 ( ( ! [Xx1: a,Xy1: a] :
% 1.50/1.29 ( ( S @ Xx1 @ Xy1 )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.50/1.29 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.50/1.29 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.50/1.29 & ( Xp1 @ Xy1 @ Xz ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xz ) ) )
% 1.50/1.29 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 1.50/1.29 => ! [Xp1: a > a > $o] :
% 1.50/1.29 ( ( ! [Xx1: a,Xy1: a] :
% 1.50/1.29 ( ( ( R @ Xx1 @ Xy1 )
% 1.50/1.29 | ( S @ Xx1 @ Xy1 ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.50/1.29 & ! [Xx1: a,Xy1: a,Xz: a] :
% 1.50/1.29 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.50/1.29 & ( Xp1 @ Xy1 @ Xz ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xz ) ) )
% 1.50/1.29 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 1.50/1.29 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.50/1.29 ( ( ! [Xp1: a > a > $o] :
% 1.50/1.29 ( ( ! [Xx1: a,Xy1: a] :
% 1.50/1.29 ( ( ( R @ Xx1 @ Xy1 )
% 1.50/1.29 | ( S @ Xx1 @ Xy1 ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.50/1.29 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 1.50/1.29 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.50/1.29 & ( Xp1 @ Xy1 @ Xz0 ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 1.50/1.29 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.50/1.29 & ! [Xp1: a > a > $o] :
% 1.50/1.29 ( ( ! [Xx1: a,Xy1: a] :
% 1.50/1.29 ( ( ( R @ Xx1 @ Xy1 )
% 1.50/1.29 | ( S @ Xx1 @ Xy1 ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.50/1.29 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 1.50/1.29 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.50/1.29 & ( Xp1 @ Xy1 @ Xz0 ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 1.50/1.29 => ( Xp1 @ Xy0 @ Xz ) ) )
% 1.50/1.29 => ! [Xp1: a > a > $o] :
% 1.50/1.29 ( ( ! [Xx1: a,Xy1: a] :
% 1.50/1.29 ( ( ( R @ Xx1 @ Xy1 )
% 1.50/1.29 | ( S @ Xx1 @ Xy1 ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xy1 ) )
% 1.50/1.29 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 1.50/1.29 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 1.50/1.29 & ( Xp1 @ Xy1 @ Xz0 ) )
% 1.50/1.29 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 1.50/1.29 => ( Xp1 @ Xx0 @ Xz ) ) ) )
% 1.50/1.29 => ! [Xp1: a > a > $o] :
% 1.50/1.29 ( ( ! [Xx0: a,Xy0: a] :
% 1.50/1.29 ( ( ( R @ Xx0 @ Xy0 )
% 1.50/1.29 | ( S @ Xx0 @ Xy0 ) )
% 1.50/1.29 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.50/1.29 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.50/1.29 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 1.50/1.29 & ( Xp1 @ Xy0 @ Xz ) )
% 1.50/1.29 => ( Xp1 @ Xx0 @ Xz ) ) )
% 1.50/1.29 => ( Xp1 @ Xx @ Xy ) ) )
% 1.50/1.29 => ! [Xp1: a > a > $o] :
% 1.50/1.29 ( ( ! [Xx0: a,Xy0: a] :
% 1.50/1.29 ( ( ( R @ Xx0 @ Xy0 )
% 1.50/1.29 | ( S @ Xx0 @ Xy0 ) )
% 1.50/1.29 => ( Xp1 @ Xx0 @ Xy0 ) )
% 1.50/1.29 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.50/1.29 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 1.50/1.29 & ( Xp1 @ Xy0 @ Xz ) )
% 1.50/1.29 => ( Xp1 @ Xx0 @ Xz ) ) )
% 1.50/1.29 => ( Xp1 @ Xx @ Xy ) ) ) ).
% 1.50/1.29 ------------------------
% 1.65/1.30 % (29299)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_29067 for (2999ds/275Mi)
% 1.65/1.30 % (29297)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/2Mi)
% 1.65/1.30 % (29297)Instruction limit reached!
% 1.65/1.30 % (29297)------------------------------
% 1.65/1.30 % (29297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (29297)Termination reason: Unknown
% 1.65/1.30 % (29297)Termination phase: Unused predicate definition removal
% 1.65/1.30
% 1.65/1.30 % (29297)Memory used [KB]: 1023
% 1.65/1.30 % (29297)Time elapsed: 0.002 s
% 1.65/1.30 % (29297)Instructions burned: 3 (million)
% 1.65/1.30 % (29297)------------------------------
% 1.65/1.30 % (29297)------------------------------
% 1.65/1.31 % (29295)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_29067 for (2999ds/4Mi)
% 1.65/1.31 % (29296)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_29067 for (2999ds/27Mi)
% 1.65/1.31 % (29294)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/183Mi)
% 1.65/1.31 % (29298)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_29067 for (2999ds/2Mi)
% 1.65/1.31 % (29300)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/18Mi)
% 1.65/1.31 % (29298)Instruction limit reached!
% 1.65/1.31 % (29298)------------------------------
% 1.65/1.31 % (29298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (29298)Termination reason: Unknown
% 1.65/1.31 % (29298)Termination phase: shuffling
% 1.65/1.31
% 1.65/1.31 % (29298)Memory used [KB]: 1023
% 1.65/1.31 % (29298)Time elapsed: 0.003 s
% 1.65/1.31 % (29298)Instructions burned: 2 (million)
% 1.65/1.31 % (29298)------------------------------
% 1.65/1.31 % (29298)------------------------------
% 1.65/1.31 % (29295)Instruction limit reached!
% 1.65/1.31 % (29295)------------------------------
% 1.65/1.31 % (29295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (29295)Termination reason: Unknown
% 1.65/1.31 % (29295)Termination phase: Naming
% 1.65/1.31
% 1.65/1.31 % (29295)Memory used [KB]: 1023
% 1.65/1.31 % (29295)Time elapsed: 0.004 s
% 1.65/1.31 % (29295)Instructions burned: 4 (million)
% 1.65/1.31 % (29295)------------------------------
% 1.65/1.31 % (29295)------------------------------
% 1.65/1.31 % (29301)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/3Mi)
% 1.65/1.31 % (29301)Instruction limit reached!
% 1.65/1.31 % (29301)------------------------------
% 1.65/1.31 % (29301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (29301)Termination reason: Unknown
% 1.65/1.31 % (29301)Termination phase: Preprocessing 3
% 1.65/1.31
% 1.65/1.31 % (29301)Memory used [KB]: 1023
% 1.65/1.31 % (29301)Time elapsed: 0.003 s
% 1.65/1.31 % (29301)Instructions burned: 4 (million)
% 1.65/1.31 % (29301)------------------------------
% 1.65/1.31 % (29301)------------------------------
% 1.65/1.32 % (29300)Instruction limit reached!
% 1.65/1.32 % (29300)------------------------------
% 1.65/1.32 % (29300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (29300)Termination reason: Unknown
% 1.65/1.32 % (29300)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (29300)Memory used [KB]: 5628
% 1.65/1.32 % (29300)Time elapsed: 0.012 s
% 1.65/1.32 % (29300)Instructions burned: 19 (million)
% 1.65/1.32 % (29300)------------------------------
% 1.65/1.32 % (29300)------------------------------
% 1.65/1.32 % (29296)Instruction limit reached!
% 1.65/1.32 % (29296)------------------------------
% 1.65/1.32 % (29296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (29296)Termination reason: Unknown
% 1.65/1.32 % (29296)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (29296)Memory used [KB]: 5756
% 1.65/1.32 % (29296)Time elapsed: 0.017 s
% 1.65/1.32 % (29296)Instructions burned: 27 (million)
% 1.65/1.32 % (29296)------------------------------
% 1.65/1.32 % (29296)------------------------------
% 1.65/1.32 % (29304)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_29067 for (2999ds/3Mi)
% 1.65/1.33 % (29302)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_29067 for (2999ds/37Mi)
% 1.65/1.33 % (29304)Instruction limit reached!
% 1.65/1.33 % (29304)------------------------------
% 1.65/1.33 % (29304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (29304)Termination reason: Unknown
% 1.65/1.33 % (29304)Termination phase: Preprocessing 3
% 1.65/1.33
% 1.65/1.33 % (29304)Memory used [KB]: 1023
% 1.65/1.33 % (29304)Time elapsed: 0.003 s
% 1.65/1.33 % (29304)Instructions burned: 4 (million)
% 1.65/1.33 % (29304)------------------------------
% 1.65/1.33 % (29304)------------------------------
% 1.65/1.33 % (29303)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_29067 for (2999ds/15Mi)
% 1.65/1.34 % (29302)Instruction limit reached!
% 1.65/1.34 % (29302)------------------------------
% 1.65/1.34 % (29302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (29302)Termination reason: Unknown
% 1.65/1.34 % (29302)Termination phase: Saturation
% 1.65/1.34
% 1.65/1.34 % (29302)Memory used [KB]: 5628
% 1.65/1.34 % (29302)Time elapsed: 0.012 s
% 1.65/1.34 % (29302)Instructions burned: 37 (million)
% 1.65/1.34 % (29302)------------------------------
% 1.65/1.34 % (29302)------------------------------
% 1.65/1.34 % (29307)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/16Mi)
% 1.65/1.34 % (29305)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_29067 for (2999ds/1041Mi)
% 1.65/1.34 % (29303)Instruction limit reached!
% 1.65/1.34 % (29303)------------------------------
% 1.65/1.34 % (29303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (29303)Termination reason: Unknown
% 1.65/1.34 % (29303)Termination phase: Saturation
% 1.65/1.34
% 1.65/1.34 % (29303)Memory used [KB]: 5756
% 1.65/1.34 % (29303)Time elapsed: 0.011 s
% 1.65/1.34 % (29303)Instructions burned: 16 (million)
% 1.65/1.34 % (29303)------------------------------
% 1.65/1.34 % (29303)------------------------------
% 1.65/1.34 % (29307)Instruction limit reached!
% 1.65/1.34 % (29307)------------------------------
% 1.65/1.34 % (29307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (29307)Termination reason: Unknown
% 1.65/1.34 % (29307)Termination phase: Property scanning
% 1.65/1.34
% 1.65/1.34 % (29307)Memory used [KB]: 1151
% 1.65/1.34 % (29307)Time elapsed: 0.007 s
% 1.65/1.34 % (29307)Instructions burned: 19 (million)
% 1.65/1.34 % (29307)------------------------------
% 1.65/1.34 % (29307)------------------------------
% 1.65/1.34 % (29306)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/7Mi)
% 1.65/1.35 % (29306)Instruction limit reached!
% 1.65/1.35 % (29306)------------------------------
% 1.65/1.35 % (29306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (29306)Termination reason: Unknown
% 1.65/1.35 % (29306)Termination phase: Property scanning
% 1.65/1.35
% 1.65/1.35 % (29306)Memory used [KB]: 1151
% 1.65/1.35 % (29306)Time elapsed: 0.006 s
% 1.65/1.35 % (29306)Instructions burned: 8 (million)
% 1.65/1.35 % (29306)------------------------------
% 1.65/1.35 % (29306)------------------------------
% 1.65/1.35 % (29308)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_29067 for (2999ds/3Mi)
% 1.65/1.35 % (29308)Instruction limit reached!
% 1.65/1.35 % (29308)------------------------------
% 1.65/1.35 % (29308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (29308)Termination reason: Unknown
% 1.65/1.35 % (29308)Termination phase: Naming
% 1.65/1.35
% 1.65/1.35 % (29308)Memory used [KB]: 1023
% 1.65/1.35 % (29308)Time elapsed: 0.003 s
% 1.65/1.35 % (29308)Instructions burned: 4 (million)
% 1.65/1.35 % (29308)------------------------------
% 1.65/1.35 % (29308)------------------------------
% 1.65/1.35 % (29310)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/7Mi)
% 1.65/1.35 % (29310)Instruction limit reached!
% 1.65/1.35 % (29310)------------------------------
% 1.65/1.35 % (29310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (29310)Termination reason: Unknown
% 1.65/1.35 % (29310)Termination phase: Property scanning
% 1.65/1.35
% 1.65/1.35 % (29310)Memory used [KB]: 1151
% 1.65/1.35 % (29310)Time elapsed: 0.004 s
% 1.65/1.35 % (29310)Instructions burned: 8 (million)
% 1.65/1.35 % (29310)------------------------------
% 1.65/1.35 % (29310)------------------------------
% 1.65/1.36 % (29309)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_29067 for (2999ds/3Mi)
% 1.65/1.36 % (29309)Instruction limit reached!
% 1.65/1.36 % (29309)------------------------------
% 1.65/1.36 % (29309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (29309)Termination reason: Unknown
% 1.65/1.36 % (29309)Termination phase: Naming
% 1.65/1.36
% 1.65/1.36 % (29309)Memory used [KB]: 1023
% 1.65/1.36 % (29309)Time elapsed: 0.004 s
% 1.65/1.36 % (29309)Instructions burned: 4 (million)
% 1.65/1.36 % (29309)------------------------------
% 1.65/1.36 % (29309)------------------------------
% 1.65/1.36 % (29312)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/4Mi)
% 1.65/1.36 % (29312)Instruction limit reached!
% 1.65/1.36 % (29312)------------------------------
% 1.65/1.36 % (29312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (29312)Termination reason: Unknown
% 1.65/1.36 % (29312)Termination phase: Preprocessing 3
% 1.65/1.36
% 1.65/1.36 % (29312)Memory used [KB]: 1023
% 1.65/1.36 % (29312)Time elapsed: 0.003 s
% 1.65/1.36 % (29312)Instructions burned: 4 (million)
% 1.65/1.36 % (29312)------------------------------
% 1.65/1.36 % (29312)------------------------------
% 1.65/1.36 % (29311)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/3Mi)
% 1.65/1.36 % (29313)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/18Mi)
% 1.65/1.36 % (29311)Instruction limit reached!
% 1.65/1.36 % (29311)------------------------------
% 1.65/1.36 % (29311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (29311)Termination reason: Unknown
% 1.65/1.36 % (29311)Termination phase: shuffling
% 1.65/1.36
% 1.65/1.36 % (29311)Memory used [KB]: 1023
% 1.65/1.36 % (29311)Time elapsed: 0.003 s
% 1.65/1.36 % (29311)Instructions burned: 3 (million)
% 1.65/1.36 % (29311)------------------------------
% 1.65/1.36 % (29311)------------------------------
% 1.65/1.37 % (29315)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/6Mi)
% 1.65/1.37 % (29313)Instruction limit reached!
% 1.65/1.37 % (29313)------------------------------
% 1.65/1.37 % (29313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.37 % (29313)Termination reason: Unknown
% 1.65/1.37 % (29313)Termination phase: Saturation
% 1.65/1.37
% 1.65/1.37 % (29313)Memory used [KB]: 5756
% 1.65/1.37 % (29313)Time elapsed: 0.008 s
% 1.65/1.37 % (29313)Instructions burned: 20 (million)
% 1.65/1.37 % (29313)------------------------------
% 1.65/1.37 % (29313)------------------------------
% 1.65/1.37 % (29315)Instruction limit reached!
% 1.65/1.37 % (29315)------------------------------
% 1.65/1.37 % (29315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.37 % (29315)Termination reason: Unknown
% 1.65/1.37 % (29315)Termination phase: Property scanning
% 1.65/1.37
% 1.65/1.37 % (29315)Memory used [KB]: 1151
% 1.65/1.37 % (29315)Time elapsed: 0.004 s
% 1.65/1.37 % (29315)Instructions burned: 8 (million)
% 1.65/1.37 % (29315)------------------------------
% 1.65/1.37 % (29315)------------------------------
% 1.65/1.37 % (29314)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/710Mi)
% 1.65/1.38 % (29317)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_29067 for (2999ds/21Mi)
% 1.65/1.38 % (29318)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/5Mi)
% 1.65/1.38 % (29316)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_29067 for (2999ds/902Mi)
% 1.65/1.38 % (29318)Instruction limit reached!
% 1.65/1.38 % (29318)------------------------------
% 1.65/1.38 % (29318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.38 % (29318)Termination reason: Unknown
% 1.65/1.38 % (29318)Termination phase: Property scanning
% 1.65/1.38
% 1.65/1.38 % (29318)Memory used [KB]: 1023
% 1.65/1.38 % (29318)Time elapsed: 0.003 s
% 1.65/1.38 % (29318)Instructions burned: 5 (million)
% 1.65/1.38 % (29318)------------------------------
% 1.65/1.38 % (29318)------------------------------
% 1.65/1.38 % (29299)Instruction limit reached!
% 1.65/1.38 % (29299)------------------------------
% 1.65/1.38 % (29299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.38 % (29299)Termination reason: Unknown
% 1.65/1.38 % (29299)Termination phase: Saturation
% 1.65/1.38
% 1.65/1.38 % (29299)Memory used [KB]: 6396
% 1.65/1.38 % (29299)Time elapsed: 0.084 s
% 1.65/1.38 % (29299)Instructions burned: 276 (million)
% 1.65/1.38 % (29299)------------------------------
% 1.65/1.38 % (29299)------------------------------
% 1.65/1.39 % (29317)Instruction limit reached!
% 1.65/1.39 % (29317)------------------------------
% 1.65/1.39 % (29317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (29317)Termination reason: Unknown
% 1.65/1.39 % (29317)Termination phase: Saturation
% 1.65/1.39
% 1.65/1.39 % (29317)Memory used [KB]: 5756
% 1.65/1.39 % (29317)Time elapsed: 0.008 s
% 1.65/1.39 % (29317)Instructions burned: 21 (million)
% 1.65/1.39 % (29317)------------------------------
% 1.65/1.39 % (29317)------------------------------
% 1.65/1.39 % (29319)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_29067 for (2999ds/6Mi)
% 1.65/1.39 % (29320)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29067 for (2999ds/377Mi)
% 1.65/1.39 % (29319)Instruction limit reached!
% 1.65/1.39 % (29319)------------------------------
% 1.65/1.39 % (29319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (29319)Termination reason: Unknown
% 1.65/1.39 % (29319)Termination phase: Saturation
% 1.65/1.39
% 1.65/1.39 % (29319)Memory used [KB]: 5500
% 1.65/1.39 % (29319)Time elapsed: 0.004 s
% 1.65/1.39 % (29319)Instructions burned: 8 (million)
% 1.65/1.39 % (29319)------------------------------
% 1.65/1.39 % (29319)------------------------------
% 1.65/1.40 % (29321)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_29067 for (2999ds/779Mi)
% 1.65/1.40 % (29323)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_29067 for (2999ds/19Mi)
% 1.65/1.41 % (29294)Instruction limit reached!
% 1.65/1.41 % (29294)------------------------------
% 1.65/1.41 % (29294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (29294)Termination reason: Unknown
% 1.65/1.41 % (29294)Termination phase: Saturation
% 1.65/1.41
% 1.65/1.41 % (29294)Memory used [KB]: 6140
% 1.65/1.41 % (29294)Time elapsed: 0.102 s
% 1.65/1.41 % (29294)Instructions burned: 183 (million)
% 1.65/1.41 % (29294)------------------------------
% 1.65/1.41 % (29294)------------------------------
% 1.65/1.41 % (29323)Instruction limit reached!
% 1.65/1.41 % (29323)------------------------------
% 1.65/1.41 % (29323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (29323)Termination reason: Unknown
% 1.65/1.41 % (29323)Termination phase: Saturation
% 1.65/1.41
% 1.65/1.41 % (29323)Memory used [KB]: 5500
% 1.65/1.41 % (29323)Time elapsed: 0.007 s
% 1.65/1.41 % (29323)Instructions burned: 20 (million)
% 1.65/1.41 % (29323)------------------------------
% 1.65/1.41 % (29323)------------------------------
% 1.65/1.42 % (29325)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29067 for (2998ds/17Mi)
% 1.65/1.42 % (29324)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29067 for (2998ds/879Mi)
% 1.65/1.43 % (29325)Instruction limit reached!
% 1.65/1.43 % (29325)------------------------------
% 1.65/1.43 % (29325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.43 % (29325)Termination reason: Unknown
% 1.65/1.43 % (29325)Termination phase: Saturation
% 1.65/1.43
% 1.65/1.43 % (29325)Memory used [KB]: 5756
% 1.65/1.43 % (29325)Time elapsed: 0.029 s
% 1.65/1.43 % (29325)Instructions burned: 19 (million)
% 1.65/1.43 % (29325)------------------------------
% 1.65/1.43 % (29325)------------------------------
% 1.65/1.44 % (29326)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29067 for (2998ds/3Mi)
% 1.65/1.44 % (29326)Instruction limit reached!
% 1.65/1.44 % (29326)------------------------------
% 1.65/1.44 % (29326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.44 % (29326)Termination reason: Unknown
% 1.65/1.44 % (29326)Termination phase: Naming
% 1.65/1.44
% 1.65/1.44 % (29326)Memory used [KB]: 1023
% 1.65/1.44 % (29326)Time elapsed: 0.003 s
% 1.65/1.44 % (29326)Instructions burned: 4 (million)
% 1.65/1.44 % (29326)------------------------------
% 1.65/1.44 % (29326)------------------------------
% 1.65/1.45 % (29327)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29067 for (2998ds/30Mi)
% 1.65/1.46 % (29327)Instruction limit reached!
% 1.65/1.46 % (29327)------------------------------
% 1.65/1.46 % (29327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (29327)Termination reason: Unknown
% 1.65/1.46 % (29327)Termination phase: Saturation
% 1.65/1.46
% 1.65/1.46 % (29327)Memory used [KB]: 5756
% 1.65/1.46 % (29327)Time elapsed: 0.012 s
% 1.65/1.46 % (29327)Instructions burned: 31 (million)
% 1.65/1.46 % (29327)------------------------------
% 1.65/1.46 % (29327)------------------------------
% 1.65/1.47 % (29328)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29067 for (2998ds/127Mi)
% 1.65/1.49 % (29305)First to succeed.
% 1.65/1.50 % (29305)Refutation found. Thanks to Tanya!
% 1.65/1.50 % SZS status Theorem for DTF2THF_29067
% 1.65/1.50 % SZS output start Proof for DTF2THF_29067
% 1.65/1.50 thf(type_def_5, type, a: $tType).
% 1.65/1.50 thf(func_def_0, type, a: $tType).
% 1.65/1.50 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.65/1.50 thf(func_def_21, type, sK2: a > a > $o).
% 1.65/1.50 thf(func_def_22, type, sK3: a).
% 1.65/1.50 thf(func_def_23, type, sK4: a > a > $o).
% 1.65/1.50 thf(func_def_24, type, sK5: a).
% 1.65/1.50 thf(func_def_25, type, sK6: a > a > $o).
% 1.65/1.50 thf(func_def_26, type, sK7: a).
% 1.65/1.50 thf(func_def_27, type, sK8: a).
% 1.65/1.50 thf(func_def_28, type, sK9: a > a > $o).
% 1.65/1.50 thf(func_def_29, type, sK10: a).
% 1.65/1.50 thf(func_def_30, type, sK11: a).
% 1.65/1.50 thf(func_def_31, type, sK12: a).
% 1.65/1.50 thf(func_def_32, type, sK13: a > a > $o).
% 1.65/1.50 thf(func_def_33, type, sK14: a).
% 1.65/1.50 thf(func_def_34, type, sK15: a).
% 1.65/1.50 thf(func_def_35, type, sK16: a).
% 1.65/1.50 thf(func_def_36, type, sK17: a).
% 1.65/1.50 thf(func_def_37, type, sK18: a).
% 1.65/1.50 thf(func_def_38, type, sK19: a).
% 1.65/1.50 thf(func_def_39, type, sK20: a).
% 1.65/1.50 thf(func_def_40, type, sK21: a).
% 1.65/1.50 thf(func_def_41, type, sK22: a).
% 1.65/1.50 thf(func_def_42, type, sK23: a).
% 1.65/1.50 thf(func_def_43, type, sK24: a).
% 1.65/1.50 thf(func_def_44, type, sK25: a).
% 1.65/1.50 thf(func_def_45, type, sK26: a).
% 1.65/1.50 thf(func_def_46, type, sK27: a).
% 1.65/1.50 thf(func_def_47, type, sK28: a).
% 1.65/1.50 thf(func_def_48, type, sK29: a).
% 1.65/1.50 thf(func_def_49, type, sK30: a).
% 1.65/1.50 thf(func_def_50, type, sK31: a).
% 1.65/1.50 thf(func_def_51, type, sK32: a).
% 1.65/1.50 thf(func_def_52, type, sK33: a).
% 1.65/1.50 thf(func_def_53, type, sK34: a).
% 1.65/1.50 thf(func_def_54, type, sK35: a).
% 1.65/1.50 thf(func_def_55, type, sK36: a).
% 1.65/1.50 thf(f1556,plain,(
% 1.65/1.50 $false),
% 1.65/1.50 inference(avatar_sat_refutation,[status(thm)],[f56,f75,f118,f249,f285,f401,f427,f444,f463,f578,f595,f623,f901,f956,f992,f1306,f1316,f1555])).
% 1.65/1.50 thf(f1555,plain,(
% 1.65/1.50 ~spl0_4 | ~spl0_11),
% 1.65/1.50 inference(avatar_contradiction_clause,[status(thm)],[f1554])).
% 1.65/1.50 thf(f1554,plain,(
% 1.65/1.50 $false | (~spl0_4 | ~spl0_11)),
% 1.65/1.50 inference(trivial_inequality_removal,[status(thm)],[f1553])).
% 1.65/1.50 thf(f1553,plain,(
% 1.65/1.50 ($true = $false) | (~spl0_4 | ~spl0_11)),
% 1.65/1.50 inference(forward_demodulation,[status(thm)],[f1546,f1462])).
% 1.65/1.50 thf(f1462,plain,(
% 1.65/1.50 ($false = (sK13 @ sK33 @ sK34)) | ~spl0_11),
% 1.65/1.50 inference(boolean_simplification,[status(thm)],[f1461])).
% 1.65/1.50 thf(f1461,plain,(
% 1.65/1.50 (($true => (sK13 @ sK33 @ sK34)) = $false) | ~spl0_11),
% 1.65/1.50 inference(backward_demodulation,[status(thm)],[f1450,f1460])).
% 1.65/1.50 thf(f1460,plain,(
% 1.65/1.50 ($true = ((sK13 @ sK33 @ sK35) & (sK13 @ sK35 @ sK34))) | ~spl0_11),
% 1.65/1.50 inference(binary_proxy_clausification,[status(thm)],[f1450])).
% 1.65/1.50 thf(f1450,plain,(
% 1.65/1.50 ($false = (((sK13 @ sK33 @ sK35) & (sK13 @ sK35 @ sK34)) => (sK13 @ sK33 @ sK34))) | ~spl0_11),
% 1.65/1.50 inference(beta_eta_normalization,[status(thm)],[f1449])).
% 1.65/1.50 thf(f1449,plain,(
% 1.65/1.50 ($false = ((^[Y0 : a]: (((sK13 @ sK33 @ Y0) & (sK13 @ Y0 @ sK34)) => (sK13 @ sK33 @ sK34))) @ sK35)) | ~spl0_11),
% 1.65/1.50 inference(sigma_clausification,[status(thm)],[f1445])).
% 1.65/1.50 thf(f1445,plain,(
% 1.65/1.50 ((!! @ a @ (^[Y0 : a]: (((sK13 @ sK33 @ Y0) & (sK13 @ Y0 @ sK34)) => (sK13 @ sK33 @ sK34)))) = $false) | ~spl0_11),
% 1.65/1.50 inference(beta_eta_normalization,[status(thm)],[f1444])).
% 1.65/1.50 thf(f1444,plain,(
% 1.65/1.50 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ sK33 @ Y1) & (sK13 @ Y1 @ Y0)) => (sK13 @ sK33 @ Y0))))) @ sK34)) | ~spl0_11),
% 1.65/1.50 inference(sigma_clausification,[status(thm)],[f1432])).
% 1.65/1.50 thf(f1432,plain,(
% 1.65/1.50 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ sK33 @ Y1) & (sK13 @ Y1 @ Y0)) => (sK13 @ sK33 @ Y0))))))) | ~spl0_11),
% 1.65/1.50 inference(beta_eta_normalization,[status(thm)],[f1430])).
% 1.65/1.50 thf(f1430,plain,(
% 1.65/1.50 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y2) & (sK13 @ Y2 @ Y1)) => (sK13 @ Y0 @ Y1))))))) @ sK33) = $false) | ~spl0_11),
% 1.65/1.50 inference(sigma_clausification,[status(thm)],[f400])).
% 1.65/1.50 thf(f400,plain,(
% 1.65/1.50 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y2) & (sK13 @ Y2 @ Y1)) => (sK13 @ Y0 @ Y1)))))))) = $false) | ~spl0_11),
% 1.65/1.50 inference(avatar_component_clause,[status(thm)],[f399])).
% 1.65/1.50 thf(f399,definition,(
% 1.65/1.50 spl0_11 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y2) & (sK13 @ Y2 @ Y1)) => (sK13 @ Y0 @ Y1)))))))) = $false)),
% 1.65/1.50 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.65/1.50 thf(f1546,plain,(
% 1.65/1.51 ($true = (sK13 @ sK33 @ sK34)) | (~spl0_4 | ~spl0_11)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1544])).
% 1.65/1.51 thf(f1544,plain,(
% 1.65/1.51 ($true = ($true => (sK13 @ sK33 @ sK34))) | (~spl0_4 | ~spl0_11)),
% 1.65/1.51 inference(superposition,[status(thm)],[f1508,f1500])).
% 1.65/1.51 thf(f1500,plain,(
% 1.65/1.51 ($true = (sK13 @ sK36 @ sK34)) | ~spl0_11),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f1487])).
% 1.65/1.51 thf(f1487,plain,(
% 1.65/1.51 ($true = ((sK13 @ sK33 @ sK36) & (sK13 @ sK36 @ sK34))) | ~spl0_11),
% 1.65/1.51 inference(not_proxy_clausification,[status(thm)],[f1476])).
% 1.65/1.51 thf(f1476,plain,(
% 1.65/1.51 ($false = (~ ((sK13 @ sK33 @ sK36) & (sK13 @ sK36 @ sK34)))) | ~spl0_11),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1475])).
% 1.65/1.51 thf(f1475,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (~ ((sK13 @ sK33 @ Y0) & (sK13 @ Y0 @ sK34)))) @ sK36)) | ~spl0_11),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f1464])).
% 1.65/1.51 thf(f1464,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (~ ((sK13 @ sK33 @ Y0) & (sK13 @ Y0 @ sK34))))) = $false) | ~spl0_11),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1463])).
% 1.65/1.51 thf(f1463,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (((sK13 @ sK33 @ Y0) & (sK13 @ Y0 @ sK34)) => $false))) = $false) | ~spl0_11),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f1445,f1462])).
% 1.65/1.51 thf(f1508,plain,(
% 1.65/1.51 ( ! [X0 : a] : (($true = ((sK13 @ sK36 @ X0) => (sK13 @ sK33 @ X0)))) ) | (~spl0_4 | ~spl0_11)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1505])).
% 1.65/1.51 thf(f1505,plain,(
% 1.65/1.51 ( ! [X0 : a] : (($true = (((sK13 @ sK36 @ X0) & $true) => (sK13 @ sK33 @ X0)))) ) | (~spl0_4 | ~spl0_11)),
% 1.65/1.51 inference(superposition,[status(thm)],[f1342,f1503])).
% 1.65/1.51 thf(f1503,plain,(
% 1.65/1.51 ($true = (sK13 @ sK33 @ sK36)) | ~spl0_11),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1502])).
% 1.65/1.51 thf(f1502,plain,(
% 1.65/1.51 ($true = ((sK13 @ sK33 @ sK36) & $true)) | ~spl0_11),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f1487,f1500])).
% 1.65/1.51 thf(f1342,plain,(
% 1.65/1.51 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK13 @ X1 @ X2) & (sK13 @ X3 @ X1)) => (sK13 @ X3 @ X2)) = $true)) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1341])).
% 1.65/1.51 thf(f1341,plain,(
% 1.65/1.51 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK13 @ X1 @ X2) & (sK13 @ Y0 @ X1)) => (sK13 @ Y0 @ X2))) @ X3))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f1332])).
% 1.65/1.51 thf(f1332,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK13 @ X1 @ X2) & (sK13 @ Y0 @ X1)) => (sK13 @ Y0 @ X2)))))) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1331])).
% 1.65/1.51 thf(f1331,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ X1 @ Y0) & (sK13 @ Y1 @ X1)) => (sK13 @ Y1 @ Y0))))) @ X2))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f1320])).
% 1.65/1.51 thf(f1320,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ X1 @ Y0) & (sK13 @ Y1 @ X1)) => (sK13 @ Y1 @ Y0)))))))) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1317])).
% 1.65/1.51 thf(f1317,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y1) & (sK13 @ Y2 @ Y0)) => (sK13 @ Y2 @ Y1))))))) @ X1))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f1111])).
% 1.65/1.51 thf(f1111,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y1) & (sK13 @ Y2 @ Y0)) => (sK13 @ Y2 @ Y1))))))))) | ~spl0_4),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f1053])).
% 1.65/1.51 thf(f1053,plain,(
% 1.65/1.51 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK13 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y1) & (sK13 @ Y2 @ Y0)) => (sK13 @ Y2 @ Y1))))))))) = $true) | ~spl0_4),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f1046])).
% 1.65/1.51 thf(f1046,plain,(
% 1.65/1.51 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK13 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y1) & (sK13 @ Y2 @ Y0)) => (sK13 @ Y2 @ Y1))))))))) => (sK13 @ sK10 @ sK12))) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1045])).
% 1.65/1.51 thf(f1045,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK12))) @ sK13)) | ~spl0_4),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f1025])).
% 1.65/1.51 thf(f1025,plain,(
% 1.65/1.51 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK12))))) | ~spl0_4),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f1021])).
% 1.65/1.51 thf(f1021,plain,(
% 1.65/1.51 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK10 @ sK11)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK11 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK12)))))) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1020])).
% 1.65/1.51 thf(f1020,plain,(
% 1.65/1.51 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK10 @ sK11)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK11 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))))) @ sK12) = $false) | ~spl0_4),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f1015])).
% 1.65/1.51 thf(f1015,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK10 @ sK11)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK11 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))))))) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1014])).
% 1.65/1.51 thf(f1014,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK10 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ sK10 @ Y1)))))))) @ sK11)) | ~spl0_4),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f1001])).
% 1.65/1.51 thf(f1001,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK10 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ sK10 @ Y1)))))))))) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1000])).
% 1.65/1.51 thf(f1000,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2)))))))))) @ sK10)) | ~spl0_4),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f74])).
% 1.65/1.51 thf(f74,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))) = $false) | ~spl0_4),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.65/1.51 thf(f73,definition,(
% 1.65/1.51 spl0_4 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))) = $false)),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.65/1.51 thf(f1316,plain,(
% 1.65/1.51 ~spl0_4 | ~spl0_7 | ~spl0_10),
% 1.65/1.51 inference(avatar_contradiction_clause,[status(thm)],[f1315])).
% 1.65/1.51 thf(f1315,plain,(
% 1.65/1.51 $false | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.65/1.51 inference(trivial_inequality_removal,[status(thm)],[f1314])).
% 1.65/1.51 thf(f1314,plain,(
% 1.65/1.51 ($true = $false) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1313])).
% 1.65/1.51 thf(f1313,plain,(
% 1.65/1.51 ($true = (~ $true)) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1312])).
% 1.65/1.51 thf(f1312,plain,(
% 1.65/1.51 ($true = (~ ($true | (sK4 @ sK14 @ sK15)))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.65/1.51 inference(forward_demodulation,[status(thm)],[f1311,f284])).
% 1.65/1.51 thf(f284,plain,(
% 1.65/1.51 ($true = (sK2 @ sK14 @ sK15)) | ~spl0_10),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f283])).
% 1.65/1.51 thf(f283,definition,(
% 1.65/1.51 spl0_10 <=> ($true = (sK2 @ sK14 @ sK15))),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.65/1.51 thf(f1311,plain,(
% 1.65/1.51 ($true = (~ ((sK2 @ sK14 @ sK15) | (sK4 @ sK14 @ sK15)))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1310])).
% 1.65/1.51 thf(f1310,plain,(
% 1.65/1.51 ($true = (((sK2 @ sK14 @ sK15) | (sK4 @ sK14 @ sK15)) => $false)) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.65/1.51 inference(superposition,[status(thm)],[f1156,f1309])).
% 1.65/1.51 thf(f1309,plain,(
% 1.65/1.51 ((sK13 @ sK14 @ sK15) = $false) | (~spl0_7 | ~spl0_10)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1308])).
% 1.65/1.51 thf(f1308,plain,(
% 1.65/1.51 ($false = ($true => (sK13 @ sK14 @ sK15))) | (~spl0_7 | ~spl0_10)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1307])).
% 1.65/1.51 thf(f1307,plain,(
% 1.65/1.51 ($false = (((sK4 @ sK14 @ sK15) | $true) => (sK13 @ sK14 @ sK15))) | (~spl0_7 | ~spl0_10)),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f1300,f284])).
% 1.65/1.51 thf(f1300,plain,(
% 1.65/1.51 ((((sK4 @ sK14 @ sK15) | (sK2 @ sK14 @ sK15)) => (sK13 @ sK14 @ sK15)) = $false) | ~spl0_7),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1299])).
% 1.65/1.51 thf(f1299,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (((sK4 @ sK14 @ Y0) | (sK2 @ sK14 @ Y0)) => (sK13 @ sK14 @ Y0))) @ sK15)) | ~spl0_7),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f1295])).
% 1.65/1.51 thf(f1295,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK14 @ Y0) | (sK2 @ sK14 @ Y0)) => (sK13 @ sK14 @ Y0)))) = $false) | ~spl0_7),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1288])).
% 1.65/1.51 thf(f1288,plain,(
% 1.65/1.51 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1))))) @ sK14) = $false) | ~spl0_7),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f245])).
% 1.65/1.51 thf(f245,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1))))))) | ~spl0_7),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f244])).
% 1.65/1.51 thf(f244,definition,(
% 1.65/1.51 spl0_7 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1)))))))),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.65/1.51 thf(f1156,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (((((sK2 @ X2 @ X1) | (sK4 @ X2 @ X1)) => (sK13 @ X2 @ X1)) = $true)) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1155])).
% 1.65/1.51 thf(f1155,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK4 @ Y0 @ X1)) => (sK13 @ Y0 @ X1))) @ X2))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f1139])).
% 1.65/1.51 thf(f1139,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK4 @ Y0 @ X1)) => (sK13 @ Y0 @ X1)))))) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f1138])).
% 1.65/1.51 thf(f1138,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK13 @ Y1 @ Y0))))) @ X1))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f1114])).
% 1.65/1.51 thf(f1114,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK13 @ Y1 @ Y0))))))) | ~spl0_4),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1113])).
% 1.65/1.51 thf(f1113,plain,(
% 1.65/1.51 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK13 @ Y1 @ Y0)))))) & $true)) | ~spl0_4),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f1053,f1111])).
% 1.65/1.51 thf(f1306,plain,(
% 1.65/1.51 ~spl0_4 | ~spl0_7 | ~spl0_9),
% 1.65/1.51 inference(avatar_contradiction_clause,[status(thm)],[f1305])).
% 1.65/1.51 thf(f1305,plain,(
% 1.65/1.51 $false | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.65/1.51 inference(trivial_inequality_removal,[status(thm)],[f1304])).
% 1.65/1.51 thf(f1304,plain,(
% 1.65/1.51 ($true = $false) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f1170,f1303])).
% 1.65/1.51 thf(f1303,plain,(
% 1.65/1.51 ((sK13 @ sK14 @ sK15) = $false) | (~spl0_7 | ~spl0_9)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1302])).
% 1.65/1.51 thf(f1302,plain,(
% 1.65/1.51 ($false = ($true => (sK13 @ sK14 @ sK15))) | (~spl0_7 | ~spl0_9)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1301])).
% 1.65/1.51 thf(f1301,plain,(
% 1.65/1.51 ((($true | (sK2 @ sK14 @ sK15)) => (sK13 @ sK14 @ sK15)) = $false) | (~spl0_7 | ~spl0_9)),
% 1.65/1.51 inference(forward_demodulation,[status(thm)],[f1300,f281])).
% 1.65/1.51 thf(f281,plain,(
% 1.65/1.51 ($true = (sK4 @ sK14 @ sK15)) | ~spl0_9),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f280])).
% 1.65/1.51 thf(f280,definition,(
% 1.65/1.51 spl0_9 <=> ($true = (sK4 @ sK14 @ sK15))),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.65/1.51 thf(f1170,plain,(
% 1.65/1.51 ($true = (sK13 @ sK14 @ sK15)) | (~spl0_4 | ~spl0_9)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1169])).
% 1.65/1.51 thf(f1169,plain,(
% 1.65/1.51 ($true = ($true => (sK13 @ sK14 @ sK15))) | (~spl0_4 | ~spl0_9)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f1165])).
% 1.65/1.51 thf(f1165,plain,(
% 1.65/1.51 ($true = (((sK2 @ sK14 @ sK15) | $true) => (sK13 @ sK14 @ sK15))) | (~spl0_4 | ~spl0_9)),
% 1.65/1.51 inference(superposition,[status(thm)],[f1156,f281])).
% 1.65/1.51 thf(f992,plain,(
% 1.65/1.51 ~spl0_3 | ~spl0_6 | ~spl0_22),
% 1.65/1.51 inference(avatar_contradiction_clause,[status(thm)],[f991])).
% 1.65/1.51 thf(f991,plain,(
% 1.65/1.51 $false | (~spl0_3 | ~spl0_6 | ~spl0_22)),
% 1.65/1.51 inference(trivial_inequality_removal,[status(thm)],[f987])).
% 1.65/1.51 thf(f987,plain,(
% 1.65/1.51 ($true = $false) | (~spl0_3 | ~spl0_6 | ~spl0_22)),
% 1.65/1.51 inference(superposition,[status(thm)],[f976,f672])).
% 1.65/1.51 thf(f672,plain,(
% 1.65/1.51 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK9 @ X1 @ X2) & (sK9 @ X2 @ X3)) => (sK9 @ X1 @ X3)))) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f671])).
% 1.65/1.51 thf(f671,plain,(
% 1.65/1.51 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK9 @ X1 @ X2) & (sK9 @ X2 @ Y0)) => (sK9 @ X1 @ Y0))) @ X3))) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f656])).
% 1.65/1.51 thf(f656,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK9 @ X1 @ X2) & (sK9 @ X2 @ Y0)) => (sK9 @ X1 @ Y0)))))) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f655])).
% 1.65/1.51 thf(f655,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK9 @ X1 @ Y0) & (sK9 @ Y0 @ Y1)) => (sK9 @ X1 @ Y1))))) @ X2))) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f651])).
% 1.65/1.51 thf(f651,plain,(
% 1.65/1.51 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK9 @ X1 @ Y0) & (sK9 @ Y0 @ Y1)) => (sK9 @ X1 @ Y1)))))) = $true)) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f650])).
% 1.65/1.51 thf(f650,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2))))))) @ X1))) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f641])).
% 1.65/1.51 thf(f641,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2))))))))) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f640])).
% 1.65/1.51 thf(f640,plain,(
% 1.65/1.51 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2)))))))))) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f633,f639])).
% 1.65/1.51 thf(f639,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK9 @ Y0 @ Y1))))))) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f633])).
% 1.65/1.51 thf(f633,plain,(
% 1.65/1.51 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK9 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2)))))))))) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f628])).
% 1.65/1.51 thf(f628,plain,(
% 1.65/1.51 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK9 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2))))))))) => (sK9 @ sK8 @ sK7))) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f627])).
% 1.65/1.51 thf(f627,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7))) @ sK9)) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f626])).
% 1.65/1.51 thf(f626,plain,(
% 1.65/1.51 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7)))) = $false) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f625])).
% 1.65/1.51 thf(f625,plain,(
% 1.65/1.51 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7))))) = $false) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f624])).
% 1.65/1.51 thf(f624,plain,(
% 1.65/1.51 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | $true) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7)))))) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f473,f117])).
% 1.65/1.51 thf(f117,plain,(
% 1.65/1.51 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))))) | ~spl0_6),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f116])).
% 1.65/1.51 thf(f116,definition,(
% 1.65/1.51 spl0_6 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))))),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.65/1.51 thf(f473,plain,(
% 1.65/1.51 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7)))))) | ~spl0_3),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f472])).
% 1.65/1.51 thf(f472,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK7))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK7)))))) @ sK8)) | ~spl0_3),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f469])).
% 1.65/1.51 thf(f469,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK7))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK7))))))) = $false) | ~spl0_3),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f468])).
% 1.65/1.51 thf(f468,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK7)) | ~spl0_3),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f71])).
% 1.65/1.51 thf(f71,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false) | ~spl0_3),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.65/1.51 thf(f70,definition,(
% 1.65/1.51 spl0_3 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false)),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.65/1.51 thf(f976,plain,(
% 1.65/1.51 ($false = (((sK9 @ sK32 @ sK31) & (sK9 @ sK31 @ sK30)) => (sK9 @ sK32 @ sK30))) | ~spl0_22),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f975])).
% 1.65/1.51 thf(f975,plain,(
% 1.65/1.51 (((^[Y0 : a]: (((sK9 @ Y0 @ sK31) & (sK9 @ sK31 @ sK30)) => (sK9 @ Y0 @ sK30))) @ sK32) = $false) | ~spl0_22),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f968])).
% 1.65/1.51 thf(f968,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (((sK9 @ Y0 @ sK31) & (sK9 @ sK31 @ sK30)) => (sK9 @ Y0 @ sK30))))) | ~spl0_22),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f967])).
% 1.65/1.51 thf(f967,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK9 @ Y1 @ Y0) & (sK9 @ Y0 @ sK30)) => (sK9 @ Y1 @ sK30))))) @ sK31)) | ~spl0_22),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f963])).
% 1.65/1.51 thf(f963,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK9 @ Y1 @ Y0) & (sK9 @ Y0 @ sK30)) => (sK9 @ Y1 @ sK30))))))) | ~spl0_22),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f959])).
% 1.65/1.51 thf(f959,plain,(
% 1.65/1.51 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y2 @ Y1) & (sK9 @ Y1 @ Y0)) => (sK9 @ Y2 @ Y0))))))) @ sK30) = $false) | ~spl0_22),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f897])).
% 1.65/1.51 thf(f897,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y2 @ Y1) & (sK9 @ Y1 @ Y0)) => (sK9 @ Y2 @ Y0)))))))) = $false) | ~spl0_22),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f896])).
% 1.65/1.51 thf(f896,definition,(
% 1.65/1.51 spl0_22 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y2 @ Y1) & (sK9 @ Y1 @ Y0)) => (sK9 @ Y2 @ Y0)))))))) = $false)),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition])).
% 1.65/1.51 thf(f956,plain,(
% 1.65/1.51 ~spl0_3 | ~spl0_6 | ~spl0_23),
% 1.65/1.51 inference(avatar_contradiction_clause,[status(thm)],[f955])).
% 1.65/1.51 thf(f955,plain,(
% 1.65/1.51 $false | (~spl0_3 | ~spl0_6 | ~spl0_23)),
% 1.65/1.51 inference(trivial_inequality_removal,[status(thm)],[f954])).
% 1.65/1.51 thf(f954,plain,(
% 1.65/1.51 ($true = $false) | (~spl0_3 | ~spl0_6 | ~spl0_23)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f953])).
% 1.65/1.51 thf(f953,plain,(
% 1.65/1.51 ($true = (~ $true)) | (~spl0_3 | ~spl0_6 | ~spl0_23)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f952])).
% 1.65/1.51 thf(f952,plain,(
% 1.65/1.51 ($true = (~ ((sK4 @ sK29 @ sK28) | $true))) | (~spl0_3 | ~spl0_6 | ~spl0_23)),
% 1.65/1.51 inference(forward_demodulation,[status(thm)],[f951,f939])).
% 1.65/1.51 thf(f939,plain,(
% 1.65/1.51 ($true = (sK2 @ sK29 @ sK28)) | ~spl0_23),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f927])).
% 1.65/1.51 thf(f927,plain,(
% 1.65/1.51 (((sK2 @ sK29 @ sK28) => (sK9 @ sK29 @ sK28)) = $false) | ~spl0_23),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f926])).
% 1.65/1.51 thf(f926,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: ((sK2 @ Y0 @ sK28) => (sK9 @ Y0 @ sK28))) @ sK29)) | ~spl0_23),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f914])).
% 1.65/1.51 thf(f914,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ sK28) => (sK9 @ Y0 @ sK28)))) = $false) | ~spl0_23),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f910])).
% 1.65/1.51 thf(f910,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))) @ sK28)) | ~spl0_23),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f900])).
% 1.65/1.51 thf(f900,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))) | ~spl0_23),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f899])).
% 1.65/1.51 thf(f899,definition,(
% 1.65/1.51 spl0_23 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0)))))))),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])).
% 1.65/1.51 thf(f951,plain,(
% 1.65/1.51 ($true = (~ ((sK4 @ sK29 @ sK28) | (sK2 @ sK29 @ sK28)))) | (~spl0_3 | ~spl0_6 | ~spl0_23)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f942])).
% 1.65/1.51 thf(f942,plain,(
% 1.65/1.51 ($true = (((sK4 @ sK29 @ sK28) | (sK2 @ sK29 @ sK28)) => $false)) | (~spl0_3 | ~spl0_6 | ~spl0_23)),
% 1.65/1.51 inference(superposition,[status(thm)],[f840,f941])).
% 1.65/1.51 thf(f941,plain,(
% 1.65/1.51 ((sK9 @ sK29 @ sK28) = $false) | ~spl0_23),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f940])).
% 1.65/1.51 thf(f940,plain,(
% 1.65/1.51 ($false = ($true => (sK9 @ sK29 @ sK28))) | ~spl0_23),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f927,f939])).
% 1.65/1.51 thf(f840,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = (((sK4 @ X1 @ X2) | (sK2 @ X1 @ X2)) => (sK9 @ X1 @ X2)))) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f839])).
% 1.65/1.51 thf(f839,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK4 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK9 @ X1 @ Y0))) @ X2))) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f824])).
% 1.65/1.51 thf(f824,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK9 @ X1 @ Y0)))))) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f823])).
% 1.65/1.51 thf(f823,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK9 @ Y0 @ Y1))))) @ X1))) ) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f639])).
% 1.65/1.51 thf(f901,plain,(
% 1.65/1.51 spl0_22 | spl0_23 | ~spl0_3 | ~spl0_6),
% 1.65/1.51 inference(avatar_split_clause,[status(thm)],[f892,f116,f70,f899,f896])).
% 1.65/1.51 thf(f892,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y2 @ Y1) & (sK9 @ Y1 @ Y0)) => (sK9 @ Y2 @ Y0)))))))) = $false) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f886])).
% 1.65/1.51 thf(f886,plain,(
% 1.65/1.51 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y2 @ Y1) & (sK9 @ Y1 @ Y0)) => (sK9 @ Y2 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0)))))))) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(not_proxy_clausification,[status(thm)],[f743])).
% 1.65/1.51 thf(f743,plain,(
% 1.65/1.51 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y2 @ Y1) & (sK9 @ Y1 @ Y0)) => (sK9 @ Y2 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))))) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f740])).
% 1.65/1.51 thf(f740,plain,(
% 1.65/1.51 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y2 @ Y1) & (sK9 @ Y1 @ Y0)) => (sK9 @ Y2 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))) => $false)) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(superposition,[status(thm)],[f729,f632])).
% 1.65/1.51 thf(f632,plain,(
% 1.65/1.51 ((sK9 @ sK8 @ sK7) = $false) | (~spl0_3 | ~spl0_6)),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f628])).
% 1.65/1.51 thf(f729,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y2 @ Y1) & (X1 @ Y1 @ Y0)) => (X1 @ Y2 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK8 @ sK7)))) ) | ~spl0_6),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f728])).
% 1.65/1.51 thf(f728,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))) @ X1))) ) | ~spl0_6),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f117])).
% 1.65/1.51 thf(f623,plain,(
% 1.65/1.51 ~spl0_3 | ~spl0_5 | ~spl0_15),
% 1.65/1.51 inference(avatar_contradiction_clause,[status(thm)],[f622])).
% 1.65/1.51 thf(f622,plain,(
% 1.65/1.51 $false | (~spl0_3 | ~spl0_5 | ~spl0_15)),
% 1.65/1.51 inference(trivial_inequality_removal,[status(thm)],[f621])).
% 1.65/1.51 thf(f621,plain,(
% 1.65/1.51 ($true = $false) | (~spl0_3 | ~spl0_5 | ~spl0_15)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f620])).
% 1.65/1.51 thf(f620,plain,(
% 1.65/1.51 ($true = (~ $true)) | (~spl0_3 | ~spl0_5 | ~spl0_15)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f619])).
% 1.65/1.51 thf(f619,plain,(
% 1.65/1.51 ($true = (~ ($true | (sK2 @ sK25 @ sK24)))) | (~spl0_3 | ~spl0_5 | ~spl0_15)),
% 1.65/1.51 inference(forward_demodulation,[status(thm)],[f617,f606])).
% 1.65/1.51 thf(f606,plain,(
% 1.65/1.51 ($true = (sK4 @ sK25 @ sK24)) | ~spl0_15),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f604])).
% 1.65/1.51 thf(f604,plain,(
% 1.65/1.51 (((sK4 @ sK25 @ sK24) => (sK9 @ sK25 @ sK24)) = $false) | ~spl0_15),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f603])).
% 1.65/1.51 thf(f603,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: ((sK4 @ Y0 @ sK24) => (sK9 @ Y0 @ sK24))) @ sK25)) | ~spl0_15),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f602])).
% 1.65/1.51 thf(f602,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0 @ sK24) => (sK9 @ Y0 @ sK24)))) = $false) | ~spl0_15),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f598])).
% 1.65/1.51 thf(f598,plain,(
% 1.65/1.51 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))) @ sK24) = $false) | ~spl0_15),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f577])).
% 1.65/1.51 thf(f577,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))) | ~spl0_15),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f576])).
% 1.65/1.51 thf(f576,definition,(
% 1.65/1.51 spl0_15 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0)))))))),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.65/1.51 thf(f617,plain,(
% 1.65/1.51 ($true = (~ ((sK4 @ sK25 @ sK24) | (sK2 @ sK25 @ sK24)))) | (~spl0_3 | ~spl0_5 | ~spl0_15)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f612])).
% 1.65/1.51 thf(f612,plain,(
% 1.65/1.51 ($true = (((sK4 @ sK25 @ sK24) | (sK2 @ sK25 @ sK24)) => $false)) | (~spl0_3 | ~spl0_5 | ~spl0_15)),
% 1.65/1.51 inference(superposition,[status(thm)],[f498,f608])).
% 1.65/1.51 thf(f608,plain,(
% 1.65/1.51 ($false = (sK9 @ sK25 @ sK24)) | ~spl0_15),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f607])).
% 1.65/1.51 thf(f607,plain,(
% 1.65/1.51 (($true => (sK9 @ sK25 @ sK24)) = $false) | ~spl0_15),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f604,f606])).
% 1.65/1.51 thf(f498,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = (((sK4 @ X1 @ X2) | (sK2 @ X1 @ X2)) => (sK9 @ X1 @ X2)))) ) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f497])).
% 1.65/1.51 thf(f497,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK4 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK9 @ X1 @ Y0))) @ X2))) ) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f494])).
% 1.65/1.51 thf(f494,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK9 @ X1 @ Y0)))))) ) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f493])).
% 1.65/1.51 thf(f493,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK9 @ Y0 @ Y1))))) @ X1))) ) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f490])).
% 1.65/1.51 thf(f490,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK9 @ Y0 @ Y1))))))) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f481])).
% 1.65/1.51 thf(f481,plain,(
% 1.65/1.51 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK9 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2)))))))))) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f479])).
% 1.65/1.51 thf(f479,plain,(
% 1.65/1.51 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK9 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2))))))))) => (sK9 @ sK8 @ sK7))) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f478])).
% 1.65/1.51 thf(f478,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7))) @ sK9)) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f476])).
% 1.65/1.51 thf(f476,plain,(
% 1.65/1.51 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7)))) = $false) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f475])).
% 1.65/1.51 thf(f475,plain,(
% 1.65/1.51 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7))))) = $false) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f474])).
% 1.65/1.51 thf(f474,plain,(
% 1.65/1.51 ((($true | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7))))) = $false) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(forward_demodulation,[status(thm)],[f473,f114])).
% 1.65/1.51 thf(f114,plain,(
% 1.65/1.51 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))))) | ~spl0_5),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f113])).
% 1.65/1.51 thf(f113,definition,(
% 1.65/1.51 spl0_5 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))))),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.65/1.51 thf(f595,plain,(
% 1.65/1.51 ~spl0_3 | ~spl0_5 | ~spl0_14),
% 1.65/1.51 inference(avatar_contradiction_clause,[status(thm)],[f594])).
% 1.65/1.51 thf(f594,plain,(
% 1.65/1.51 $false | (~spl0_3 | ~spl0_5 | ~spl0_14)),
% 1.65/1.51 inference(trivial_inequality_removal,[status(thm)],[f590])).
% 1.65/1.51 thf(f590,plain,(
% 1.65/1.51 ($true = $false) | (~spl0_3 | ~spl0_5 | ~spl0_14)),
% 1.65/1.51 inference(superposition,[status(thm)],[f500,f587])).
% 1.65/1.51 thf(f587,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (((sK9 @ sK22 @ sK21) & (sK9 @ sK21 @ Y0)) => (sK9 @ sK22 @ Y0)))) = $false) | ~spl0_14),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f586])).
% 1.65/1.51 thf(f586,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK9 @ Y0 @ sK21) & (sK9 @ sK21 @ Y1)) => (sK9 @ Y0 @ Y1))))) @ sK22)) | ~spl0_14),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f583])).
% 1.65/1.51 thf(f583,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK9 @ Y0 @ sK21) & (sK9 @ sK21 @ Y1)) => (sK9 @ Y0 @ Y1)))))) = $false) | ~spl0_14),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f581])).
% 1.65/1.51 thf(f581,plain,(
% 1.65/1.51 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y1 @ Y0) & (sK9 @ Y0 @ Y2)) => (sK9 @ Y1 @ Y2))))))) @ sK21) = $false) | ~spl0_14),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f574])).
% 1.65/1.51 thf(f574,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y1 @ Y0) & (sK9 @ Y0 @ Y2)) => (sK9 @ Y1 @ Y2)))))))) = $false) | ~spl0_14),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f573])).
% 1.65/1.51 thf(f573,definition,(
% 1.65/1.51 spl0_14 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y1 @ Y0) & (sK9 @ Y0 @ Y2)) => (sK9 @ Y1 @ Y2)))))))) = $false)),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.65/1.51 thf(f500,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK9 @ X1 @ X2) & (sK9 @ X2 @ Y0)) => (sK9 @ X1 @ Y0)))))) ) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f499])).
% 1.65/1.51 thf(f499,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK9 @ X1 @ Y0) & (sK9 @ Y0 @ Y1)) => (sK9 @ X1 @ Y1))))) @ X2))) ) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f496])).
% 1.65/1.51 thf(f496,plain,(
% 1.65/1.51 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK9 @ X1 @ Y0) & (sK9 @ Y0 @ Y1)) => (sK9 @ X1 @ Y1)))))) = $true)) ) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f495])).
% 1.65/1.51 thf(f495,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2))))))) @ X1))) ) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f492])).
% 1.65/1.51 thf(f492,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2))))))))) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f491])).
% 1.65/1.51 thf(f491,plain,(
% 1.65/1.51 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y1) & (sK9 @ Y1 @ Y2)) => (sK9 @ Y0 @ Y2)))))))))) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f481,f490])).
% 1.65/1.51 thf(f578,plain,(
% 1.65/1.51 spl0_14 | spl0_15 | ~spl0_3 | ~spl0_5),
% 1.65/1.51 inference(avatar_split_clause,[status(thm)],[f569,f113,f70,f576,f573])).
% 1.65/1.51 thf(f569,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y1 @ Y0) & (sK9 @ Y0 @ Y2)) => (sK9 @ Y1 @ Y2)))))))) = $false) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f486])).
% 1.65/1.51 thf(f486,plain,(
% 1.65/1.51 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y1 @ Y0) & (sK9 @ Y0 @ Y2)) => (sK9 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0)))))))) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(not_proxy_clausification,[status(thm)],[f485])).
% 1.65/1.51 thf(f485,plain,(
% 1.65/1.51 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y1 @ Y0) & (sK9 @ Y0 @ Y2)) => (sK9 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))))) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f484])).
% 1.65/1.51 thf(f484,plain,(
% 1.65/1.51 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y1 @ Y0) & (sK9 @ Y0 @ Y2)) => (sK9 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))) => $false)) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(superposition,[status(thm)],[f471,f483])).
% 1.65/1.51 thf(f483,plain,(
% 1.65/1.51 ((sK9 @ sK8 @ sK7) = $false) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f482])).
% 1.65/1.51 thf(f482,plain,(
% 1.65/1.51 ($false = ($true => (sK9 @ sK8 @ sK7))) | (~spl0_3 | ~spl0_5)),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f479,f481])).
% 1.65/1.51 thf(f471,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y0) & (X1 @ Y0 @ Y2)) => (X1 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK8 @ sK7)))) ) | ~spl0_5),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f470])).
% 1.65/1.51 thf(f470,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))) @ X1))) ) | ~spl0_5),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f114])).
% 1.65/1.51 thf(f463,plain,(
% 1.65/1.51 ~spl0_13),
% 1.65/1.51 inference(avatar_contradiction_clause,[status(thm)],[f462])).
% 1.65/1.51 thf(f462,plain,(
% 1.65/1.51 $false | ~spl0_13),
% 1.65/1.51 inference(trivial_inequality_removal,[status(thm)],[f457])).
% 1.65/1.51 thf(f457,plain,(
% 1.65/1.51 ($true = $false) | ~spl0_13),
% 1.65/1.51 inference(superposition,[status(thm)],[f455,f37])).
% 1.65/1.51 thf(f37,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0 @ X2) & (sK6 @ X2 @ X1)) => (sK6 @ Y0 @ X1)))))) )),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.65/1.51 thf(f36,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ X1)) => (sK6 @ Y1 @ X1))))) @ X2))) )),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f35])).
% 1.65/1.51 thf(f35,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ X1)) => (sK6 @ Y1 @ X1)))))))) )),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.65/1.51 thf(f34,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0))))))) @ X1))) )),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f33])).
% 1.65/1.51 thf(f33,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0)))))))))),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f32])).
% 1.65/1.51 thf(f32,plain,(
% 1.65/1.51 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0)))))))) & $true))),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f25,f30])).
% 1.65/1.51 thf(f30,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))))),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.65/1.51 thf(f25,plain,(
% 1.65/1.51 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))))))),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.65/1.51 thf(f23,plain,(
% 1.65/1.51 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))))) => (sK6 @ sK5 @ sK3)))),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.65/1.51 thf(f22,plain,(
% 1.65/1.51 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK5 @ sK3))) @ sK6) = $false)),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f21])).
% 1.65/1.51 thf(f21,plain,(
% 1.65/1.51 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK5 @ sK3)))) = $false)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f20])).
% 1.65/1.51 thf(f20,plain,(
% 1.65/1.51 ($false = ($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK5 @ sK3))))))),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f17,f19])).
% 1.65/1.51 thf(f19,plain,(
% 1.65/1.51 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))))))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK5 @ sK3))))))),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.65/1.51 thf(f17,plain,(
% 1.65/1.51 (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))))))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK5 @ sK3))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK4 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK5 @ sK3))))) = $false)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.65/1.51 thf(f16,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK4 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y1 @ Y2)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK4 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y3))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK4 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))))))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK3))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK3)))))) @ sK5))),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f15])).
% 1.65/1.51 thf(f15,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK4 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y1 @ Y2)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK4 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y3))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK4 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))))))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK3))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK4 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK3))))))) = $false)),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.65/1.51 thf(f14,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y2 @ Y3)))) & (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y8 @ Y6)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y8 @ Y6)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y2 @ Y4))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y3 @ Y2)))))))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (Y0 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK3))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (Y0 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ sK3)))))))) @ sK4))),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f13])).
% 1.65/1.51 thf(f13,plain,(
% 1.65/1.51 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y2 @ Y3)))) & (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y8 @ Y6)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y8 @ Y6)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y2 @ Y4))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y3 @ Y2)))))))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (Y0 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ sK3))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (Y0 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ sK3))))))))))),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.65/1.51 thf(f12,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: ((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y3 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y4 @ Y5))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y3 @ Y5))))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y1 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y8 @ Y6)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y1 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8))))))))) => (Y5 @ Y4 @ Y3)))))))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (Y1 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (Y1 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0)))))))))) @ sK3))),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f11])).
% 1.65/1.51 thf(f11,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: ((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y3 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y4 @ Y5))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y3 @ Y5))))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y1 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y8 @ Y6)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y1 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8))))))))) => (Y5 @ Y4 @ Y3)))))))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (Y1 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (Y1 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y0))))))))))))),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.65/1.51 thf(f10,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y4 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y5 @ Y6))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y4 @ Y6))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y9 @ Y7)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y3 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y1)))))))))))) @ sK2))),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f7])).
% 1.65/1.51 thf(f7,plain,(
% 1.65/1.51 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y4 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y5 @ Y6))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y4 @ Y6))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y9 @ Y7)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y3 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y1))))))))))))) = $false)),
% 1.65/1.51 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.65/1.51 thf(f6,plain,(
% 1.65/1.51 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y4 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y5 @ Y6))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y4 @ Y6))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y9 @ Y7)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y3 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y1)))))))))))))))),
% 1.65/1.51 inference(cnf_transformation,[status(thm)],[f5])).
% 1.65/1.51 thf(f5,plain,(
% 1.65/1.51 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y4 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y2 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y5 @ Y6))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y10 @ Y8)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y4 @ Y6))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y7) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y9 @ Y7)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y3 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y5 @ Y6) | (Y2 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y1)))))))))))))))),
% 1.65/1.51 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.51 thf(f4,plain,(
% 1.65/1.51 ~! [X0 : a,X1 : a > a > $o,X2 : a,X3 : a > a > $o] : (((! [X4 : a,X5 : a] : ((! [X6 : a > a > $o] : ((! [X7 : a,X8 : a] : ((X3 @ X7 @ X8) => (X6 @ X7 @ X8)) & ! [X9 : a,X10 : a,X11 : a] : (((X6 @ X10 @ X11) & (X6 @ X9 @ X10)) => (X6 @ X9 @ X11))) => (X6 @ X4 @ X5)) | ! [X12 : a > a > $o] : ((! [X13 : a,X14 : a] : ((X1 @ X13 @ X14) => (X12 @ X13 @ X14)) & ! [X15 : a,X16 : a,X17 : a] : (((X12 @ X17 @ X15) & (X12 @ X16 @ X17)) => (X12 @ X16 @ X15))) => (X12 @ X4 @ X5))) => ! [X18 : a > a > $o] : ((! [X19 : a,X20 : a,X21 : a] : (((X18 @ X20 @ X19) & (X18 @ X21 @ X20)) => (X18 @ X21 @ X19)) & ! [X22 : a,X23 : a] : (((X3 @ X23 @ X22) | (X1 @ X23 @ X22)) => (X18 @ X23 @ X22))) => (X18 @ X4 @ X5))) & ! [X24 : a,X25 : a,X26 : a] : ((! [X27 : a > a > $o] : ((! [X28 : a,X29 : a,X30 : a] : (((X27 @ X28 @ X30) & (X27 @ X30 @ X29)) => (X27 @ X28 @ X29)) & ! [X31 : a,X32 : a] : (((X3 @ X32 @ X31) | (X1 @ X32 @ X31)) => (X27 @ X32 @ X31))) => (X27 @ X25 @ X24)) & ! [X33 : a > a > $o] : ((! [X34 : a,X35 : a] : (((X3 @ X35 @ X34) | (X1 @ X35 @ X34)) => (X33 @ X35 @ X34)) & ! [X36 : a,X37 : a,X38 : a] : (((X33 @ X36 @ X37) & (X33 @ X38 @ X36)) => (X33 @ X38 @ X37))) => (X33 @ X26 @ X25))) => ! [X39 : a > a > $o] : ((! [X40 : a,X41 : a,X42 : a] : (((X39 @ X40 @ X42) & (X39 @ X42 @ X41)) => (X39 @ X40 @ X41)) & ! [X43 : a,X44 : a] : (((X1 @ X43 @ X44) | (X3 @ X43 @ X44)) => (X39 @ X43 @ X44))) => (X39 @ X26 @ X24)))) => ! [X45 : a > a > $o] : ((! [X46 : a,X47 : a,X48 : a] : (((X45 @ X48 @ X47) & (X45 @ X46 @ X48)) => (X45 @ X46 @ X47)) & ! [X49 : a,X50 : a] : (((X1 @ X49 @ X50) | (X3 @ X49 @ X50)) => (X45 @ X49 @ X50))) => (X45 @ X0 @ X2))) => ! [X51 : a > a > $o] : ((! [X52 : a,X53 : a] : (((X1 @ X53 @ X52) | (X3 @ X53 @ X52)) => (X51 @ X53 @ X52)) & ! [X54 : a,X55 : a,X56 : a] : (((X51 @ X55 @ X56) & (X51 @ X54 @ X55)) => (X51 @ X54 @ X56))) => (X51 @ X0 @ X2)))),
% 1.65/1.51 inference(rectify,[status(thm)],[f2])).
% 1.65/1.51 thf(f2,negated_conjecture,(
% 1.65/1.51 ~! [X2 : a,X1 : a > a > $o,X3 : a,X0 : a > a > $o] : (((! [X4 : a,X5 : a] : ((! [X6 : a > a > $o] : ((! [X7 : a,X8 : a] : ((X0 @ X7 @ X8) => (X6 @ X7 @ X8)) & ! [X7 : a,X8 : a,X9 : a] : (((X6 @ X8 @ X9) & (X6 @ X7 @ X8)) => (X6 @ X7 @ X9))) => (X6 @ X4 @ X5)) | ! [X6 : a > a > $o] : ((! [X7 : a,X8 : a] : ((X1 @ X7 @ X8) => (X6 @ X7 @ X8)) & ! [X9 : a,X7 : a,X8 : a] : (((X6 @ X8 @ X9) & (X6 @ X7 @ X8)) => (X6 @ X7 @ X9))) => (X6 @ X4 @ X5))) => ! [X6 : a > a > $o] : ((! [X9 : a,X8 : a,X7 : a] : (((X6 @ X8 @ X9) & (X6 @ X7 @ X8)) => (X6 @ X7 @ X9)) & ! [X8 : a,X7 : a] : (((X0 @ X7 @ X8) | (X1 @ X7 @ X8)) => (X6 @ X7 @ X8))) => (X6 @ X4 @ X5))) & ! [X9 : a,X5 : a,X4 : a] : ((! [X6 : a > a > $o] : ((! [X7 : a,X10 : a,X8 : a] : (((X6 @ X7 @ X8) & (X6 @ X8 @ X10)) => (X6 @ X7 @ X10)) & ! [X8 : a,X7 : a] : (((X0 @ X7 @ X8) | (X1 @ X7 @ X8)) => (X6 @ X7 @ X8))) => (X6 @ X5 @ X9)) & ! [X6 : a > a > $o] : ((! [X8 : a,X7 : a] : (((X0 @ X7 @ X8) | (X1 @ X7 @ X8)) => (X6 @ X7 @ X8)) & ! [X8 : a,X10 : a,X7 : a] : (((X6 @ X8 @ X10) & (X6 @ X7 @ X8)) => (X6 @ X7 @ X10))) => (X6 @ X4 @ X5))) => ! [X6 : a > a > $o] : ((! [X7 : a,X10 : a,X8 : a] : (((X6 @ X7 @ X8) & (X6 @ X8 @ X10)) => (X6 @ X7 @ X10)) & ! [X7 : a,X8 : a] : (((X1 @ X7 @ X8) | (X0 @ X7 @ X8)) => (X6 @ X7 @ X8))) => (X6 @ X4 @ X9)))) => ! [X6 : a > a > $o] : ((! [X4 : a,X9 : a,X5 : a] : (((X6 @ X5 @ X9) & (X6 @ X4 @ X5)) => (X6 @ X4 @ X9)) & ! [X4 : a,X5 : a] : (((X1 @ X4 @ X5) | (X0 @ X4 @ X5)) => (X6 @ X4 @ X5))) => (X6 @ X2 @ X3))) => ! [X6 : a > a > $o] : ((! [X5 : a,X4 : a] : (((X1 @ X4 @ X5) | (X0 @ X4 @ X5)) => (X6 @ X4 @ X5)) & ! [X4 : a,X5 : a,X9 : a] : (((X6 @ X5 @ X9) & (X6 @ X4 @ X5)) => (X6 @ X4 @ X9))) => (X6 @ X2 @ X3)))),
% 1.65/1.51 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.51 thf(f1,conjecture,(
% 1.65/1.51 ! [X2 : a,X1 : a > a > $o,X3 : a,X0 : a > a > $o] : (((! [X4 : a,X5 : a] : ((! [X6 : a > a > $o] : ((! [X7 : a,X8 : a] : ((X0 @ X7 @ X8) => (X6 @ X7 @ X8)) & ! [X7 : a,X8 : a,X9 : a] : (((X6 @ X8 @ X9) & (X6 @ X7 @ X8)) => (X6 @ X7 @ X9))) => (X6 @ X4 @ X5)) | ! [X6 : a > a > $o] : ((! [X7 : a,X8 : a] : ((X1 @ X7 @ X8) => (X6 @ X7 @ X8)) & ! [X9 : a,X7 : a,X8 : a] : (((X6 @ X8 @ X9) & (X6 @ X7 @ X8)) => (X6 @ X7 @ X9))) => (X6 @ X4 @ X5))) => ! [X6 : a > a > $o] : ((! [X9 : a,X8 : a,X7 : a] : (((X6 @ X8 @ X9) & (X6 @ X7 @ X8)) => (X6 @ X7 @ X9)) & ! [X8 : a,X7 : a] : (((X0 @ X7 @ X8) | (X1 @ X7 @ X8)) => (X6 @ X7 @ X8))) => (X6 @ X4 @ X5))) & ! [X9 : a,X5 : a,X4 : a] : ((! [X6 : a > a > $o] : ((! [X7 : a,X10 : a,X8 : a] : (((X6 @ X7 @ X8) & (X6 @ X8 @ X10)) => (X6 @ X7 @ X10)) & ! [X8 : a,X7 : a] : (((X0 @ X7 @ X8) | (X1 @ X7 @ X8)) => (X6 @ X7 @ X8))) => (X6 @ X5 @ X9)) & ! [X6 : a > a > $o] : ((! [X8 : a,X7 : a] : (((X0 @ X7 @ X8) | (X1 @ X7 @ X8)) => (X6 @ X7 @ X8)) & ! [X8 : a,X10 : a,X7 : a] : (((X6 @ X8 @ X10) & (X6 @ X7 @ X8)) => (X6 @ X7 @ X10))) => (X6 @ X4 @ X5))) => ! [X6 : a > a > $o] : ((! [X7 : a,X10 : a,X8 : a] : (((X6 @ X7 @ X8) & (X6 @ X8 @ X10)) => (X6 @ X7 @ X10)) & ! [X7 : a,X8 : a] : (((X1 @ X7 @ X8) | (X0 @ X7 @ X8)) => (X6 @ X7 @ X8))) => (X6 @ X4 @ X9)))) => ! [X6 : a > a > $o] : ((! [X4 : a,X9 : a,X5 : a] : (((X6 @ X5 @ X9) & (X6 @ X4 @ X5)) => (X6 @ X4 @ X9)) & ! [X4 : a,X5 : a] : (((X1 @ X4 @ X5) | (X0 @ X4 @ X5)) => (X6 @ X4 @ X5))) => (X6 @ X2 @ X3))) => ! [X6 : a > a > $o] : ((! [X5 : a,X4 : a] : (((X1 @ X4 @ X5) | (X0 @ X4 @ X5)) => (X6 @ X4 @ X5)) & ! [X4 : a,X5 : a,X9 : a] : (((X6 @ X5 @ X9) & (X6 @ X4 @ X5)) => (X6 @ X4 @ X9))) => (X6 @ X2 @ X3)))),
% 1.65/1.51 file('/export/starexec/sandbox2/tmp/tmp.QkaXZIWX9l/DTF2THF_29067.p',cTHM250D_pme)).
% 1.65/1.51 thf(f455,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0 @ sK18) & (sK6 @ sK18 @ sK19)) => (sK6 @ Y0 @ sK19))))) | ~spl0_13),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f454])).
% 1.65/1.51 thf(f454,plain,(
% 1.65/1.51 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ sK18) & (sK6 @ sK18 @ Y0)) => (sK6 @ Y1 @ Y0))))) @ sK19) = $false) | ~spl0_13),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f453])).
% 1.65/1.51 thf(f453,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ sK18) & (sK6 @ sK18 @ Y0)) => (sK6 @ Y1 @ Y0))))))) | ~spl0_13),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f449])).
% 1.65/1.51 thf(f449,plain,(
% 1.65/1.51 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1))))))) @ sK18) = $false) | ~spl0_13),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f426])).
% 1.65/1.51 thf(f426,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) = $false) | ~spl0_13),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f425])).
% 1.65/1.51 thf(f425,definition,(
% 1.65/1.51 spl0_13 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) = $false)),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.65/1.51 thf(f444,plain,(
% 1.65/1.51 ~spl0_12),
% 1.65/1.51 inference(avatar_contradiction_clause,[status(thm)],[f443])).
% 1.65/1.51 thf(f443,plain,(
% 1.65/1.51 $false | ~spl0_12),
% 1.65/1.51 inference(trivial_inequality_removal,[status(thm)],[f440])).
% 1.65/1.51 thf(f440,plain,(
% 1.65/1.51 ($true = $false) | ~spl0_12),
% 1.65/1.51 inference(superposition,[status(thm)],[f92,f436])).
% 1.65/1.51 thf(f436,plain,(
% 1.65/1.51 ($false = (((sK2 @ sK17 @ sK16) | (sK4 @ sK17 @ sK16)) => (sK6 @ sK17 @ sK16))) | ~spl0_12),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f435])).
% 1.65/1.51 thf(f435,plain,(
% 1.65/1.51 (((^[Y0 : a]: (((sK2 @ Y0 @ sK16) | (sK4 @ Y0 @ sK16)) => (sK6 @ Y0 @ sK16))) @ sK17) = $false) | ~spl0_12),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f432])).
% 1.65/1.51 thf(f432,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK16) | (sK4 @ Y0 @ sK16)) => (sK6 @ Y0 @ sK16))))) | ~spl0_12),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f430])).
% 1.65/1.51 thf(f430,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0))))) @ sK16)) | ~spl0_12),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f423])).
% 1.65/1.51 thf(f423,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false) | ~spl0_12),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f422])).
% 1.65/1.51 thf(f422,definition,(
% 1.65/1.51 spl0_12 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false)),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.65/1.51 thf(f92,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = (((sK2 @ X1 @ X2) | (sK4 @ X1 @ X2)) => (sK6 @ X1 @ X2)))) )),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.65/1.51 thf(f91,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK2 @ X1 @ Y0) | (sK4 @ X1 @ Y0)) => (sK6 @ X1 @ Y0))) @ X2))) )),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f88])).
% 1.65/1.51 thf(f88,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK2 @ X1 @ Y0) | (sK4 @ X1 @ Y0)) => (sK6 @ X1 @ Y0)))))) )),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f87])).
% 1.65/1.51 thf(f87,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK4 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))) @ X1))) )),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f30])).
% 1.65/1.51 thf(f427,plain,(
% 1.65/1.51 spl0_12 | spl0_13 | ~spl0_1),
% 1.65/1.51 inference(avatar_split_clause,[status(thm)],[f418,f51,f425,f422])).
% 1.65/1.51 thf(f51,definition,(
% 1.65/1.51 spl0_1 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK5 @ sK3)))))),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.65/1.51 thf(f418,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false) | ~spl0_1),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f415])).
% 1.65/1.51 thf(f415,plain,(
% 1.65/1.51 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1)))))))))) | ~spl0_1),
% 1.65/1.51 inference(not_proxy_clausification,[status(thm)],[f414])).
% 1.65/1.51 thf(f414,plain,(
% 1.65/1.51 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1))))))))))) | ~spl0_1),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f408])).
% 1.65/1.51 thf(f408,plain,(
% 1.65/1.51 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y2 @ Y1))))))))) => $false)) | ~spl0_1),
% 1.65/1.51 inference(superposition,[status(thm)],[f405,f24])).
% 1.65/1.51 thf(f24,plain,(
% 1.65/1.51 ($false = (sK6 @ sK5 @ sK3))),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.65/1.51 thf(f405,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y2 @ Y0) & (X1 @ Y0 @ Y1)) => (X1 @ Y2 @ Y1))))))))) => (X1 @ sK5 @ sK3)))) ) | ~spl0_1),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f404])).
% 1.65/1.51 thf(f404,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK5 @ sK3))) @ X1))) ) | ~spl0_1),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f52])).
% 1.65/1.51 thf(f52,plain,(
% 1.65/1.51 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK5 @ sK3))))) | ~spl0_1),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.65/1.51 thf(f401,plain,(
% 1.65/1.51 spl0_11 | spl0_7 | ~spl0_4 | ~spl0_8),
% 1.65/1.51 inference(avatar_split_clause,[status(thm)],[f395,f247,f73,f244,f399])).
% 1.65/1.51 thf(f247,definition,(
% 1.65/1.51 spl0_8 <=> ($true = (sK13 @ sK11 @ sK12))),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.65/1.51 thf(f395,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y2) & (sK13 @ Y2 @ Y1)) => (sK13 @ Y0 @ Y1)))))))) = $false) | (~spl0_4 | ~spl0_8)),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f392])).
% 1.65/1.51 thf(f392,plain,(
% 1.65/1.51 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y2) & (sK13 @ Y2 @ Y1)) => (sK13 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1)))))))) | (~spl0_4 | ~spl0_8)),
% 1.65/1.51 inference(not_proxy_clausification,[status(thm)],[f321])).
% 1.65/1.51 thf(f321,plain,(
% 1.65/1.51 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y2) & (sK13 @ Y2 @ Y1)) => (sK13 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1))))))))) | (~spl0_4 | ~spl0_8)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f319])).
% 1.65/1.51 thf(f319,plain,(
% 1.65/1.51 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y2) & (sK13 @ Y2 @ Y1)) => (sK13 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1))))))) => $false)) | (~spl0_4 | ~spl0_8)),
% 1.65/1.51 inference(superposition,[status(thm)],[f224,f296])).
% 1.65/1.51 thf(f296,plain,(
% 1.65/1.51 ((sK13 @ sK10 @ sK11) = $false) | (~spl0_4 | ~spl0_8)),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f288])).
% 1.65/1.51 thf(f288,plain,(
% 1.65/1.51 ($false = ($true & (sK13 @ sK10 @ sK11))) | (~spl0_4 | ~spl0_8)),
% 1.65/1.51 inference(superposition,[status(thm)],[f225,f248])).
% 1.65/1.51 thf(f248,plain,(
% 1.65/1.51 ($true = (sK13 @ sK11 @ sK12)) | ~spl0_8),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f247])).
% 1.65/1.51 thf(f225,plain,(
% 1.65/1.51 ( ! [X0 : a] : (($false = ((sK13 @ X0 @ sK12) & (sK13 @ sK10 @ X0)))) ) | ~spl0_4),
% 1.65/1.51 inference(not_proxy_clausification,[status(thm)],[f214])).
% 1.65/1.51 thf(f214,plain,(
% 1.65/1.51 ( ! [X0 : a] : (($true = (~ ((sK13 @ X0 @ sK12) & (sK13 @ sK10 @ X0))))) ) | ~spl0_4),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f207])).
% 1.65/1.51 thf(f207,plain,(
% 1.65/1.51 ( ! [X0 : a] : (($true = (((sK13 @ X0 @ sK12) & (sK13 @ sK10 @ X0)) => $false))) ) | ~spl0_4),
% 1.65/1.51 inference(superposition,[status(thm)],[f197,f152])).
% 1.65/1.51 thf(f152,plain,(
% 1.65/1.51 ((sK13 @ sK10 @ sK12) = $false) | ~spl0_4),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f151])).
% 1.65/1.51 thf(f151,plain,(
% 1.65/1.51 ($false = ($true => (sK13 @ sK10 @ sK12))) | ~spl0_4),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f148,f150])).
% 1.65/1.51 thf(f150,plain,(
% 1.65/1.51 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK13 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y1) & (sK13 @ Y2 @ Y0)) => (sK13 @ Y2 @ Y1))))))))) = $true) | ~spl0_4),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f148])).
% 1.65/1.51 thf(f148,plain,(
% 1.65/1.51 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK13 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y1) & (sK13 @ Y2 @ Y0)) => (sK13 @ Y2 @ Y1))))))))) => (sK13 @ sK10 @ sK12))) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f147])).
% 1.65/1.51 thf(f147,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK12))) @ sK13)) | ~spl0_4),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f141])).
% 1.65/1.51 thf(f141,plain,(
% 1.65/1.51 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK12))))) | ~spl0_4),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.65/1.51 thf(f140,plain,(
% 1.65/1.51 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK10 @ sK11)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK11 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK10 @ sK12)))))) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f139])).
% 1.65/1.51 thf(f139,plain,(
% 1.65/1.51 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK10 @ sK11)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK11 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))))) @ sK12) = $false) | ~spl0_4),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f134])).
% 1.65/1.51 thf(f134,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK10 @ sK11)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK11 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK10 @ Y0)))))))) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f133])).
% 1.65/1.51 thf(f133,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK10 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ sK10 @ Y1)))))))) @ sK11)) | ~spl0_4),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f128])).
% 1.65/1.51 thf(f128,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK10 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ sK10 @ Y1)))))))))) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f127])).
% 1.65/1.51 thf(f127,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2)))))))))) @ sK10)) | ~spl0_4),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f74])).
% 1.65/1.51 thf(f197,plain,(
% 1.65/1.51 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK13 @ X1 @ X2) & (sK13 @ X3 @ X1)) => (sK13 @ X3 @ X2)) = $true)) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f196])).
% 1.65/1.51 thf(f196,plain,(
% 1.65/1.51 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK13 @ X1 @ X2) & (sK13 @ Y0 @ X1)) => (sK13 @ Y0 @ X2))) @ X3))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f187])).
% 1.65/1.51 thf(f187,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK13 @ X1 @ X2) & (sK13 @ Y0 @ X1)) => (sK13 @ Y0 @ X2)))))) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f186])).
% 1.65/1.51 thf(f186,plain,(
% 1.65/1.51 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ X1 @ Y0) & (sK13 @ Y1 @ X1)) => (sK13 @ Y1 @ Y0))))) @ X2))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f182])).
% 1.65/1.51 thf(f182,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ X1 @ Y0) & (sK13 @ Y1 @ X1)) => (sK13 @ Y1 @ Y0)))))))) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f179])).
% 1.65/1.51 thf(f179,plain,(
% 1.65/1.51 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y1) & (sK13 @ Y2 @ Y0)) => (sK13 @ Y2 @ Y1))))))) @ X1))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f156])).
% 1.65/1.51 thf(f156,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y1) & (sK13 @ Y2 @ Y0)) => (sK13 @ Y2 @ Y1))))))))) | ~spl0_4),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f155])).
% 1.65/1.51 thf(f155,plain,(
% 1.65/1.51 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK13 @ Y0 @ Y1) & (sK13 @ Y2 @ Y0)) => (sK13 @ Y2 @ Y1)))))))))) | ~spl0_4),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f150,f154])).
% 1.65/1.51 thf(f154,plain,(
% 1.65/1.51 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0)) => (sK13 @ Y1 @ Y0))))))) | ~spl0_4),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f150])).
% 1.65/1.51 thf(f224,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y2) & (X1 @ Y2 @ Y1)) => (X1 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK10 @ sK11)))) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f223])).
% 1.65/1.51 thf(f223,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK10 @ sK11))) @ X1))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f158])).
% 1.65/1.51 thf(f158,plain,(
% 1.65/1.51 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK10 @ sK11))))) | ~spl0_4),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f142])).
% 1.65/1.51 thf(f142,plain,(
% 1.65/1.51 ($true = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK10 @ sK11)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK11 @ sK12)))))) | ~spl0_4),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.65/1.51 thf(f285,plain,(
% 1.65/1.51 spl0_9 | spl0_10 | ~spl0_7),
% 1.65/1.51 inference(avatar_split_clause,[status(thm)],[f278,f244,f283,f280])).
% 1.65/1.51 thf(f278,plain,(
% 1.65/1.51 ($true = (sK4 @ sK14 @ sK15)) | ($true = (sK2 @ sK14 @ sK15)) | ~spl0_7),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f263])).
% 1.65/1.51 thf(f263,plain,(
% 1.65/1.51 ($true = ((sK4 @ sK14 @ sK15) | (sK2 @ sK14 @ sK15))) | ~spl0_7),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f261])).
% 1.65/1.51 thf(f261,plain,(
% 1.65/1.51 ((((sK4 @ sK14 @ sK15) | (sK2 @ sK14 @ sK15)) => (sK13 @ sK14 @ sK15)) = $false) | ~spl0_7),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f260])).
% 1.65/1.51 thf(f260,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (((sK4 @ sK14 @ Y0) | (sK2 @ sK14 @ Y0)) => (sK13 @ sK14 @ Y0))) @ sK15)) | ~spl0_7),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f257])).
% 1.65/1.51 thf(f257,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK14 @ Y0) | (sK2 @ sK14 @ Y0)) => (sK13 @ sK14 @ Y0)))) = $false) | ~spl0_7),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f252])).
% 1.65/1.51 thf(f252,plain,(
% 1.65/1.51 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1))))) @ sK14) = $false) | ~spl0_7),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f245])).
% 1.65/1.51 thf(f249,plain,(
% 1.65/1.51 spl0_7 | spl0_8 | ~spl0_4),
% 1.65/1.51 inference(avatar_split_clause,[status(thm)],[f242,f73,f247,f244])).
% 1.65/1.51 thf(f242,plain,(
% 1.65/1.51 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1))))))) | ($true = (sK13 @ sK11 @ sK12)) | ~spl0_4),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f181])).
% 1.65/1.51 thf(f181,plain,(
% 1.65/1.51 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1)))))) => (sK13 @ sK11 @ sK12)) = $true) | ~spl0_4),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f180])).
% 1.65/1.51 thf(f180,plain,(
% 1.65/1.51 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK13 @ Y0 @ Y1)))))) & $true) => (sK13 @ sK11 @ sK12))) | ~spl0_4),
% 1.65/1.51 inference(superposition,[status(thm)],[f164,f156])).
% 1.65/1.51 thf(f164,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y1) & (X1 @ Y2 @ Y0)) => (X1 @ Y2 @ Y1))))))))) => (X1 @ sK11 @ sK12)))) ) | ~spl0_4),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f163])).
% 1.65/1.51 thf(f163,plain,(
% 1.65/1.51 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK11 @ sK12))) @ X1))) ) | ~spl0_4),
% 1.65/1.51 inference(pi_clausification,[status(thm)],[f160])).
% 1.65/1.51 thf(f160,plain,(
% 1.65/1.51 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK11 @ sK12))))) | ~spl0_4),
% 1.65/1.51 inference(boolean_simplification,[status(thm)],[f159])).
% 1.65/1.51 thf(f159,plain,(
% 1.65/1.51 ($true = ($true & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK11 @ sK12)))))) | ~spl0_4),
% 1.65/1.51 inference(backward_demodulation,[status(thm)],[f142,f158])).
% 1.65/1.51 thf(f118,plain,(
% 1.65/1.51 spl0_5 | spl0_6 | ~spl0_3),
% 1.65/1.51 inference(avatar_split_clause,[status(thm)],[f111,f70,f116,f113])).
% 1.65/1.51 thf(f111,plain,(
% 1.65/1.51 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))))) | ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))))) | ~spl0_3),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.65/1.51 thf(f94,plain,(
% 1.65/1.51 ($true = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))))) | ~spl0_3),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.65/1.51 thf(f90,plain,(
% 1.65/1.51 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK8 @ sK7)))))) | ~spl0_3),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.65/1.51 thf(f89,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK7))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK7)))))) @ sK8)) | ~spl0_3),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f86])).
% 1.65/1.51 thf(f86,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK7)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK7))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK4 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK7))))))) = $false) | ~spl0_3),
% 1.65/1.51 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.65/1.51 thf(f85,plain,(
% 1.65/1.51 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK7)) | ~spl0_3),
% 1.65/1.51 inference(sigma_clausification,[status(thm)],[f71])).
% 1.65/1.51 thf(f75,plain,(
% 1.65/1.51 spl0_3 | spl0_4 | ~spl0_2),
% 1.65/1.51 inference(avatar_split_clause,[status(thm)],[f68,f54,f73,f70])).
% 1.65/1.51 thf(f54,definition,(
% 1.65/1.51 spl0_2 <=> (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))))))))) = $false)),
% 1.65/1.51 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.65/1.51 thf(f68,plain,(
% 1.65/1.51 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false) | ~spl0_2),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.65/1.51 thf(f55,plain,(
% 1.65/1.51 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))))))))) = $false) | ~spl0_2),
% 1.65/1.51 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.65/1.51 thf(f56,plain,(
% 1.65/1.51 spl0_1 | spl0_2),
% 1.65/1.51 inference(avatar_split_clause,[status(thm)],[f49,f54,f51])).
% 1.65/1.51 thf(f49,plain,(
% 1.65/1.51 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK4 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK4 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))))))))) = $false) | ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK5 @ sK3)))))),
% 1.65/1.51 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.65/1.51 % SZS output end Proof for DTF2THF_29067
% 1.65/1.51 % (29305)------------------------------
% 1.65/1.51 % (29305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.51 % (29305)Termination reason: Refutation
% 1.65/1.51
% 1.65/1.51 % (29305)Memory used [KB]: 7036
% 1.65/1.51 % (29305)Time elapsed: 0.168 s
% 1.65/1.51 % (29305)Instructions burned: 353 (million)
% 1.65/1.51 % (29305)------------------------------
% 1.65/1.51 % (29305)------------------------------
% 1.65/1.51 % (29293)Success in time 0.201 s
%------------------------------------------------------------------------------