%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV040^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 09:40:08 AM UTC 2026
% Result : Theorem 1.51s 1.32s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 23
% Syntax : Number of formulae : 400 ( 4 unt; 0 typ; 22 def)
% Number of atoms : 4598 ( 638 equ; 0 cnn)
% Maximal formula atoms : 7 ( 11 avg)
% Number of connectives : 10809 ( 693 ~; 648 |; 945 &;6365 @)
% ( 22 <=>; 706 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 434 ( 434 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 77 usr; 59 con; 0-2 aty)
% (1430 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1755 (1547 ^; 208 !; 0 ?;1755 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a > a > $o ).
thf(func_def_18,type,
sK3: a > a > $o ).
thf(func_def_19,type,
sK4: a > a > $o ).
thf(func_def_20,type,
sK5: a > a > $o ).
thf(func_def_21,type,
sK6: a > a > $o ).
thf(func_def_22,type,
sK7: a > a > $o ).
thf(func_def_23,type,
sK8: a > a > $o ).
thf(func_def_24,type,
sK9: a ).
thf(func_def_25,type,
sK10: a ).
thf(func_def_26,type,
sK11: a ).
thf(func_def_27,type,
sK12: a ).
thf(func_def_28,type,
sK13: a ).
thf(func_def_29,type,
sK14: a > a > $o ).
thf(func_def_30,type,
sK15: a > a > $o ).
thf(func_def_31,type,
sK16: a ).
thf(func_def_32,type,
sK17: a ).
thf(func_def_33,type,
sK18: a ).
thf(func_def_34,type,
sK19: a ).
thf(func_def_35,type,
sK20: a ).
thf(func_def_36,type,
sK21: a ).
thf(func_def_37,type,
sK22: a ).
thf(func_def_38,type,
sK23: a > a > $o ).
thf(func_def_39,type,
sK24: a ).
thf(func_def_40,type,
sK25: a ).
thf(func_def_41,type,
sK26: a ).
thf(func_def_42,type,
sK27: a ).
thf(func_def_43,type,
sK28: a ).
thf(func_def_44,type,
sK29: a ).
thf(func_def_45,type,
sK30: a ).
thf(func_def_46,type,
sK31: a ).
thf(func_def_47,type,
sK32: a ).
thf(func_def_48,type,
sK33: a > a > $o ).
thf(func_def_49,type,
sK34: a ).
thf(func_def_50,type,
sK35: a > a > $o ).
thf(func_def_51,type,
sK36: a ).
thf(func_def_52,type,
sK37: a > a > $o ).
thf(func_def_53,type,
sK38: a > a > $o ).
thf(func_def_54,type,
sK39: a > a > $o ).
thf(func_def_55,type,
sK40: a > a > $o ).
thf(func_def_56,type,
sK41: a ).
thf(func_def_57,type,
sK42: a ).
thf(func_def_58,type,
sK43: a ).
thf(func_def_59,type,
sK44: a ).
thf(func_def_60,type,
sK45: a ).
thf(func_def_61,type,
sK46: a > a > $o ).
thf(func_def_62,type,
sK47: a ).
thf(func_def_63,type,
sK48: a > a > $o ).
thf(func_def_64,type,
sK49: a ).
thf(func_def_65,type,
sK50: a ).
thf(func_def_66,type,
sK51: a > a > $o ).
thf(func_def_67,type,
sK52: a ).
thf(func_def_68,type,
sK53: a > a > $o ).
thf(func_def_69,type,
sK54: a ).
thf(func_def_70,type,
sK55: a ).
thf(f1654,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f17,f27,f51,f399,f447,f610,f625,f697,f744,f883,f920,f927,f931,f987,f991,f1009,f1016,f1032,f1041,f1170,f1298,f1323,f1473,f1653]) ).
thf(f1653,plain,
( ~ spl0_4
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f1652]) ).
thf(f1652,plain,
( $false
| ~ spl0_4
| ~ spl0_28 ),
inference(trivial_inequality_removal,[status(thm)],[f1651]) ).
thf(f1651,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1650]) ).
thf(f1650,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_4
| ~ spl0_28 ),
inference(forward_demodulation,[status(thm)],[f1644,f1568]) ).
thf(f1568,plain,
( ( $true
= ( sK33 @ sK52 @ sK55 ) )
| ~ spl0_28 ),
inference(binary_proxy_clausification,[status(thm)],[f1563]) ).
thf(f1563,plain,
( ( ( ( sK33 @ sK55 @ sK50 )
& ( sK33 @ sK52 @ sK55 ) )
= $true )
| ~ spl0_28 ),
inference(not_proxy_clausification,[status(thm)],[f1560]) ).
thf(f1560,plain,
( ( $false
= ( ~ ( ( sK33 @ sK55 @ sK50 )
& ( sK33 @ sK52 @ sK55 ) ) ) )
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1559]) ).
thf(f1559,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK33 @ Y0 @ sK50 )
& ( sK33 @ sK52 @ Y0 ) )
@ sK55 ) )
| ~ spl0_28 ),
inference(sigma_clausification,[status(thm)],[f1556]) ).
thf(f1556,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK33 @ Y0 @ sK50 )
& ( sK33 @ sK52 @ Y0 ) ) ) )
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1554]) ).
thf(f1554,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK33 @ Y0 @ sK50 )
& ( sK33 @ sK52 @ Y0 ) )
=> $false ) ) )
| ~ spl0_28 ),
inference(backward_demodulation,[status(thm)],[f1502,f1551]) ).
thf(f1551,plain,
( ( $false
= ( sK33 @ sK52 @ sK50 ) )
| ~ spl0_28 ),
inference(binary_proxy_clausification,[status(thm)],[f1549]) ).
thf(f1549,plain,
( ( $false
= ( ( ( sK33 @ sK54 @ sK50 )
& ( sK33 @ sK52 @ sK54 ) )
=> ( sK33 @ sK52 @ sK50 ) ) )
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1548]) ).
thf(f1548,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK33 @ Y0 @ sK50 )
& ( sK33 @ sK52 @ Y0 ) )
=> ( sK33 @ sK52 @ sK50 ) )
@ sK54 ) )
| ~ spl0_28 ),
inference(sigma_clausification,[status(thm)],[f1502]) ).
thf(f1502,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK33 @ Y0 @ sK50 )
& ( sK33 @ sK52 @ Y0 ) )
=> ( sK33 @ sK52 @ sK50 ) ) ) )
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1501]) ).
thf(f1501,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK33 @ Y1 @ sK50 )
& ( sK33 @ Y0 @ Y1 ) )
=> ( sK33 @ Y0 @ sK50 ) ) )
@ sK52 ) )
| ~ spl0_28 ),
inference(sigma_clausification,[status(thm)],[f1498]) ).
thf(f1498,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK33 @ Y1 @ sK50 )
& ( sK33 @ Y0 @ Y1 ) )
=> ( sK33 @ Y0 @ sK50 ) ) ) )
= $false )
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1497]) ).
thf(f1497,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
@ sK50 ) )
| ~ spl0_28 ),
inference(sigma_clausification,[status(thm)],[f986]) ).
thf(f986,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_28 ),
inference(avatar_component_clause,[status(thm)],[f985]) ).
thf(f985,definition,
( spl0_28
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition]) ).
thf(f1644,plain,
( ( $true
= ( ~ ( sK33 @ sK52 @ sK55 ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1639]) ).
thf(f1639,plain,
( ( ( ( sK33 @ sK52 @ sK55 )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_28 ),
inference(superposition,[status(thm)],[f1612,f1551]) ).
thf(f1612,plain,
( ! [X0: a] :
( $true
= ( ( sK33 @ X0 @ sK55 )
=> ( sK33 @ X0 @ sK50 ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1607]) ).
thf(f1607,plain,
( ! [X0: a] :
( $true
= ( ( ( sK33 @ X0 @ sK55 )
& $true )
=> ( sK33 @ X0 @ sK50 ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(superposition,[status(thm)],[f1598,f1571]) ).
thf(f1571,plain,
( ( $true
= ( sK33 @ sK55 @ sK50 ) )
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1570]) ).
thf(f1570,plain,
( ( $true
= ( ( sK33 @ sK55 @ sK50 )
& $true ) )
| ~ spl0_28 ),
inference(backward_demodulation,[status(thm)],[f1563,f1568]) ).
thf(f1598,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK33 @ X2 @ X1 )
& ( sK33 @ X1 @ X3 ) )
=> ( sK33 @ X2 @ X3 ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1597]) ).
thf(f1597,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK33 @ X2 @ X1 )
& ( sK33 @ X1 @ Y0 ) )
=> ( sK33 @ X2 @ Y0 ) )
@ X3 ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(pi_clausification,[status(thm)],[f1581]) ).
thf(f1581,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK33 @ X2 @ X1 )
& ( sK33 @ X1 @ Y0 ) )
=> ( sK33 @ X2 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1580]) ).
thf(f1580,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK33 @ Y0 @ X1 )
& ( sK33 @ X1 @ Y1 ) )
=> ( sK33 @ Y0 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(pi_clausification,[status(thm)],[f1577]) ).
thf(f1577,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK33 @ Y0 @ X1 )
& ( sK33 @ X1 @ Y1 ) )
=> ( sK33 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(beta_eta_normalization,[status(thm)],[f1576]) ).
thf(f1576,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(pi_clausification,[status(thm)],[f1575]) ).
thf(f1575,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1574]) ).
thf(f1574,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(backward_demodulation,[status(thm)],[f1504,f1572]) ).
thf(f1572,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(binary_proxy_clausification,[status(thm)],[f1504]) ).
thf(f1504,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(binary_proxy_clausification,[status(thm)],[f1486]) ).
thf(f1486,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK39 ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1485]) ).
thf(f1485,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK39 ) )
!= ( $false
& ( sK33 = sK39 ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(boolean_simplification,[status(thm)],[f1484]) ).
thf(f1484,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK39 ) )
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& $false
& ( sK33 = sK39 ) ) )
| ~ spl0_4
| ~ spl0_28 ),
inference(forward_demodulation,[status(thm)],[f1046,f986]) ).
thf(f1046,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK39 ) )
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK39 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1045]) ).
thf(f1045,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK33 @ Y2 @ Y1 )
& ( sK33 @ Y1 @ Y3 ) )
=> ( sK33 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK33 @ Y1 @ Y2 )
=> ( sK33 @ Y2 @ Y1 ) ) ) )
& ( sK33 = Y0 ) )
@ sK39 )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK33 @ Y2 @ Y1 )
=> ( sK33 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK33 @ Y3 @ Y1 )
& ( sK33 @ Y2 @ Y3 ) )
=> ( sK33 @ Y2 @ Y1 ) ) ) ) )
& ( sK33 = Y0 ) )
@ sK39 ) )
| ~ spl0_4 ),
inference(negative_extensionality,[status(thm)],[f901]) ).
thf(f901,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK33 @ Y2 @ Y1 )
=> ( sK33 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK33 @ Y3 @ Y1 )
& ( sK33 @ Y2 @ Y3 ) )
=> ( sK33 @ Y2 @ Y1 ) ) ) ) )
& ( sK33 = Y0 ) ) )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK33 @ Y2 @ Y1 )
& ( sK33 @ Y1 @ Y3 ) )
=> ( sK33 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK33 @ Y1 @ Y2 )
=> ( sK33 @ Y2 @ Y1 ) ) ) )
& ( sK33 = Y0 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f900]) ).
thf(f900,plain,
( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) )
@ sK33 )
!= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) )
@ sK33 ) )
| ~ spl0_4 ),
inference(negative_extensionality,[status(thm)],[f897]) ).
thf(f897,plain,
( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
!= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
| ~ spl0_4 ),
inference(equality_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $false
= ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl0_4
<=> ( $false
= ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1473,plain,
( ~ spl0_4
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[status(thm)],[f1472]) ).
thf(f1472,plain,
( $false
| ~ spl0_4
| ~ spl0_27 ),
inference(trivial_inequality_removal,[status(thm)],[f1469]) ).
thf(f1469,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_27 ),
inference(superposition,[status(thm)],[f1455,f1464]) ).
thf(f1464,plain,
( ( $false
= ( ( sK33 @ sK49 @ sK47 )
=> ( sK33 @ sK47 @ sK49 ) ) )
| ~ spl0_27 ),
inference(beta_eta_normalization,[status(thm)],[f1463]) ).
thf(f1463,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK33 @ Y0 @ sK47 )
=> ( sK33 @ sK47 @ Y0 ) )
@ sK49 ) )
| ~ spl0_27 ),
inference(sigma_clausification,[status(thm)],[f1406]) ).
thf(f1406,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK33 @ Y0 @ sK47 )
=> ( sK33 @ sK47 @ Y0 ) ) ) )
| ~ spl0_27 ),
inference(beta_eta_normalization,[status(thm)],[f1405]) ).
thf(f1405,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) )
@ sK47 ) )
| ~ spl0_27 ),
inference(sigma_clausification,[status(thm)],[f983]) ).
thf(f983,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_27 ),
inference(avatar_component_clause,[status(thm)],[f982]) ).
thf(f982,definition,
( spl0_27
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition]) ).
thf(f1455,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK33 @ X1 @ X2 )
=> ( sK33 @ X2 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(beta_eta_normalization,[status(thm)],[f1454]) ).
thf(f1454,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK33 @ X1 @ Y0 )
=> ( sK33 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(pi_clausification,[status(thm)],[f1452]) ).
thf(f1452,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK33 @ X1 @ Y0 )
=> ( sK33 @ Y0 @ X1 ) ) ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(beta_eta_normalization,[status(thm)],[f1451]) ).
thf(f1451,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(pi_clausification,[status(thm)],[f1448]) ).
thf(f1448,plain,
( ( $false
!= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(boolean_simplification,[status(thm)],[f1447]) ).
thf(f1447,plain,
( ( $false
!= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(backward_demodulation,[status(thm)],[f1412,f1445]) ).
thf(f1445,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(binary_proxy_clausification,[status(thm)],[f1412]) ).
thf(f1412,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(boolean_simplification,[status(thm)],[f1409]) ).
thf(f1409,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(backward_demodulation,[status(thm)],[f1387,f1407]) ).
thf(f1407,plain,
( ( $true
= ( sK33 = sK35 ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(binary_proxy_clausification,[status(thm)],[f1387]) ).
thf(f1387,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(boolean_simplification,[status(thm)],[f1386]) ).
thf(f1386,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) )
!= ( $false
& ( sK33 = sK35 ) ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(boolean_simplification,[status(thm)],[f1385]) ).
thf(f1385,plain,
( ( ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK35 ) )
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(forward_demodulation,[status(thm)],[f905,f983]) ).
thf(f905,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) )
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK35 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f904]) ).
thf(f904,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK33 @ Y2 @ Y1 )
=> ( sK33 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK33 @ Y3 @ Y1 )
& ( sK33 @ Y2 @ Y3 ) )
=> ( sK33 @ Y2 @ Y1 ) ) ) ) )
& ( sK33 = Y0 ) )
@ sK35 )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK33 @ Y2 @ Y1 )
& ( sK33 @ Y1 @ Y3 ) )
=> ( sK33 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK33 @ Y1 @ Y2 )
=> ( sK33 @ Y2 @ Y1 ) ) ) )
& ( sK33 = Y0 ) )
@ sK35 ) )
| ~ spl0_4 ),
inference(negative_extensionality,[status(thm)],[f901]) ).
thf(f1323,plain,
( ~ spl0_4
| ~ spl0_29
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[status(thm)],[f1322]) ).
thf(f1322,plain,
( $false
| ~ spl0_4
| ~ spl0_29
| ~ spl0_33 ),
inference(trivial_inequality_removal,[status(thm)],[f1321]) ).
thf(f1321,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_33 ),
inference(backward_demodulation,[status(thm)],[f1306,f1316]) ).
thf(f1316,plain,
( ( $false
= ( sK33 @ sK44 @ sK45 ) )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_33 ),
inference(trivial_inequality_removal,[status(thm)],[f1315]) ).
thf(f1315,plain,
( ( $false
= ( sK33 @ sK44 @ sK45 ) )
| ( $false = $true )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_33 ),
inference(boolean_simplification,[status(thm)],[f1307]) ).
thf(f1307,plain,
( ( $false
= ( ( sK33 @ sK44 @ sK45 )
=> $true ) )
| ( $false
= ( sK33 @ sK44 @ sK45 ) )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_33 ),
inference(superposition,[status(thm)],[f1304,f1155]) ).
thf(f1155,plain,
( ! [X2: a,X1: a] :
( ( $true
= ( sK33 @ X1 @ X2 ) )
| ( $false
= ( sK33 @ X2 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(binary_proxy_clausification,[status(thm)],[f1153]) ).
thf(f1153,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK33 @ X2 @ X1 )
=> ( sK33 @ X1 @ X2 ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(beta_eta_normalization,[status(thm)],[f1152]) ).
thf(f1152,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK33 @ Y0 @ X1 )
=> ( sK33 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(pi_clausification,[status(thm)],[f1150]) ).
thf(f1150,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK33 @ Y0 @ X1 )
=> ( sK33 @ X1 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(beta_eta_normalization,[status(thm)],[f1149]) ).
thf(f1149,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(pi_clausification,[status(thm)],[f1108]) ).
thf(f1108,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(binary_proxy_clausification,[status(thm)],[f1075]) ).
thf(f1075,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1071]) ).
thf(f1071,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(backward_demodulation,[status(thm)],[f1042,f1068]) ).
thf(f1068,plain,
( ( $true
= ( sK33 = sK38 ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(binary_proxy_clausification,[status(thm)],[f1042]) ).
thf(f1042,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK38 ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(forward_demodulation,[status(thm)],[f996,f1005]) ).
thf(f1005,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK38 ) ) )
| ~ spl0_29 ),
inference(avatar_component_clause,[status(thm)],[f1004]) ).
thf(f1004,definition,
( spl0_29
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK38 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition]) ).
thf(f996,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK38 ) )
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK38 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f995]) ).
thf(f995,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK33 @ Y2 @ Y1 )
=> ( sK33 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK33 @ Y3 @ Y1 )
& ( sK33 @ Y2 @ Y3 ) )
=> ( sK33 @ Y2 @ Y1 ) ) ) ) )
& ( sK33 = Y0 ) )
@ sK38 )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK33 @ Y2 @ Y1 )
& ( sK33 @ Y1 @ Y3 ) )
=> ( sK33 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK33 @ Y1 @ Y2 )
=> ( sK33 @ Y2 @ Y1 ) ) ) )
& ( sK33 = Y0 ) )
@ sK38 ) )
| ~ spl0_4 ),
inference(negative_extensionality,[status(thm)],[f901]) ).
thf(f1304,plain,
( ( $false
= ( ( sK33 @ sK44 @ sK45 )
=> ( sK33 @ sK45 @ sK44 ) ) )
| ~ spl0_33 ),
inference(beta_eta_normalization,[status(thm)],[f1303]) ).
thf(f1303,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK33 @ sK44 @ Y0 )
=> ( sK33 @ Y0 @ sK44 ) )
@ sK45 ) )
| ~ spl0_33 ),
inference(sigma_clausification,[status(thm)],[f1302]) ).
thf(f1302,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK33 @ sK44 @ Y0 )
=> ( sK33 @ Y0 @ sK44 ) ) ) )
| ~ spl0_33 ),
inference(beta_eta_normalization,[status(thm)],[f1301]) ).
thf(f1301,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) )
@ sK44 ) )
| ~ spl0_33 ),
inference(sigma_clausification,[status(thm)],[f1166]) ).
thf(f1166,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_33 ),
inference(avatar_component_clause,[status(thm)],[f1165]) ).
thf(f1165,definition,
( spl0_33
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_33])],[avatar_definition]) ).
thf(f1306,plain,
( ( $true
= ( sK33 @ sK44 @ sK45 ) )
| ~ spl0_33 ),
inference(binary_proxy_clausification,[status(thm)],[f1304]) ).
thf(f1298,plain,
( ~ spl0_4
| ~ spl0_29
| ~ spl0_34 ),
inference(avatar_contradiction_clause,[status(thm)],[f1297]) ).
thf(f1297,plain,
( $false
| ~ spl0_4
| ~ spl0_29
| ~ spl0_34 ),
inference(trivial_inequality_removal,[status(thm)],[f1296]) ).
thf(f1296,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_34 ),
inference(boolean_simplification,[status(thm)],[f1295]) ).
thf(f1295,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_34 ),
inference(forward_demodulation,[status(thm)],[f1288,f1202]) ).
thf(f1202,plain,
( ( ( sK33 @ sK41 @ sK43 )
= $true )
| ~ spl0_34 ),
inference(binary_proxy_clausification,[status(thm)],[f1182]) ).
thf(f1182,plain,
( ( $true
= ( ( sK33 @ sK42 @ sK41 )
& ( sK33 @ sK41 @ sK43 ) ) )
| ~ spl0_34 ),
inference(binary_proxy_clausification,[status(thm)],[f1180]) ).
thf(f1180,plain,
( ( $false
= ( ( ( sK33 @ sK42 @ sK41 )
& ( sK33 @ sK41 @ sK43 ) )
=> ( sK33 @ sK42 @ sK43 ) ) )
| ~ spl0_34 ),
inference(beta_eta_normalization,[status(thm)],[f1179]) ).
thf(f1179,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK33 @ sK42 @ sK41 )
& ( sK33 @ sK41 @ Y0 ) )
=> ( sK33 @ sK42 @ Y0 ) )
@ sK43 ) )
| ~ spl0_34 ),
inference(sigma_clausification,[status(thm)],[f1178]) ).
thf(f1178,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK33 @ sK42 @ sK41 )
& ( sK33 @ sK41 @ Y0 ) )
=> ( sK33 @ sK42 @ Y0 ) ) ) )
| ~ spl0_34 ),
inference(beta_eta_normalization,[status(thm)],[f1177]) ).
thf(f1177,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK33 @ Y0 @ sK41 )
& ( sK33 @ sK41 @ Y1 ) )
=> ( sK33 @ Y0 @ Y1 ) ) )
@ sK42 ) )
| ~ spl0_34 ),
inference(sigma_clausification,[status(thm)],[f1176]) ).
thf(f1176,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK33 @ Y0 @ sK41 )
& ( sK33 @ sK41 @ Y1 ) )
=> ( sK33 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_34 ),
inference(beta_eta_normalization,[status(thm)],[f1175]) ).
thf(f1175,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) )
@ sK41 ) )
| ~ spl0_34 ),
inference(sigma_clausification,[status(thm)],[f1169]) ).
thf(f1169,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_34 ),
inference(avatar_component_clause,[status(thm)],[f1168]) ).
thf(f1168,definition,
( spl0_34
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_34])],[avatar_definition]) ).
thf(f1288,plain,
( ( $true
= ( ~ ( sK33 @ sK41 @ sK43 ) ) )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_34 ),
inference(boolean_simplification,[status(thm)],[f1280]) ).
thf(f1280,plain,
( ( $true
= ( ( sK33 @ sK41 @ sK43 )
=> $false ) )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_34 ),
inference(superposition,[status(thm)],[f1211,f1181]) ).
thf(f1181,plain,
( ( $false
= ( sK33 @ sK42 @ sK43 ) )
| ~ spl0_34 ),
inference(binary_proxy_clausification,[status(thm)],[f1180]) ).
thf(f1211,plain,
( ! [X0: a] :
( $true
= ( ( sK33 @ sK41 @ X0 )
=> ( sK33 @ sK42 @ X0 ) ) )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_34 ),
inference(boolean_simplification,[status(thm)],[f1209]) ).
thf(f1209,plain,
( ! [X0: a] :
( $true
= ( ( ( sK33 @ sK41 @ X0 )
& $true )
=> ( sK33 @ sK42 @ X0 ) ) )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_34 ),
inference(superposition,[status(thm)],[f1129,f1205]) ).
thf(f1205,plain,
( ( $true
= ( sK33 @ sK42 @ sK41 ) )
| ~ spl0_34 ),
inference(boolean_simplification,[status(thm)],[f1204]) ).
thf(f1204,plain,
( ( ( ( sK33 @ sK42 @ sK41 )
& $true )
= $true )
| ~ spl0_34 ),
inference(backward_demodulation,[status(thm)],[f1182,f1202]) ).
thf(f1129,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK33 @ X3 @ X1 )
& ( sK33 @ X2 @ X3 ) )
=> ( sK33 @ X2 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(beta_eta_normalization,[status(thm)],[f1128]) ).
thf(f1128,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK33 @ Y0 @ X1 )
& ( sK33 @ X2 @ Y0 ) )
=> ( sK33 @ X2 @ X1 ) )
@ X3 ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(pi_clausification,[status(thm)],[f1124]) ).
thf(f1124,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK33 @ Y0 @ X1 )
& ( sK33 @ X2 @ Y0 ) )
=> ( sK33 @ X2 @ X1 ) ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(beta_eta_normalization,[status(thm)],[f1123]) ).
thf(f1123,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK33 @ Y1 @ X1 )
& ( sK33 @ Y0 @ Y1 ) )
=> ( sK33 @ Y0 @ X1 ) ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(pi_clausification,[status(thm)],[f1118]) ).
thf(f1118,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK33 @ Y1 @ X1 )
& ( sK33 @ Y0 @ Y1 ) )
=> ( sK33 @ Y0 @ X1 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_29 ),
inference(beta_eta_normalization,[status(thm)],[f1117]) ).
thf(f1117,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(pi_clausification,[status(thm)],[f1111]) ).
thf(f1111,plain,
( ( $false
!= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1110]) ).
thf(f1110,plain,
( ( $false
!= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_29 ),
inference(backward_demodulation,[status(thm)],[f1075,f1108]) ).
thf(f1170,plain,
( spl0_33
| spl0_34
| ~ spl0_4
| ~ spl0_23
| ~ spl0_26
| ~ spl0_29
| ~ spl0_32 ),
inference(avatar_split_clause,[status(thm)],[f1163,f1014,f1004,f925,f915,f25,f1168,f1165]) ).
thf(f915,definition,
( spl0_23
<=> ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK35 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition]) ).
thf(f925,definition,
( spl0_26
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition]) ).
thf(f1014,definition,
( spl0_32
<=> ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK38 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_32])],[avatar_definition]) ).
thf(f1163,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_23
| ~ spl0_26
| ~ spl0_29
| ~ spl0_32 ),
inference(binary_proxy_clausification,[status(thm)],[f1084]) ).
thf(f1084,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_23
| ~ spl0_26
| ~ spl0_29
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f1083]) ).
thf(f1083,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_23
| ~ spl0_26
| ~ spl0_29
| ~ spl0_32 ),
inference(backward_demodulation,[status(thm)],[f926,f1082]) ).
thf(f1082,plain,
( ( $true
= ( sK33 = sK35 ) )
| ~ spl0_4
| ~ spl0_23
| ~ spl0_29
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f1077]) ).
thf(f1077,plain,
( ( $true
= ( $true
& ( sK33 = sK35 ) ) )
| ~ spl0_4
| ~ spl0_23
| ~ spl0_29
| ~ spl0_32 ),
inference(backward_demodulation,[status(thm)],[f916,f1074]) ).
thf(f1074,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f1070]) ).
thf(f1070,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_29
| ~ spl0_32 ),
inference(backward_demodulation,[status(thm)],[f1015,f1068]) ).
thf(f1015,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK38 ) ) )
| ~ spl0_32 ),
inference(avatar_component_clause,[status(thm)],[f1014]) ).
thf(f916,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK35 ) ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[status(thm)],[f915]) ).
thf(f926,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) ) )
| ~ spl0_26 ),
inference(avatar_component_clause,[status(thm)],[f925]) ).
thf(f1041,plain,
( ~ spl0_29
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[status(thm)],[f1040]) ).
thf(f1040,plain,
( $false
| ~ spl0_29
| ~ spl0_31 ),
inference(trivial_inequality_removal,[status(thm)],[f1039]) ).
thf(f1039,plain,
( ( $false = $true )
| ~ spl0_29
| ~ spl0_31 ),
inference(backward_demodulation,[status(thm)],[f1012,f1005]) ).
thf(f1012,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK38 ) ) )
| ~ spl0_31 ),
inference(avatar_component_clause,[status(thm)],[f1011]) ).
thf(f1011,definition,
( spl0_31
<=> ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK38 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition]) ).
thf(f1032,plain,
( ~ spl0_4
| ~ spl0_23
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[status(thm)],[f1031]) ).
thf(f1031,plain,
( $false
| ~ spl0_4
| ~ spl0_23
| ~ spl0_30 ),
inference(trivial_inequality_removal,[status(thm)],[f1030]) ).
thf(f1030,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_23
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f1028]) ).
thf(f1028,plain,
( ( $true
= ( $false
& ( sK33 = sK35 ) ) )
| ~ spl0_4
| ~ spl0_23
| ~ spl0_30 ),
inference(backward_demodulation,[status(thm)],[f916,f1027]) ).
thf(f1027,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f1024]) ).
thf(f1024,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_30 ),
inference(backward_demodulation,[status(thm)],[f1008,f1020]) ).
thf(f1020,plain,
( ( $true
= ( sK33 = sK38 ) )
| ~ spl0_4
| ~ spl0_30 ),
inference(binary_proxy_clausification,[status(thm)],[f1017]) ).
thf(f1017,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK38 ) ) )
| ~ spl0_4
| ~ spl0_30 ),
inference(backward_demodulation,[status(thm)],[f996,f1008]) ).
thf(f1008,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK38 ) ) )
| ~ spl0_30 ),
inference(avatar_component_clause,[status(thm)],[f1007]) ).
thf(f1007,definition,
( spl0_30
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK38 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition]) ).
thf(f1016,plain,
( spl0_31
| spl0_32
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f1001,f25,f1014,f1011]) ).
thf(f1001,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK38 ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK38 ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f996]) ).
thf(f1009,plain,
( spl0_29
| spl0_30
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f1002,f25,f1007,f1004]) ).
thf(f1002,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK38 ) ) )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK38 ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f996]) ).
thf(f991,plain,
( ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f990]) ).
thf(f990,plain,
( $false
| ~ spl0_23
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f989]) ).
thf(f989,plain,
( ( $false = $true )
| ~ spl0_23
| ~ spl0_25 ),
inference(backward_demodulation,[status(thm)],[f916,f923]) ).
thf(f923,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK35 ) ) )
| ~ spl0_25 ),
inference(avatar_component_clause,[status(thm)],[f922]) ).
thf(f922,definition,
( spl0_25
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK35 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition]) ).
thf(f987,plain,
( spl0_27
| spl0_28
| ~ spl0_24
| ~ spl0_25 ),
inference(avatar_split_clause,[status(thm)],[f980,f922,f918,f985,f982]) ).
thf(f918,definition,
( spl0_24
<=> ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition]) ).
thf(f980,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_24
| ~ spl0_25 ),
inference(binary_proxy_clausification,[status(thm)],[f963]) ).
thf(f963,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_24
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f962]) ).
thf(f962,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& $true ) )
| ~ spl0_24
| ~ spl0_25 ),
inference(backward_demodulation,[status(thm)],[f923,f961]) ).
thf(f961,plain,
( ( $true
= ( sK33 = sK35 ) )
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f957]) ).
thf(f957,plain,
( ( $true
= ( $true
& ( sK33 = sK35 ) ) )
| ~ spl0_24 ),
inference(backward_demodulation,[status(thm)],[f919,f956]) ).
thf(f956,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_24 ),
inference(binary_proxy_clausification,[status(thm)],[f919]) ).
thf(f919,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[status(thm)],[f918]) ).
thf(f931,plain,
( ~ spl0_24
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[status(thm)],[f930]) ).
thf(f930,plain,
( $false
| ~ spl0_24
| ~ spl0_26 ),
inference(trivial_inequality_removal,[status(thm)],[f929]) ).
thf(f929,plain,
( ( $false = $true )
| ~ spl0_24
| ~ spl0_26 ),
inference(forward_demodulation,[status(thm)],[f919,f926]) ).
thf(f927,plain,
( spl0_25
| spl0_26
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f913,f25,f925,f922]) ).
thf(f913,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) ) )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK35 ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f905]) ).
thf(f920,plain,
( spl0_23
| spl0_24
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f912,f25,f918,f915]) ).
thf(f912,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y1 @ Y0 )
=> ( sK33 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y2 @ Y0 )
& ( sK33 @ Y1 @ Y2 ) )
=> ( sK33 @ Y1 @ Y0 ) ) ) ) )
& ( sK33 = sK35 ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK33 @ Y1 @ Y0 )
& ( sK33 @ Y0 @ Y2 ) )
=> ( sK33 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK33 @ Y0 @ Y1 )
=> ( sK33 @ Y1 @ Y0 ) ) ) )
& ( sK33 = sK35 ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f905]) ).
thf(f883,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f882]) ).
thf(f882,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f881]) ).
thf(f881,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f875,f793]) ).
thf(f793,plain,
( ( $false
= ( sK2 @ sK28 @ sK27 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f792]) ).
thf(f792,plain,
( ( ( $true
=> ( sK2 @ sK28 @ sK27 ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f780,f791]) ).
thf(f791,plain,
( ( ( ( sK2 @ sK28 @ sK29 )
& ( sK2 @ sK29 @ sK27 ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f780]) ).
thf(f780,plain,
( ( $false
= ( ( ( sK2 @ sK28 @ sK29 )
& ( sK2 @ sK29 @ sK27 ) )
=> ( sK2 @ sK28 @ sK27 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f779,f774]) ).
thf(f774,plain,
( ! [X2: a,X1: a] :
( ( sK2 @ X1 @ X2 )
= ( sK3 @ X1 @ X2 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(argument_congruence,[status(thm)],[f773]) ).
thf(f773,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( sK3 @ X1 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(argument_congruence,[status(thm)],[f770]) ).
thf(f770,plain,
( ( sK2 = sK3 )
| ~ spl0_3
| ~ spl0_6 ),
inference(equality_proxy_clausification,[status(thm)],[f768]) ).
thf(f768,plain,
( ( ( sK2 = sK3 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f767]) ).
thf(f767,plain,
( ( ( $true
& ( sK2 = sK3 ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f762,f766]) ).
thf(f766,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK2 @ Y0 @ Y2 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f762]) ).
thf(f762,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK2 @ Y0 @ Y2 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK2 = sK3 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f760,f761]) ).
thf(f761,plain,
( ( sK2 = sK23 )
| ~ spl0_3
| ~ spl0_6 ),
inference(equality_proxy_clausification,[status(thm)],[f757]) ).
thf(f757,plain,
( ( $true
= ( sK23 = sK2 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f752]) ).
thf(f752,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 )
& ( sK23 = sK2 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(not_proxy_clausification,[status(thm)],[f749]) ).
thf(f749,plain,
( ( $false
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 )
& ( sK23 = sK2 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f748]) ).
thf(f748,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
~ ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
@ sK23 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f747]) ).
thf(f747,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
~ ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f746]) ).
thf(f746,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> $false ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f745]) ).
thf(f745,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK3 @ Y2 @ Y1 ) ) ) )
& ( sK3 = sK2 )
& $false ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f629,f50]) ).
thf(f50,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl0_6
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f629,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK3 @ Y2 @ Y1 ) ) ) )
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f628]) ).
thf(f628,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y4 @ Y2 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( Y1 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y4 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK3 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f617]) ).
thf(f617,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y4 @ Y2 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( Y1 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y4 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f616]) ).
thf(f616,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
@ sK2 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl0_3
<=> ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f760,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f759]) ).
thf(f759,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 )
& $true ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f752,f757]) ).
thf(f779,plain,
( ( $false
= ( ( ( sK2 @ sK28 @ sK29 )
& ( sK3 @ sK29 @ sK27 ) )
=> ( sK2 @ sK28 @ sK27 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f778,f774]) ).
thf(f778,plain,
( ( $false
= ( ( ( sK3 @ sK28 @ sK29 )
& ( sK3 @ sK29 @ sK27 ) )
=> ( sK2 @ sK28 @ sK27 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f777]) ).
thf(f777,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ sK28 @ Y0 )
& ( sK3 @ Y0 @ sK27 ) )
=> ( sK2 @ sK28 @ sK27 ) )
@ sK29 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f775]) ).
thf(f775,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK28 @ Y0 )
& ( sK3 @ Y0 @ sK27 ) )
=> ( sK2 @ sK28 @ sK27 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f756,f774]) ).
thf(f756,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK28 @ Y0 )
& ( sK3 @ Y0 @ sK27 ) )
=> ( sK3 @ sK28 @ sK27 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f755]) ).
thf(f755,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y1 @ sK27 ) )
=> ( sK3 @ Y0 @ sK27 ) ) )
@ sK28 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f751]) ).
thf(f751,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y1 @ sK27 ) )
=> ( sK3 @ Y0 @ sK27 ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f750]) ).
thf(f750,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
@ sK27 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f50]) ).
thf(f875,plain,
( ( $true
= ( sK2 @ sK28 @ sK27 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f872]) ).
thf(f872,plain,
( ( ( $true
=> ( sK2 @ sK28 @ sK27 ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f851,f805]) ).
thf(f805,plain,
( ( $true
= ( sK2 @ sK30 @ sK27 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f800]) ).
thf(f800,plain,
( ( $true
= ( ( sK2 @ sK28 @ sK30 )
& ( sK2 @ sK30 @ sK27 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(not_proxy_clausification,[status(thm)],[f799]) ).
thf(f799,plain,
( ( $false
= ( ~ ( ( sK2 @ sK28 @ sK30 )
& ( sK2 @ sK30 @ sK27 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f798,f774]) ).
thf(f798,plain,
( ( $false
= ( ~ ( ( sK2 @ sK28 @ sK30 )
& ( sK3 @ sK30 @ sK27 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f797,f774]) ).
thf(f797,plain,
( ( $false
= ( ~ ( ( sK3 @ sK28 @ sK30 )
& ( sK3 @ sK30 @ sK27 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f796]) ).
thf(f796,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK3 @ sK28 @ Y0 )
& ( sK3 @ Y0 @ sK27 ) )
@ sK30 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f795]) ).
thf(f795,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK3 @ sK28 @ Y0 )
& ( sK3 @ Y0 @ sK27 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f794]) ).
thf(f794,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK28 @ Y0 )
& ( sK3 @ Y0 @ sK27 ) )
=> $false ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f775,f793]) ).
thf(f851,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ sK30 @ X0 )
=> ( sK2 @ sK28 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f842]) ).
thf(f842,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK2 @ sK30 @ X0 ) )
=> ( sK2 @ sK28 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f826,f808]) ).
thf(f808,plain,
( ( $true
= ( sK2 @ sK28 @ sK30 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f807]) ).
thf(f807,plain,
( ( $true
= ( ( sK2 @ sK28 @ sK30 )
& $true ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f800,f805]) ).
thf(f826,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK2 @ X2 @ X1 )
& ( sK2 @ X1 @ X3 ) )
=> ( sK2 @ X2 @ X3 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f825]) ).
thf(f825,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X2 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK2 @ X2 @ Y0 ) )
@ X3 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f824]) ).
thf(f824,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X2 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK2 @ X2 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f823]) ).
thf(f823,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ X1 )
& ( sK2 @ X1 @ Y1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) )
@ X2 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f822]) ).
thf(f822,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ X1 )
& ( sK2 @ X1 @ Y1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f821]) ).
thf(f821,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK2 @ Y0 @ Y2 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f816]) ).
thf(f816,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK2 @ Y0 @ Y2 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f815]) ).
thf(f815,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK2 @ Y0 @ Y2 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f812,f814]) ).
thf(f814,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f812]) ).
thf(f812,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK2 @ Y0 @ Y2 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f811]) ).
thf(f811,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK2 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK2 @ Y0 @ Y2 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) )
& $true )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f766,f809]) ).
thf(f809,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f766]) ).
thf(f744,plain,
( ~ spl0_3
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f743]) ).
thf(f743,plain,
( $false
| ~ spl0_3
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f742]) ).
thf(f742,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f740,f621]) ).
thf(f621,plain,
( ( $false
= ( sK3 = sK2 ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f620]) ).
thf(f620,definition,
( spl0_17
<=> ( $false
= ( sK3 = sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f740,plain,
( ( ( sK3 = sK2 )
= $true )
| ~ spl0_3
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f712,f738]) ).
thf(f738,plain,
( ( sK3 = sK23 )
| ~ spl0_3
| ~ spl0_17 ),
inference(equality_proxy_clausification,[status(thm)],[f737]) ).
thf(f737,plain,
( ( ( sK23 = sK3 )
= $true )
| ~ spl0_3
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f736]) ).
thf(f736,plain,
( ( $true
= ( $true
& ( sK23 = sK3 ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f715,f735]) ).
thf(f735,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f715]) ).
thf(f715,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f714]) ).
thf(f714,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 )
& $true ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f708,f712]) ).
thf(f708,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 )
& ( sK23 = sK2 ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(not_proxy_clausification,[status(thm)],[f706]) ).
thf(f706,plain,
( ( $false
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 )
& ( sK23 = sK2 ) ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f705]) ).
thf(f705,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
~ ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
@ sK23 ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(sigma_clausification,[status(thm)],[f703]) ).
thf(f703,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
~ ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f702]) ).
thf(f702,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> $false ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f701]) ).
thf(f701,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> ( $false
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f700]) ).
thf(f700,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK3 @ Y2 @ Y1 ) ) ) )
& $false
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f629,f621]) ).
thf(f712,plain,
( ( $true
= ( sK23 = sK2 ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f708]) ).
thf(f697,plain,
( ~ spl0_3
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f696]) ).
thf(f696,plain,
( $false
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f695]) ).
thf(f695,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[status(thm)],[f687,f643]) ).
thf(f643,plain,
( ( $false
= ( sK3 @ sK24 @ sK22 ) )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f639]) ).
thf(f639,plain,
( ( $false
= ( ( sK3 @ sK22 @ sK24 )
=> ( sK3 @ sK24 @ sK22 ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f638]) ).
thf(f638,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK22 @ Y0 )
=> ( sK3 @ Y0 @ sK22 ) )
@ sK24 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[status(thm)],[f635]) ).
thf(f635,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK22 @ Y0 )
=> ( sK3 @ Y0 @ sK22 ) ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f634]) ).
thf(f634,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ sK22 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[status(thm)],[f624]) ).
thf(f624,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f623]) ).
thf(f623,definition,
( spl0_18
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f687,plain,
( ( $true
= ( sK3 @ sK24 @ sK22 ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f685]) ).
thf(f685,plain,
( ( $true
= ( $true
=> ( sK3 @ sK24 @ sK22 ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f669,f644]) ).
thf(f644,plain,
( ( $true
= ( sK3 @ sK22 @ sK24 ) )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f639]) ).
thf(f669,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X2 @ X1 )
=> ( sK3 @ X1 @ X2 ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f668]) ).
thf(f668,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK3 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(pi_clausification,[status(thm)],[f666]) ).
thf(f666,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK3 @ X1 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f665]) ).
thf(f665,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(pi_clausification,[status(thm)],[f660]) ).
thf(f660,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f659]) ).
thf(f659,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(backward_demodulation,[status(thm)],[f656,f658]) ).
thf(f658,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f656]) ).
thf(f656,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f655]) ).
thf(f655,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& $true ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(backward_demodulation,[status(thm)],[f652,f653]) ).
thf(f653,plain,
( ( ( sK23 = sK3 )
= $true )
| ~ spl0_3
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f652]) ).
thf(f652,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f651]) ).
thf(f651,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 )
& $true ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(backward_demodulation,[status(thm)],[f640,f649]) ).
thf(f649,plain,
( ( $true
= ( sK23 = sK2 ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f640]) ).
thf(f640,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 )
& ( sK23 = sK2 ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(not_proxy_clausification,[status(thm)],[f637]) ).
thf(f637,plain,
( ( $false
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK23 @ Y0 @ Y1 )
=> ( sK23 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK23 @ Y1 @ Y0 )
& ( sK23 @ Y0 @ Y2 ) )
=> ( sK23 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK23 = sK3 )
& ( sK23 = sK2 ) ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f636]) ).
thf(f636,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
~ ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
@ sK23 ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(sigma_clausification,[status(thm)],[f633]) ).
thf(f633,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
~ ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f632]) ).
thf(f632,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> $false ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f631]) ).
thf(f631,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> ( $false
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f630]) ).
thf(f630,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> ( $false
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[status(thm)],[f629,f624]) ).
thf(f625,plain,
( spl0_17
| spl0_18
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f618,f46,f623,f620]) ).
thf(f46,definition,
( spl0_5
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
& ( sK3 = sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f618,plain,
( ( $false
= ( sK3 = sK2 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
& ( sK3 = sK2 ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f610,plain,
( ~ spl0_1
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[status(thm)],[f609]) ).
thf(f609,plain,
( $false
| ~ spl0_1
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f608]) ).
thf(f608,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f607]) ).
thf(f607,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f599,f505]) ).
thf(f505,plain,
( ( $true
= ( sK14 @ sK21 @ sK19 ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f502]) ).
thf(f502,plain,
( ( $true
= ( ( sK14 @ sK18 @ sK21 )
& ( sK14 @ sK21 @ sK19 ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(not_proxy_clausification,[status(thm)],[f487]) ).
thf(f487,plain,
( ( $false
= ( ~ ( ( sK14 @ sK18 @ sK21 )
& ( sK14 @ sK21 @ sK19 ) ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f486]) ).
thf(f486,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK14 @ sK18 @ Y0 )
& ( sK14 @ Y0 @ sK19 ) )
@ sK21 ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f470]) ).
thf(f470,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK14 @ sK18 @ Y0 )
& ( sK14 @ Y0 @ sK19 ) ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f469]) ).
thf(f469,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ sK18 @ Y0 )
& ( sK14 @ Y0 @ sK19 ) )
=> $false ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f461,f468]) ).
thf(f468,plain,
( ( $false
= ( sK14 @ sK18 @ sK19 ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f467]) ).
thf(f467,plain,
( ( $false
= ( $true
=> ( sK14 @ sK18 @ sK19 ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f464,f466]) ).
thf(f466,plain,
( ( ( ( sK14 @ sK18 @ sK20 )
& ( sK14 @ sK20 @ sK19 ) )
= $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(binary_proxy_clausification,[status(thm)],[f464]) ).
thf(f464,plain,
( ( $false
= ( ( ( sK14 @ sK18 @ sK20 )
& ( sK14 @ sK20 @ sK19 ) )
=> ( sK14 @ sK18 @ sK19 ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f463]) ).
thf(f463,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK14 @ sK18 @ Y0 )
& ( sK14 @ Y0 @ sK19 ) )
=> ( sK14 @ sK18 @ sK19 ) )
@ sK20 ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f461]) ).
thf(f461,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ sK18 @ Y0 )
& ( sK14 @ Y0 @ sK19 ) )
=> ( sK14 @ sK18 @ sK19 ) ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f460]) ).
thf(f460,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ sK18 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ sK18 @ Y0 ) ) )
@ sK19 ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f457]) ).
thf(f457,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ sK18 @ Y1 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ sK18 @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f456]) ).
thf(f456,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y2 @ Y1 ) )
=> ( sK14 @ Y0 @ Y1 ) ) ) )
@ sK18 ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(sigma_clausification,[status(thm)],[f450]) ).
thf(f450,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y2 @ Y1 ) )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f449]) ).
thf(f449,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y2 @ Y1 ) )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) )
& $true )
= $false )
| ~ spl0_1
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f448]) ).
thf(f448,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y2 @ Y1 ) )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) )
& ( sK14 = sK14 ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f398,f425]) ).
thf(f425,plain,
( ( sK15 = sK14 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f424]) ).
thf(f424,plain,
( ( $true
= ( sK15 = sK14 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f423]) ).
thf(f423,plain,
( ( $true
= ( $true
& ( sK15 = sK14 ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f413,f422]) ).
thf(f422,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y0 @ Y1 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f413]) ).
thf(f413,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y0 @ Y1 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) )
& ( sK15 = sK14 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f389]) ).
thf(f389,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y0 @ Y1 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) )
& ( sK15 = sK14 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK14 @ Y0 @ Y1 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f387]) ).
thf(f387,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y0 @ Y1 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) )
& ( sK15 = sK14 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK14 @ Y0 @ Y1 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK15 @ Y0 @ Y2 )
& ( sK15 @ Y2 @ Y1 ) )
=> ( sK15 @ Y0 @ Y1 ) ) ) ) )
& ( sK15 = sK14 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ Y0 @ Y1 )
=> ( sK15 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f386]) ).
thf(f386,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK14 @ Y2 @ Y3 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y1 @ Y3 ) ) ) ) )
& ( Y0 = sK14 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK14 @ Y1 @ Y2 )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( Y0 = sK14 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ sK15 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f385]) ).
thf(f385,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK14 @ Y2 @ Y3 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y1 @ Y3 ) ) ) ) )
& ( Y0 = sK14 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK14 @ Y1 @ Y2 )
=> ( sK14 @ Y2 @ Y1 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( Y0 = sK14 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f384]) ).
thf(f384,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
@ sK14 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f12]) ).
thf(f12,definition,
( spl0_1
<=> ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f398,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK15 @ Y0 @ Y2 )
& ( sK15 @ Y2 @ Y1 ) )
=> ( sK15 @ Y0 @ Y1 ) ) ) ) )
& ( sK15 = sK14 ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f397]) ).
thf(f397,definition,
( spl0_16
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK15 @ Y0 @ Y2 )
& ( sK15 @ Y2 @ Y1 ) )
=> ( sK15 @ Y0 @ Y1 ) ) ) ) )
& ( sK15 = sK14 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f599,plain,
( ( ( ~ ( sK14 @ sK21 @ sK19 ) )
= $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f594]) ).
thf(f594,plain,
( ( ( ( sK14 @ sK21 @ sK19 )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f517,f468]) ).
thf(f517,plain,
( ! [X0: a] :
( $true
= ( ( sK14 @ sK21 @ X0 )
=> ( sK14 @ sK18 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f510]) ).
thf(f510,plain,
( ! [X0: a] :
( $true
= ( ( ( sK14 @ sK21 @ X0 )
& $true )
=> ( sK14 @ sK18 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f459,f508]) ).
thf(f508,plain,
( ( ( sK14 @ sK18 @ sK21 )
= $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f507]) ).
thf(f507,plain,
( ( $true
= ( ( sK14 @ sK18 @ sK21 )
& $true ) )
| ~ spl0_1
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f502,f505]) ).
thf(f459,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK14 @ X2 @ X3 )
& ( sK14 @ X1 @ X2 ) )
=> ( sK14 @ X1 @ X3 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f458]) ).
thf(f458,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK14 @ X2 @ Y0 )
& ( sK14 @ X1 @ X2 ) )
=> ( sK14 @ X1 @ Y0 ) )
@ X3 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f439]) ).
thf(f439,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ X2 @ Y0 )
& ( sK14 @ X1 @ X2 ) )
=> ( sK14 @ X1 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f438]) ).
thf(f438,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ X1 @ Y0 ) )
=> ( sK14 @ X1 @ Y1 ) ) )
@ X2 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f431]) ).
thf(f431,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ X1 @ Y0 ) )
=> ( sK14 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f430]) ).
thf(f430,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y0 @ Y1 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f422]) ).
thf(f447,plain,
( ~ spl0_1
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f446]) ).
thf(f446,plain,
( $false
| ~ spl0_1
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f445]) ).
thf(f445,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f444]) ).
thf(f444,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1
| ~ spl0_15 ),
inference(forward_demodulation,[status(thm)],[f443,f437]) ).
thf(f437,plain,
( ( ( sK14 @ sK16 @ sK17 )
= $true )
| ~ spl0_1
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f407,f429]) ).
thf(f429,plain,
( ! [X2: a,X1: a] :
( ( sK15 @ X1 @ X2 )
= ( sK14 @ X1 @ X2 ) )
| ~ spl0_1 ),
inference(argument_congruence,[status(thm)],[f428]) ).
thf(f428,plain,
( ! [X1: a] :
( ( sK15 @ X1 )
= ( sK14 @ X1 ) )
| ~ spl0_1 ),
inference(argument_congruence,[status(thm)],[f425]) ).
thf(f407,plain,
( ( $true
= ( sK15 @ sK16 @ sK17 ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f405]) ).
thf(f405,plain,
( ( $false
= ( ( sK15 @ sK16 @ sK17 )
=> ( sK15 @ sK17 @ sK16 ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f404]) ).
thf(f404,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK15 @ sK16 @ Y0 )
=> ( sK15 @ Y0 @ sK16 ) )
@ sK17 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f403]) ).
thf(f403,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ sK16 @ Y0 )
=> ( sK15 @ Y0 @ sK16 ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[status(thm)],[f402]) ).
thf(f402,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ Y0 @ Y1 )
=> ( sK15 @ Y1 @ Y0 ) ) )
@ sK16 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[status(thm)],[f395]) ).
thf(f395,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ Y0 @ Y1 )
=> ( sK15 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f394]) ).
thf(f394,definition,
( spl0_15
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ Y0 @ Y1 )
=> ( sK15 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f443,plain,
( ( ( ~ ( sK14 @ sK16 @ sK17 ) )
= $true )
| ~ spl0_1
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f441]) ).
thf(f441,plain,
( ( $true
= ( ( sK14 @ sK16 @ sK17 )
=> $false ) )
| ~ spl0_1
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f419,f436]) ).
thf(f436,plain,
( ( $false
= ( sK14 @ sK17 @ sK16 ) )
| ~ spl0_1
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f406,f429]) ).
thf(f406,plain,
( ( $false
= ( sK15 @ sK17 @ sK16 ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[status(thm)],[f405]) ).
thf(f419,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK14 @ X1 @ X2 )
=> ( sK14 @ X2 @ X1 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f418]) ).
thf(f418,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK14 @ X1 @ Y0 )
=> ( sK14 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f417]) ).
thf(f417,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK14 @ X1 @ Y0 )
=> ( sK14 @ Y0 @ X1 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f416]) ).
thf(f416,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK14 @ Y0 @ Y1 )
=> ( sK14 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f415]) ).
thf(f415,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK14 @ Y0 @ Y1 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f414]) ).
thf(f414,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK14 @ Y0 @ Y1 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f389,f413]) ).
thf(f399,plain,
( spl0_15
| spl0_16
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f392,f12,f397,f394]) ).
thf(f392,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK15 @ Y0 @ Y2 )
& ( sK15 @ Y2 @ Y1 ) )
=> ( sK15 @ Y0 @ Y1 ) ) ) ) )
& ( sK15 = sK14 ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ Y0 @ Y1 )
=> ( sK15 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f391]) ).
thf(f391,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK15 @ Y0 @ Y2 )
& ( sK15 @ Y2 @ Y1 ) )
=> ( sK15 @ Y0 @ Y1 ) ) ) ) )
& ( sK15 = sK14 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ Y0 @ Y1 )
=> ( sK15 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f390]) ).
thf(f390,plain,
( ( $false
= ( $true
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK15 @ Y0 @ Y2 )
& ( sK15 @ Y2 @ Y1 ) )
=> ( sK15 @ Y0 @ Y1 ) ) ) ) )
& ( sK15 = sK14 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ Y0 @ Y1 )
=> ( sK15 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f387,f389]) ).
thf(f51,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f44,f22,f49,f46]) ).
thf(f44,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
& ( sK3 = sK2 ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK4 @ Y0 @ Y2 ) )
=> ( sK4 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( sK4 = sK3 )
& ( sK4 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y2 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK3 @ Y2 @ Y1 ) ) ) )
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) )
@ sK4 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK3 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK3 )
& ( Y0 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK3 @ Y2 @ Y1 ) ) ) )
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( sK3 @ Y3 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y4 @ Y2 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( Y1 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y4 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK3 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y4 @ Y2 ) )
=> ( Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( Y1 = sK2 ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y4 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
@ sK2 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f23]) ).
thf(f27,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f20,f15,f25,f22]) ).
thf(f15,definition,
( spl0_2
<=> ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f20,plain,
( ( $false
= ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) ) )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
thf(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f10,f15,f12]) ).
thf(f10,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y1 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( Y2 = Y0 ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y5 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = Y1 ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y2 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > a > $o,X1: a > a > $o] :
( ( ! [X2: a,X3: a] :
( ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) )
& ( X0 = X1 )
& ! [X4: a,X5: a,X6: a] :
( ( ( X1 @ X6 @ X5 )
& ( X1 @ X5 @ X4 ) )
=> ( X1 @ X6 @ X4 ) ) )
=> ( ! [X7: a,X8: a] :
( ( X0 @ X8 @ X7 )
=> ( X0 @ X7 @ X8 ) )
& ( X0 = X1 )
& ! [X9: a,X10: a,X11: a] :
( ( ( X0 @ X9 @ X10 )
& ( X0 @ X11 @ X9 ) )
=> ( X0 @ X11 @ X10 ) ) ) )
& ( ( ^ [X12: a > a > $o,X13: a > a > $o] :
( ( X12 = X13 )
& ! [X14: a,X15: a] :
( ( X12 @ X15 @ X14 )
=> ( X12 @ X14 @ X15 ) )
& ! [X16: a,X17: a,X18: a] :
( ( ( X12 @ X18 @ X16 )
& ( X12 @ X17 @ X18 ) )
=> ( X12 @ X17 @ X16 ) ) ) )
= ( ^ [X19: a > a > $o,X20: a > a > $o] :
( ( X19 = X20 )
& ! [X21: a,X22: a,X23: a] :
( ( ( X19 @ X22 @ X21 )
& ( X19 @ X21 @ X23 ) )
=> ( X19 @ X22 @ X23 ) )
& ! [X24: a,X25: a] :
( ( X19 @ X24 @ X25 )
=> ( X19 @ X25 @ X24 ) ) ) ) )
& ! [X26: a > a > $o,X27: a > a > $o,X28: a > a > $o] :
( ( ( X26 = X28 )
& ( X26 = X27 )
& ! [X29: a,X30: a] :
( ( X27 @ X29 @ X30 )
=> ( X27 @ X30 @ X29 ) )
& ! [X31: a,X32: a,X33: a] :
( ( ( X26 @ X33 @ X31 )
& ( X26 @ X32 @ X33 ) )
=> ( X26 @ X32 @ X31 ) )
& ! [X34: a,X35: a] :
( ( X26 @ X35 @ X34 )
=> ( X26 @ X34 @ X35 ) )
& ! [X36: a,X37: a,X38: a] :
( ( ( X27 @ X36 @ X38 )
& ( X27 @ X38 @ X37 ) )
=> ( X27 @ X36 @ X37 ) ) )
=> ( ! [X39: a,X40: a,X41: a] :
( ( ( X27 @ X39 @ X41 )
& ( X27 @ X40 @ X39 ) )
=> ( X27 @ X40 @ X41 ) )
& ( X27 = X28 )
& ! [X42: a,X43: a] :
( ( X27 @ X43 @ X42 )
=> ( X27 @ X42 @ X43 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a > a > $o,X0: a > a > $o] :
( ( ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ( X0 = X1 )
& ! [X4: a,X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) ) )
=> ( ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ( X0 = X1 )
& ! [X3: a,X4: a,X2: a] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X4 ) ) ) )
& ( ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ( X6 = X7 )
& ! [X1: a,X0: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) )
& ! [X4: a,X0: a,X1: a] :
( ( ( X6 @ X1 @ X4 )
& ( X6 @ X0 @ X1 ) )
=> ( X6 @ X0 @ X4 ) ) ) )
= ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ( X6 = X7 )
& ! [X1: a,X0: a,X4: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ! [X0: a,X1: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) ) ) ) )
& ! [X1: a > a > $o,X0: a > a > $o,X4: a > a > $o] :
( ( ( X1 = X4 )
& ( X0 = X1 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X5: a,X2: a,X3: a] :
( ( ( X1 @ X3 @ X5 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X5 ) )
& ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ! [X2: a,X5: a,X3: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X5 ) )
=> ( X0 @ X2 @ X5 ) ) )
=> ( ! [X3: a,X2: a,X5: a] :
( ( ( X0 @ X3 @ X5 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X5 ) )
& ( X0 = X4 )
& ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: a > a > $o,X0: a > a > $o] :
( ( ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ( X0 = X1 )
& ! [X4: a,X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) ) )
=> ( ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ( X0 = X1 )
& ! [X3: a,X4: a,X2: a] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X4 ) ) ) )
& ( ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ( X6 = X7 )
& ! [X1: a,X0: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) )
& ! [X4: a,X0: a,X1: a] :
( ( ( X6 @ X1 @ X4 )
& ( X6 @ X0 @ X1 ) )
=> ( X6 @ X0 @ X4 ) ) ) )
= ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ( X6 = X7 )
& ! [X1: a,X0: a,X4: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ! [X0: a,X1: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) ) ) ) )
& ! [X1: a > a > $o,X0: a > a > $o,X4: a > a > $o] :
( ( ( X1 = X4 )
& ( X0 = X1 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X5: a,X2: a,X3: a] :
( ( ( X1 @ X3 @ X5 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X5 ) )
& ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ! [X2: a,X5: a,X3: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X5 ) )
=> ( X0 @ X2 @ X5 ) ) )
=> ( ! [X3: a,X2: a,X5: a] :
( ( ( X0 @ X3 @ X5 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X5 ) )
& ( X0 = X4 )
& ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2qyIePZdi7/DTF2THF_19242.p',cTHM515_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV040^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:38:55 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEV040^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Set Theory (Relations)
% 0.29/0.45 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_1214 [Bro09]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.33 v4.0.1, 1.00 v4.0.0
% 0.29/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.45 % Number of atoms : 8 ( 8 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 6 ( 8 avg)
% 0.29/0.45 % Number of connectives : 110 ( 0 ~; 0 |; 24 &; 70 @)
% 0.29/0.45 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 19 ( 19 avg)
% 0.29/0.45 % Number of types : 2 ( 1 usr)
% 0.29/0.45 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.45 % Number of variables : 44 ( 4 ^; 40 !; 0 ?; 44 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 % : May require description or choice.
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(a_type,type,
% 0.29/0.45 a: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(cTHM515_pme,conjecture,
% 0.29/0.45 ( ! [Xx: a > a > $o,Xy: a > a > $o] :
% 0.29/0.45 ( ( ! [Xx0: a,Xy0: a] :
% 0.29/0.45 ( ( Xx @ Xx0 @ Xy0 )
% 0.29/0.45 => ( Xx @ Xy0 @ Xx0 ) )
% 0.29/0.45 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.29/0.45 ( ( ( Xx @ Xx0 @ Xy0 )
% 0.29/0.45 & ( Xx @ Xy0 @ Xz ) )
% 0.29/0.45 => ( Xx @ Xx0 @ Xz ) )
% 0.29/0.45 & ( Xx = Xy ) )
% 0.29/0.45 => ( ! [Xx0: a,Xy0: a] :
% 0.29/0.45 ( ( Xy @ Xx0 @ Xy0 )
% 0.29/0.45 => ( Xy @ Xy0 @ Xx0 ) )
% 0.29/0.45 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.29/0.45 ( ( ( Xy @ Xx0 @ Xy0 )
% 0.29/0.45 & ( Xy @ Xy0 @ Xz ) )
% 0.29/0.45 => ( Xy @ Xx0 @ Xz ) )
% 0.29/0.45 & ( Xy = Xx ) ) )
% 0.29/0.45 & ! [Xx: a > a > $o,Xy: a > a > $o,Xz: a > a > $o] :
% 0.29/0.45 ( ( ! [Xx0: a,Xy0: a] :
% 0.29/0.45 ( ( Xx @ Xx0 @ Xy0 )
% 0.29/0.45 => ( Xx @ Xy0 @ Xx0 ) )
% 0.29/0.45 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 0.29/0.45 ( ( ( Xx @ Xx0 @ Xy0 )
% 0.29/0.45 & ( Xx @ Xy0 @ Xz0 ) )
% 0.29/0.45 => ( Xx @ Xx0 @ Xz0 ) )
% 0.29/0.45 & ( Xx = Xy )
% 0.29/0.45 & ! [Xx0: a,Xy0: a] :
% 0.29/0.45 ( ( Xy @ Xx0 @ Xy0 )
% 0.29/0.45 => ( Xy @ Xy0 @ Xx0 ) )
% 0.29/0.45 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 0.29/0.45 ( ( ( Xy @ Xx0 @ Xy0 )
% 0.29/0.45 & ( Xy @ Xy0 @ Xz0 ) )
% 0.29/0.45 => ( Xy @ Xx0 @ Xz0 ) )
% 0.29/0.45 & ( Xy = Xz ) )
% 0.29/0.45 => ( ! [Xx0: a,Xy0: a] :
% 0.29/0.45 ( ( Xx @ Xx0 @ Xy0 )
% 0.29/0.45 => ( Xx @ Xy0 @ Xx0 ) )
% 0.29/0.45 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 0.29/0.45 ( ( ( Xx @ Xx0 @ Xy0 )
% 0.29/0.45 & ( Xx @ Xy0 @ Xz0 ) )
% 0.29/0.45 => ( Xx @ Xx0 @ Xz0 ) )
% 0.29/0.45 & ( Xx = Xz ) ) )
% 0.29/0.45 & ( ( ^ [Xp: a > a > $o,Xq: a > a > $o] :
% 0.29/0.45 ( ! [Xx: a,Xy: a] :
% 0.29/0.45 ( ( Xp @ Xx @ Xy )
% 0.29/0.45 => ( Xp @ Xy @ Xx ) )
% 0.29/0.45 & ! [Xx: a,Xy: a,Xz: a] :
% 0.29/0.45 ( ( ( Xp @ Xx @ Xy )
% 0.29/0.45 & ( Xp @ Xy @ Xz ) )
% 0.29/0.45 => ( Xp @ Xx @ Xz ) )
% 0.29/0.45 & ( Xp = Xq ) ) )
% 0.29/0.45 = ( ^ [Xp: a > a > $o,Xq: a > a > $o] :
% 0.29/0.45 ( ! [Xx: a,Xy: a] :
% 0.29/0.45 ( ( Xp @ Xx @ Xy )
% 0.29/0.45 => ( Xp @ Xy @ Xx ) )
% 0.29/0.45 & ! [Xx: a,Xy: a,Xz: a] :
% 0.29/0.45 ( ( ( Xp @ Xx @ Xy )
% 0.29/0.45 & ( Xp @ Xy @ Xz ) )
% 0.29/0.45 => ( Xp @ Xx @ Xz ) )
% 0.29/0.45 & ( Xp = Xq ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.48/1.14 ---- Embedded in THF ---
% 1.48/1.14 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.14 %%% Generated on Tue Feb 24 12:38:56 EST 2026
% 1.48/1.14 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.14 %%% Logic specification used:
% 1.48/1.14 %%% thf(spec, logic, $$dhol).
% 1.48/1.14
% 1.48/1.14 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.2qyIePZdi7/DTF2DTF19242.p
% See solution above
% 1.48/1.14 ------------------------
% 1.48/1.15 ---- Cleaned THF ---
% 1.48/1.15 thf(a_type,type,
% 1.48/1.15 a: $tType ).
% 1.48/1.15
% 1.48/1.15 thf(cTHM515_pme,conjecture,
% 1.48/1.15 ( ! [Xx: a > a > $o,Xy: a > a > $o] :
% 1.48/1.15 ( ( ! [Xx0: a,Xy0: a] :
% 1.48/1.15 ( ( Xx @ Xx0 @ Xy0 )
% 1.48/1.15 => ( Xx @ Xy0 @ Xx0 ) )
% 1.48/1.15 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.48/1.15 ( ( ( Xx @ Xx0 @ Xy0 )
% 1.48/1.15 & ( Xx @ Xy0 @ Xz ) )
% 1.48/1.15 => ( Xx @ Xx0 @ Xz ) )
% 1.48/1.15 & ( Xx = Xy ) )
% 1.48/1.15 => ( ! [Xx0: a,Xy0: a] :
% 1.48/1.15 ( ( Xy @ Xx0 @ Xy0 )
% 1.48/1.15 => ( Xy @ Xy0 @ Xx0 ) )
% 1.48/1.15 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.48/1.15 ( ( ( Xy @ Xx0 @ Xy0 )
% 1.48/1.15 & ( Xy @ Xy0 @ Xz ) )
% 1.48/1.15 => ( Xy @ Xx0 @ Xz ) )
% 1.48/1.15 & ( Xy = Xx ) ) )
% 1.48/1.15 & ! [Xx: a > a > $o,Xy: a > a > $o,Xz: a > a > $o] :
% 1.48/1.15 ( ( ! [Xx0: a,Xy0: a] :
% 1.48/1.15 ( ( Xx @ Xx0 @ Xy0 )
% 1.48/1.15 => ( Xx @ Xy0 @ Xx0 ) )
% 1.48/1.15 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 1.48/1.15 ( ( ( Xx @ Xx0 @ Xy0 )
% 1.48/1.15 & ( Xx @ Xy0 @ Xz0 ) )
% 1.48/1.15 => ( Xx @ Xx0 @ Xz0 ) )
% 1.48/1.15 & ( Xx = Xy )
% 1.48/1.15 & ! [Xx0: a,Xy0: a] :
% 1.48/1.15 ( ( Xy @ Xx0 @ Xy0 )
% 1.48/1.15 => ( Xy @ Xy0 @ Xx0 ) )
% 1.48/1.15 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 1.48/1.15 ( ( ( Xy @ Xx0 @ Xy0 )
% 1.48/1.15 & ( Xy @ Xy0 @ Xz0 ) )
% 1.48/1.15 => ( Xy @ Xx0 @ Xz0 ) )
% 1.48/1.15 & ( Xy = Xz ) )
% 1.48/1.15 => ( ! [Xx0: a,Xy0: a] :
% 1.48/1.15 ( ( Xx @ Xx0 @ Xy0 )
% 1.48/1.15 => ( Xx @ Xy0 @ Xx0 ) )
% 1.48/1.15 & ! [Xx0: a,Xy0: a,Xz0: a] :
% 1.48/1.15 ( ( ( Xx @ Xx0 @ Xy0 )
% 1.48/1.15 & ( Xx @ Xy0 @ Xz0 ) )
% 1.48/1.15 => ( Xx @ Xx0 @ Xz0 ) )
% 1.48/1.15 & ( Xx = Xz ) ) )
% 1.48/1.15 & ( ( ^ [Xp: a > a > $o,Xq: a > a > $o] :
% 1.48/1.15 ( ! [Xx: a,Xy: a] :
% 1.48/1.15 ( ( Xp @ Xx @ Xy )
% 1.48/1.15 => ( Xp @ Xy @ Xx ) )
% 1.48/1.15 & ! [Xx: a,Xy: a,Xz: a] :
% 1.48/1.15 ( ( ( Xp @ Xx @ Xy )
% 1.48/1.15 & ( Xp @ Xy @ Xz ) )
% 1.48/1.15 => ( Xp @ Xx @ Xz ) )
% 1.48/1.15 & ( Xp = Xq ) ) )
% 1.48/1.15 = ( ^ [Xp: a > a > $o,Xq: a > a > $o] :
% 1.48/1.15 ( ! [Xx: a,Xy: a] :
% 1.48/1.15 ( ( Xp @ Xx @ Xy )
% 1.48/1.15 => ( Xp @ Xy @ Xx ) )
% 1.48/1.15 & ! [Xx: a,Xy: a,Xz: a] :
% 1.48/1.15 ( ( ( Xp @ Xx @ Xy )
% 1.48/1.15 & ( Xp @ Xy @ Xz ) )
% 1.48/1.15 => ( Xp @ Xx @ Xz ) )
% 1.48/1.15 & ( Xp = Xq ) ) ) ) ) ).
% 1.48/1.15 ------------------------
% 1.48/1.16 % (19519)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/18Mi)
% 1.48/1.16 % (19513)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/183Mi)
% 1.48/1.17 % (19519)Instruction limit reached!
% 1.48/1.17 % (19519)------------------------------
% 1.48/1.17 % (19519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.17 % (19519)Termination reason: Unknown
% 1.48/1.17 % (19519)Termination phase: Saturation
% 1.48/1.17
% 1.48/1.17 % (19519)Memory used [KB]: 5628
% 1.48/1.17 % (19519)Time elapsed: 0.007 s
% 1.48/1.17 % (19519)Instructions burned: 19 (million)
% 1.48/1.17 % (19519)------------------------------
% 1.48/1.17 % (19519)------------------------------
% 1.48/1.17 % (19514)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_19242 for (2999ds/4Mi)
% 1.48/1.17 % (19516)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/2Mi)
% 1.48/1.17 % (19515)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_19242 for (2999ds/27Mi)
% 1.48/1.17 % (19517)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_19242 for (2999ds/2Mi)
% 1.48/1.17 % (19518)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_19242 for (2999ds/275Mi)
% 1.48/1.17 % (19516)Instruction limit reached!
% 1.48/1.17 % (19516)------------------------------
% 1.48/1.17 % (19516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.17 % (19516)Termination reason: Unknown
% 1.48/1.17 % (19516)Termination phase: shuffling
% 1.48/1.17
% 1.48/1.17 % (19516)Memory used [KB]: 1023
% 1.48/1.17 % (19516)Time elapsed: 0.003 s
% 1.48/1.17 % (19516)Instructions burned: 2 (million)
% 1.48/1.17 % (19516)------------------------------
% 1.48/1.17 % (19516)------------------------------
% 1.48/1.17 % (19517)Instruction limit reached!
% 1.48/1.17 % (19517)------------------------------
% 1.48/1.17 % (19517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.17 % (19517)Termination reason: Unknown
% 1.48/1.17 % (19517)Termination phase: shuffling
% 1.48/1.17
% 1.48/1.17 % (19517)Memory used [KB]: 1023
% 1.48/1.17 % (19517)Time elapsed: 0.003 s
% 1.48/1.17 % (19517)Instructions burned: 2 (million)
% 1.48/1.17 % (19517)------------------------------
% 1.48/1.17 % (19517)------------------------------
% 1.48/1.17 % (19514)Instruction limit reached!
% 1.48/1.17 % (19514)------------------------------
% 1.48/1.17 % (19514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.17 % (19514)Termination reason: Unknown
% 1.48/1.17 % (19514)Termination phase: Property scanning
% 1.48/1.17
% 1.48/1.17 % (19514)Memory used [KB]: 1023
% 1.48/1.17 % (19514)Time elapsed: 0.005 s
% 1.48/1.17 % (19514)Instructions burned: 5 (million)
% 1.48/1.17 % (19514)------------------------------
% 1.48/1.17 % (19514)------------------------------
% 1.48/1.18 % (19520)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/3Mi)
% 1.48/1.18 % (19520)Instruction limit reached!
% 1.48/1.18 % (19520)------------------------------
% 1.48/1.18 % (19520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.18 % (19520)Termination reason: Unknown
% 1.48/1.18 % (19520)Termination phase: Naming
% 1.48/1.18
% 1.48/1.18 % (19520)Memory used [KB]: 1023
% 1.48/1.18 % (19520)Time elapsed: 0.002 s
% 1.48/1.18 % (19520)Instructions burned: 3 (million)
% 1.48/1.18 % (19520)------------------------------
% 1.48/1.18 % (19520)------------------------------
% 1.48/1.19 % (19515)Instruction limit reached!
% 1.48/1.19 % (19515)------------------------------
% 1.48/1.19 % (19515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.19 % (19515)Termination reason: Unknown
% 1.48/1.19 % (19515)Termination phase: Saturation
% 1.48/1.19
% 1.48/1.19 % (19515)Memory used [KB]: 5756
% 1.48/1.19 % (19515)Time elapsed: 0.017 s
% 1.48/1.19 % (19515)Instructions burned: 27 (million)
% 1.48/1.19 % (19515)------------------------------
% 1.48/1.19 % (19515)------------------------------
% 1.48/1.19 % (19524)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_19242 for (2999ds/1041Mi)
% 1.48/1.19 % (19521)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_19242 for (2999ds/37Mi)
% 1.48/1.19 % (19522)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_19242 for (2999ds/15Mi)
% 1.48/1.19 % (19523)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_19242 for (2999ds/3Mi)
% 1.48/1.19 % (19523)Instruction limit reached!
% 1.48/1.19 % (19523)------------------------------
% 1.48/1.19 % (19523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.19 % (19523)Termination reason: Unknown
% 1.48/1.19 % (19523)Termination phase: Property scanning
% 1.48/1.19
% 1.48/1.19 % (19523)Memory used [KB]: 1023
% 1.48/1.19 % (19523)Time elapsed: 0.003 s
% 1.48/1.19 % (19523)Instructions burned: 3 (million)
% 1.48/1.19 % (19523)------------------------------
% 1.48/1.19 % (19523)------------------------------
% 1.51/1.20 % (19522)Instruction limit reached!
% 1.51/1.20 % (19522)------------------------------
% 1.51/1.20 % (19522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.20 % (19522)Termination reason: Unknown
% 1.51/1.20 % (19522)Termination phase: Saturation
% 1.51/1.20
% 1.51/1.20 % (19522)Memory used [KB]: 5756
% 1.51/1.20 % (19522)Time elapsed: 0.011 s
% 1.51/1.20 % (19522)Instructions burned: 15 (million)
% 1.51/1.20 % (19522)------------------------------
% 1.51/1.20 % (19522)------------------------------
% 1.51/1.20 % (19525)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/7Mi)
% 1.51/1.21 % (19525)Instruction limit reached!
% 1.51/1.21 % (19525)------------------------------
% 1.51/1.21 % (19525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.21 % (19525)Termination reason: Unknown
% 1.51/1.21 % (19525)Termination phase: Property scanning
% 1.51/1.21
% 1.51/1.21 % (19525)Memory used [KB]: 1023
% 1.51/1.21 % (19525)Time elapsed: 0.006 s
% 1.51/1.21 % (19525)Instructions burned: 8 (million)
% 1.51/1.21 % (19525)------------------------------
% 1.51/1.21 % (19525)------------------------------
% 1.51/1.21 % (19521)Instruction limit reached!
% 1.51/1.21 % (19521)------------------------------
% 1.51/1.21 % (19521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.21 % (19521)Termination reason: Unknown
% 1.51/1.21 % (19521)Termination phase: Saturation
% 1.51/1.21
% 1.51/1.21 % (19521)Memory used [KB]: 5628
% 1.51/1.21 % (19521)Time elapsed: 0.021 s
% 1.51/1.21 % (19521)Instructions burned: 37 (million)
% 1.51/1.21 % (19521)------------------------------
% 1.51/1.21 % (19521)------------------------------
% 1.51/1.21 % (19526)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/16Mi)
% 1.51/1.22 % (19527)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_19242 for (2999ds/3Mi)
% 1.51/1.22 % (19527)Instruction limit reached!
% 1.51/1.22 % (19527)------------------------------
% 1.51/1.22 % (19527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.22 % (19527)Termination reason: Unknown
% 1.51/1.22 % (19527)Termination phase: Preprocessing 3
% 1.51/1.22
% 1.51/1.22 % (19527)Memory used [KB]: 1023
% 1.51/1.22 % (19527)Time elapsed: 0.004 s
% 1.51/1.22 % (19527)Instructions burned: 4 (million)
% 1.51/1.22 % (19527)------------------------------
% 1.51/1.22 % (19527)------------------------------
% 1.51/1.22 % (19513)Instruction limit reached!
% 1.51/1.22 % (19513)------------------------------
% 1.51/1.22 % (19513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.22 % (19513)Termination reason: Unknown
% 1.51/1.22 % (19513)Termination phase: Saturation
% 1.51/1.22
% 1.51/1.22 % (19513)Memory used [KB]: 6396
% 1.51/1.22 % (19513)Time elapsed: 0.056 s
% 1.51/1.22 % (19513)Instructions burned: 184 (million)
% 1.51/1.22 % (19513)------------------------------
% 1.51/1.22 % (19513)------------------------------
% 1.51/1.22 % (19526)Instruction limit reached!
% 1.51/1.22 % (19526)------------------------------
% 1.51/1.22 % (19526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.22 % (19526)Termination reason: Unknown
% 1.51/1.22 % (19526)Termination phase: Saturation
% 1.51/1.22
% 1.51/1.22 % (19526)Memory used [KB]: 5756
% 1.51/1.22 % (19526)Time elapsed: 0.011 s
% 1.51/1.22 % (19526)Instructions burned: 16 (million)
% 1.51/1.22 % (19526)------------------------------
% 1.51/1.22 % (19526)------------------------------
% 1.51/1.23 % (19528)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_19242 for (2999ds/3Mi)
% 1.51/1.23 % (19528)Instruction limit reached!
% 1.51/1.23 % (19528)------------------------------
% 1.51/1.23 % (19528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (19528)Termination reason: Unknown
% 1.51/1.23 % (19528)Termination phase: Property scanning
% 1.51/1.23
% 1.51/1.23 % (19528)Memory used [KB]: 1023
% 1.51/1.23 % (19528)Time elapsed: 0.003 s
% 1.51/1.23 % (19528)Instructions burned: 3 (million)
% 1.51/1.23 % (19528)------------------------------
% 1.51/1.23 % (19528)------------------------------
% 1.51/1.23 % (19529)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/7Mi)
% 1.51/1.23 % (19531)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/4Mi)
% 1.51/1.23 % (19529)Instruction limit reached!
% 1.51/1.23 % (19529)------------------------------
% 1.51/1.23 % (19529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (19529)Termination reason: Unknown
% 1.51/1.23 % (19529)Termination phase: Property scanning
% 1.51/1.23
% 1.51/1.23 % (19529)Memory used [KB]: 1023
% 1.51/1.23 % (19529)Time elapsed: 0.006 s
% 1.51/1.23 % (19529)Instructions burned: 8 (million)
% 1.51/1.23 % (19529)------------------------------
% 1.51/1.23 % (19529)------------------------------
% 1.51/1.23 % (19531)Instruction limit reached!
% 1.51/1.23 % (19531)------------------------------
% 1.51/1.23 % (19531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (19531)Termination reason: Unknown
% 1.51/1.23 % (19531)Termination phase: Preprocessing 3
% 1.51/1.23
% 1.51/1.23 % (19531)Memory used [KB]: 1023
% 1.51/1.23 % (19531)Time elapsed: 0.003 s
% 1.51/1.23 % (19531)Instructions burned: 4 (million)
% 1.51/1.23 % (19531)------------------------------
% 1.51/1.23 % (19531)------------------------------
% 1.51/1.24 % (19530)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/3Mi)
% 1.51/1.24 % (19532)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/18Mi)
% 1.51/1.24 % (19530)Instruction limit reached!
% 1.51/1.24 % (19530)------------------------------
% 1.51/1.24 % (19530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.24 % (19530)Termination reason: Unknown
% 1.51/1.24 % (19530)Termination phase: Unused predicate definition removal
% 1.51/1.24
% 1.51/1.24 % (19530)Memory used [KB]: 1023
% 1.51/1.24 % (19530)Time elapsed: 0.004 s
% 1.51/1.24 % (19530)Instructions burned: 4 (million)
% 1.51/1.24 % (19530)------------------------------
% 1.51/1.24 % (19530)------------------------------
% 1.51/1.24 % (19533)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/710Mi)
% 1.51/1.24 % (19534)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/6Mi)
% 1.51/1.24 % (19534)Instruction limit reached!
% 1.51/1.24 % (19534)------------------------------
% 1.51/1.24 % (19534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.24 % (19534)Termination reason: Unknown
% 1.51/1.24 % (19534)Termination phase: Property scanning
% 1.51/1.24
% 1.51/1.24 % (19534)Memory used [KB]: 1023
% 1.51/1.24 % (19534)Time elapsed: 0.004 s
% 1.51/1.24 % (19534)Instructions burned: 8 (million)
% 1.51/1.24 % (19534)------------------------------
% 1.51/1.24 % (19534)------------------------------
% 1.51/1.25 % (19532)Instruction limit reached!
% 1.51/1.25 % (19532)------------------------------
% 1.51/1.25 % (19532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (19532)Termination reason: Unknown
% 1.51/1.25 % (19532)Termination phase: Saturation
% 1.51/1.25
% 1.51/1.25 % (19532)Memory used [KB]: 5628
% 1.51/1.25 % (19532)Time elapsed: 0.012 s
% 1.51/1.25 % (19532)Instructions burned: 18 (million)
% 1.51/1.25 % (19532)------------------------------
% 1.51/1.25 % (19532)------------------------------
% 1.51/1.25 % (19535)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_19242 for (2999ds/902Mi)
% 1.51/1.25 % (19537)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/5Mi)
% 1.51/1.25 % (19537)Instruction limit reached!
% 1.51/1.25 % (19537)------------------------------
% 1.51/1.25 % (19537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (19537)Termination reason: Unknown
% 1.51/1.25 % (19537)Termination phase: Property scanning
% 1.51/1.25
% 1.51/1.25 % (19537)Memory used [KB]: 1023
% 1.51/1.25 % (19537)Time elapsed: 0.003 s
% 1.51/1.25 % (19537)Instructions burned: 5 (million)
% 1.51/1.25 % (19537)------------------------------
% 1.51/1.25 % (19537)------------------------------
% 1.51/1.26 % (19536)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_19242 for (2999ds/21Mi)
% 1.51/1.26 % (19538)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_19242 for (2999ds/6Mi)
% 1.51/1.26 % (19538)Instruction limit reached!
% 1.51/1.26 % (19538)------------------------------
% 1.51/1.26 % (19538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (19538)Termination reason: Unknown
% 1.51/1.26 % (19538)Termination phase: Saturation
% 1.51/1.26
% 1.51/1.26 % (19538)Memory used [KB]: 5500
% 1.51/1.26 % (19538)Time elapsed: 0.003 s
% 1.51/1.26 % (19538)Instructions burned: 7 (million)
% 1.51/1.26 % (19538)------------------------------
% 1.51/1.26 % (19538)------------------------------
% 1.51/1.26 % (19539)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19242 for (2999ds/377Mi)
% 1.51/1.27 % (19536)Instruction limit reached!
% 1.51/1.27 % (19536)------------------------------
% 1.51/1.27 % (19536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (19536)Termination reason: Unknown
% 1.51/1.27 % (19536)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (19536)Memory used [KB]: 5756
% 1.51/1.27 % (19536)Time elapsed: 0.012 s
% 1.51/1.27 % (19536)Instructions burned: 21 (million)
% 1.51/1.27 % (19536)------------------------------
% 1.51/1.27 % (19536)------------------------------
% 1.51/1.27 % (19540)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_19242 for (2999ds/779Mi)
% 1.51/1.28 % (19541)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_19242 for (2999ds/19Mi)
% 1.51/1.28 % (19541)Instruction limit reached!
% 1.51/1.28 % (19541)------------------------------
% 1.51/1.28 % (19541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.28 % (19541)Termination reason: Unknown
% 1.51/1.28 % (19541)Termination phase: Saturation
% 1.51/1.28
% 1.51/1.28 % (19541)Memory used [KB]: 5500
% 1.51/1.28 % (19541)Time elapsed: 0.007 s
% 1.51/1.28 % (19541)Instructions burned: 20 (million)
% 1.51/1.28 % (19541)------------------------------
% 1.51/1.28 % (19541)------------------------------
% 1.51/1.29 % (19542)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19242 for (2998ds/879Mi)
% 1.51/1.31 % (19524)First to succeed.
% 1.51/1.31 % (19518)Instruction limit reached!
% 1.51/1.31 % (19518)------------------------------
% 1.51/1.31 % (19518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.31 % (19518)Termination reason: Unknown
% 1.51/1.31 % (19518)Termination phase: Saturation
% 1.51/1.31
% 1.51/1.31 % (19518)Memory used [KB]: 6908
% 1.51/1.31 % (19518)Time elapsed: 0.141 s
% 1.51/1.31 % (19518)Instructions burned: 276 (million)
% 1.51/1.31 % (19518)------------------------------
% 1.51/1.31 % (19518)------------------------------
% 1.51/1.32 % (19524)Refutation found. Thanks to Tanya!
% 1.51/1.32 % SZS status Theorem for DTF2THF_19242
% 1.51/1.32 % SZS output start Proof for DTF2THF_19242
% 1.51/1.32 thf(type_def_5, type, a: $tType).
% 1.51/1.32 thf(func_def_0, type, a: $tType).
% 1.51/1.32 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.51/1.32 thf(func_def_17, type, sK2: a > a > $o).
% 1.51/1.32 thf(func_def_18, type, sK3: a > a > $o).
% 1.51/1.32 thf(func_def_19, type, sK4: a > a > $o).
% 1.51/1.32 thf(func_def_20, type, sK5: a > a > $o).
% 1.51/1.32 thf(func_def_21, type, sK6: a > a > $o).
% 1.51/1.32 thf(func_def_22, type, sK7: a > a > $o).
% 1.51/1.32 thf(func_def_23, type, sK8: a > a > $o).
% 1.51/1.32 thf(func_def_24, type, sK9: a).
% 1.51/1.32 thf(func_def_25, type, sK10: a).
% 1.51/1.32 thf(func_def_26, type, sK11: a).
% 1.51/1.32 thf(func_def_27, type, sK12: a).
% 1.51/1.32 thf(func_def_28, type, sK13: a).
% 1.51/1.32 thf(func_def_29, type, sK14: a > a > $o).
% 1.51/1.32 thf(func_def_30, type, sK15: a > a > $o).
% 1.51/1.32 thf(func_def_31, type, sK16: a).
% 1.51/1.32 thf(func_def_32, type, sK17: a).
% 1.51/1.32 thf(func_def_33, type, sK18: a).
% 1.51/1.32 thf(func_def_34, type, sK19: a).
% 1.51/1.32 thf(func_def_35, type, sK20: a).
% 1.51/1.32 thf(func_def_36, type, sK21: a).
% 1.51/1.32 thf(func_def_37, type, sK22: a).
% 1.51/1.32 thf(func_def_38, type, sK23: a > a > $o).
% 1.51/1.32 thf(func_def_39, type, sK24: a).
% 1.51/1.32 thf(func_def_40, type, sK25: a).
% 1.51/1.32 thf(func_def_41, type, sK26: a).
% 1.51/1.32 thf(func_def_42, type, sK27: a).
% 1.51/1.32 thf(func_def_43, type, sK28: a).
% 1.51/1.32 thf(func_def_44, type, sK29: a).
% 1.51/1.32 thf(func_def_45, type, sK30: a).
% 1.51/1.32 thf(func_def_46, type, sK31: a).
% 1.51/1.32 thf(func_def_47, type, sK32: a).
% 1.51/1.32 thf(func_def_48, type, sK33: a > a > $o).
% 1.51/1.32 thf(func_def_49, type, sK34: a).
% 1.51/1.32 thf(func_def_50, type, sK35: a > a > $o).
% 1.51/1.32 thf(func_def_51, type, sK36: a).
% 1.51/1.32 thf(func_def_52, type, sK37: a > a > $o).
% 1.51/1.32 thf(func_def_53, type, sK38: a > a > $o).
% 1.51/1.32 thf(func_def_54, type, sK39: a > a > $o).
% 1.51/1.32 thf(func_def_55, type, sK40: a > a > $o).
% 1.51/1.32 thf(func_def_56, type, sK41: a).
% 1.51/1.32 thf(func_def_57, type, sK42: a).
% 1.51/1.32 thf(func_def_58, type, sK43: a).
% 1.51/1.32 thf(func_def_59, type, sK44: a).
% 1.51/1.32 thf(func_def_60, type, sK45: a).
% 1.51/1.32 thf(func_def_61, type, sK46: a > a > $o).
% 1.51/1.32 thf(func_def_62, type, sK47: a).
% 1.51/1.32 thf(func_def_63, type, sK48: a > a > $o).
% 1.51/1.32 thf(func_def_64, type, sK49: a).
% 1.51/1.32 thf(func_def_65, type, sK50: a).
% 1.51/1.32 thf(func_def_66, type, sK51: a > a > $o).
% 1.51/1.32 thf(func_def_67, type, sK52: a).
% 1.51/1.32 thf(func_def_68, type, sK53: a > a > $o).
% 1.51/1.32 thf(func_def_69, type, sK54: a).
% 1.51/1.32 thf(func_def_70, type, sK55: a).
% 1.51/1.32 thf(f1654,plain,(
% 1.51/1.32 $false),
% 1.51/1.32 inference(avatar_sat_refutation,[status(thm)],[f17,f27,f51,f399,f447,f610,f625,f697,f744,f883,f920,f927,f931,f987,f991,f1009,f1016,f1032,f1041,f1170,f1298,f1323,f1473,f1653])).
% 1.51/1.32 thf(f1653,plain,(
% 1.51/1.32 ~spl0_4 | ~spl0_28),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f1652])).
% 1.51/1.32 thf(f1652,plain,(
% 1.51/1.32 $false | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f1651])).
% 1.51/1.32 thf(f1651,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1650])).
% 1.51/1.32 thf(f1650,plain,(
% 1.51/1.32 ((~ $true) = $true) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f1644,f1568])).
% 1.51/1.32 thf(f1568,plain,(
% 1.51/1.32 ($true = (sK33 @ sK52 @ sK55)) | ~spl0_28),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1563])).
% 1.51/1.32 thf(f1563,plain,(
% 1.51/1.32 (((sK33 @ sK55 @ sK50) & (sK33 @ sK52 @ sK55)) = $true) | ~spl0_28),
% 1.51/1.32 inference(not_proxy_clausification,[status(thm)],[f1560])).
% 1.51/1.32 thf(f1560,plain,(
% 1.51/1.32 ($false = (~ ((sK33 @ sK55 @ sK50) & (sK33 @ sK52 @ sK55)))) | ~spl0_28),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1559])).
% 1.51/1.32 thf(f1559,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (~ ((sK33 @ Y0 @ sK50) & (sK33 @ sK52 @ Y0)))) @ sK55)) | ~spl0_28),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f1556])).
% 1.51/1.32 thf(f1556,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK33 @ Y0 @ sK50) & (sK33 @ sK52 @ Y0)))))) | ~spl0_28),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1554])).
% 1.51/1.32 thf(f1554,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (((sK33 @ Y0 @ sK50) & (sK33 @ sK52 @ Y0)) => $false)))) | ~spl0_28),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1502,f1551])).
% 1.51/1.32 thf(f1551,plain,(
% 1.51/1.32 ($false = (sK33 @ sK52 @ sK50)) | ~spl0_28),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1549])).
% 1.51/1.32 thf(f1549,plain,(
% 1.51/1.32 ($false = (((sK33 @ sK54 @ sK50) & (sK33 @ sK52 @ sK54)) => (sK33 @ sK52 @ sK50))) | ~spl0_28),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1548])).
% 1.51/1.32 thf(f1548,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (((sK33 @ Y0 @ sK50) & (sK33 @ sK52 @ Y0)) => (sK33 @ sK52 @ sK50))) @ sK54)) | ~spl0_28),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f1502])).
% 1.51/1.32 thf(f1502,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (((sK33 @ Y0 @ sK50) & (sK33 @ sK52 @ Y0)) => (sK33 @ sK52 @ sK50))))) | ~spl0_28),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1501])).
% 1.51/1.32 thf(f1501,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK33 @ Y1 @ sK50) & (sK33 @ Y0 @ Y1)) => (sK33 @ Y0 @ sK50))))) @ sK52)) | ~spl0_28),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f1498])).
% 1.51/1.32 thf(f1498,plain,(
% 1.51/1.32 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK33 @ Y1 @ sK50) & (sK33 @ Y0 @ Y1)) => (sK33 @ Y0 @ sK50)))))) = $false) | ~spl0_28),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1497])).
% 1.51/1.32 thf(f1497,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))) @ sK50)) | ~spl0_28),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f986])).
% 1.51/1.32 thf(f986,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) | ~spl0_28),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f985])).
% 1.51/1.32 thf(f985,definition,(
% 1.51/1.32 spl0_28 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0)))))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition])).
% 1.51/1.32 thf(f1644,plain,(
% 1.51/1.32 ($true = (~ (sK33 @ sK52 @ sK55))) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1639])).
% 1.51/1.32 thf(f1639,plain,(
% 1.51/1.32 (((sK33 @ sK52 @ sK55) => $false) = $true) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(superposition,[status(thm)],[f1612,f1551])).
% 1.51/1.32 thf(f1612,plain,(
% 1.51/1.32 ( ! [X0 : a] : (($true = ((sK33 @ X0 @ sK55) => (sK33 @ X0 @ sK50)))) ) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1607])).
% 1.51/1.32 thf(f1607,plain,(
% 1.51/1.32 ( ! [X0 : a] : (($true = (((sK33 @ X0 @ sK55) & $true) => (sK33 @ X0 @ sK50)))) ) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(superposition,[status(thm)],[f1598,f1571])).
% 1.51/1.32 thf(f1571,plain,(
% 1.51/1.32 ($true = (sK33 @ sK55 @ sK50)) | ~spl0_28),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1570])).
% 1.51/1.32 thf(f1570,plain,(
% 1.51/1.32 ($true = ((sK33 @ sK55 @ sK50) & $true)) | ~spl0_28),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1563,f1568])).
% 1.51/1.32 thf(f1598,plain,(
% 1.51/1.32 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK33 @ X2 @ X1) & (sK33 @ X1 @ X3)) => (sK33 @ X2 @ X3)))) ) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1597])).
% 1.51/1.32 thf(f1597,plain,(
% 1.51/1.32 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK33 @ X2 @ X1) & (sK33 @ X1 @ Y0)) => (sK33 @ X2 @ Y0))) @ X3))) ) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1581])).
% 1.51/1.32 thf(f1581,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK33 @ X2 @ X1) & (sK33 @ X1 @ Y0)) => (sK33 @ X2 @ Y0)))))) ) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1580])).
% 1.51/1.32 thf(f1580,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK33 @ Y0 @ X1) & (sK33 @ X1 @ Y1)) => (sK33 @ Y0 @ Y1))))) @ X2))) ) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1577])).
% 1.51/1.32 thf(f1577,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK33 @ Y0 @ X1) & (sK33 @ X1 @ Y1)) => (sK33 @ Y0 @ Y1)))))))) ) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1576])).
% 1.51/1.32 thf(f1576,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2))))))) @ X1))) ) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1575])).
% 1.51/1.32 thf(f1575,plain,(
% 1.51/1.32 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2))))))))) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1574])).
% 1.51/1.32 thf(f1574,plain,(
% 1.51/1.32 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & $true)) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1504,f1572])).
% 1.51/1.32 thf(f1572,plain,(
% 1.51/1.32 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1504])).
% 1.51/1.32 thf(f1504,plain,(
% 1.51/1.32 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0)))))))) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1486])).
% 1.51/1.32 thf(f1486,plain,(
% 1.51/1.32 ($false != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK39))) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1485])).
% 1.51/1.32 thf(f1485,plain,(
% 1.51/1.32 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK39)) != ($false & (sK33 = sK39))) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1484])).
% 1.51/1.32 thf(f1484,plain,(
% 1.51/1.32 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK39)) != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & $false) & (sK33 = sK39))) | (~spl0_4 | ~spl0_28)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f1046,f986])).
% 1.51/1.32 thf(f1046,plain,(
% 1.51/1.32 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK39)) != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK39))) | ~spl0_4),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1045])).
% 1.51/1.32 thf(f1045,plain,(
% 1.51/1.32 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK33 @ Y2 @ Y1) & (sK33 @ Y1 @ Y3)) => (sK33 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK33 @ Y1 @ Y2) => (sK33 @ Y2 @ Y1))))))) & (sK33 = Y0))) @ sK39) != ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK33 @ Y2 @ Y1) => (sK33 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK33 @ Y3 @ Y1) & (sK33 @ Y2 @ Y3)) => (sK33 @ Y2 @ Y1))))))))) & (sK33 = Y0))) @ sK39)) | ~spl0_4),
% 1.51/1.32 inference(negative_extensionality,[status(thm)],[f901])).
% 1.51/1.32 thf(f901,plain,(
% 1.51/1.32 ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK33 @ Y2 @ Y1) => (sK33 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK33 @ Y3 @ Y1) & (sK33 @ Y2 @ Y3)) => (sK33 @ Y2 @ Y1))))))))) & (sK33 = Y0))) != (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK33 @ Y2 @ Y1) & (sK33 @ Y1 @ Y3)) => (sK33 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK33 @ Y1 @ Y2) => (sK33 @ Y2 @ Y1))))))) & (sK33 = Y0)))) | ~spl0_4),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f900])).
% 1.51/1.32 thf(f900,plain,(
% 1.51/1.32 (((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) @ sK33) != ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1))))) @ sK33)) | ~spl0_4),
% 1.51/1.32 inference(negative_extensionality,[status(thm)],[f897])).
% 1.51/1.32 thf(f897,plain,(
% 1.51/1.32 ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) != (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1)))))) | ~spl0_4),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f26])).
% 1.51/1.32 thf(f26,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1))))))) | ~spl0_4),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.51/1.32 thf(f25,definition,(
% 1.51/1.32 spl0_4 <=> ($false = ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1)))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.51/1.32 thf(f1473,plain,(
% 1.51/1.32 ~spl0_4 | ~spl0_27),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f1472])).
% 1.51/1.32 thf(f1472,plain,(
% 1.51/1.32 $false | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f1469])).
% 1.51/1.32 thf(f1469,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(superposition,[status(thm)],[f1455,f1464])).
% 1.51/1.32 thf(f1464,plain,(
% 1.51/1.32 ($false = ((sK33 @ sK49 @ sK47) => (sK33 @ sK47 @ sK49))) | ~spl0_27),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1463])).
% 1.51/1.32 thf(f1463,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: ((sK33 @ Y0 @ sK47) => (sK33 @ sK47 @ Y0))) @ sK49)) | ~spl0_27),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f1406])).
% 1.51/1.32 thf(f1406,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: ((sK33 @ Y0 @ sK47) => (sK33 @ sK47 @ Y0))))) | ~spl0_27),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1405])).
% 1.51/1.32 thf(f1405,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1))))) @ sK47)) | ~spl0_27),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f983])).
% 1.51/1.32 thf(f983,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1))))))) | ~spl0_27),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f982])).
% 1.51/1.32 thf(f982,definition,(
% 1.51/1.32 spl0_27 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition])).
% 1.51/1.32 thf(f1455,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((sK33 @ X1 @ X2) => (sK33 @ X2 @ X1)))) ) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1454])).
% 1.51/1.32 thf(f1454,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK33 @ X1 @ Y0) => (sK33 @ Y0 @ X1))) @ X2))) ) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1452])).
% 1.51/1.32 thf(f1452,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK33 @ X1 @ Y0) => (sK33 @ Y0 @ X1)))))) ) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1451])).
% 1.51/1.32 thf(f1451,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))) @ X1))) ) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1448])).
% 1.51/1.32 thf(f1448,plain,(
% 1.51/1.32 ($false != (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1447])).
% 1.51/1.32 thf(f1447,plain,(
% 1.51/1.32 ($false != ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0)))))))) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1412,f1445])).
% 1.51/1.32 thf(f1445,plain,(
% 1.51/1.32 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2))))))))) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1412])).
% 1.51/1.32 thf(f1412,plain,(
% 1.51/1.32 ($false != ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0)))))))) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1409])).
% 1.51/1.32 thf(f1409,plain,(
% 1.51/1.32 ($false != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & $true)) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1387,f1407])).
% 1.51/1.32 thf(f1407,plain,(
% 1.51/1.32 ($true = (sK33 = sK35)) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1387])).
% 1.51/1.32 thf(f1387,plain,(
% 1.51/1.32 ($false != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35))) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1386])).
% 1.51/1.32 thf(f1386,plain,(
% 1.51/1.32 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35)) != ($false & (sK33 = sK35))) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1385])).
% 1.51/1.32 thf(f1385,plain,(
% 1.51/1.32 ((($false & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK35)) != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35))) | (~spl0_4 | ~spl0_27)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f905,f983])).
% 1.51/1.32 thf(f905,plain,(
% 1.51/1.32 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35)) != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK35))) | ~spl0_4),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f904])).
% 1.51/1.32 thf(f904,plain,(
% 1.51/1.32 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK33 @ Y2 @ Y1) => (sK33 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK33 @ Y3 @ Y1) & (sK33 @ Y2 @ Y3)) => (sK33 @ Y2 @ Y1))))))))) & (sK33 = Y0))) @ sK35) != ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK33 @ Y2 @ Y1) & (sK33 @ Y1 @ Y3)) => (sK33 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK33 @ Y1 @ Y2) => (sK33 @ Y2 @ Y1))))))) & (sK33 = Y0))) @ sK35)) | ~spl0_4),
% 1.51/1.32 inference(negative_extensionality,[status(thm)],[f901])).
% 1.51/1.32 thf(f1323,plain,(
% 1.51/1.32 ~spl0_4 | ~spl0_29 | ~spl0_33),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f1322])).
% 1.51/1.32 thf(f1322,plain,(
% 1.51/1.32 $false | (~spl0_4 | ~spl0_29 | ~spl0_33)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f1321])).
% 1.51/1.32 thf(f1321,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_4 | ~spl0_29 | ~spl0_33)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1306,f1316])).
% 1.51/1.32 thf(f1316,plain,(
% 1.51/1.32 ($false = (sK33 @ sK44 @ sK45)) | (~spl0_4 | ~spl0_29 | ~spl0_33)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f1315])).
% 1.51/1.32 thf(f1315,plain,(
% 1.51/1.32 ($false = (sK33 @ sK44 @ sK45)) | ($false = $true) | (~spl0_4 | ~spl0_29 | ~spl0_33)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1307])).
% 1.51/1.32 thf(f1307,plain,(
% 1.51/1.32 ($false = ((sK33 @ sK44 @ sK45) => $true)) | ($false = (sK33 @ sK44 @ sK45)) | (~spl0_4 | ~spl0_29 | ~spl0_33)),
% 1.51/1.32 inference(superposition,[status(thm)],[f1304,f1155])).
% 1.51/1.32 thf(f1155,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = (sK33 @ X1 @ X2)) | ($false = (sK33 @ X2 @ X1))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1153])).
% 1.51/1.32 thf(f1153,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((sK33 @ X2 @ X1) => (sK33 @ X1 @ X2)))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1152])).
% 1.51/1.32 thf(f1152,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK33 @ Y0 @ X1) => (sK33 @ X1 @ Y0))) @ X2))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1150])).
% 1.51/1.32 thf(f1150,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK33 @ Y0 @ X1) => (sK33 @ X1 @ Y0)))))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1149])).
% 1.51/1.32 thf(f1149,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1))))) @ X1))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1108])).
% 1.51/1.32 thf(f1108,plain,(
% 1.51/1.32 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1))))))) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1075])).
% 1.51/1.32 thf(f1075,plain,(
% 1.51/1.32 ($false != ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0)))))))))) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1071])).
% 1.51/1.32 thf(f1071,plain,(
% 1.51/1.32 ($false != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & $true)) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1042,f1068])).
% 1.51/1.32 thf(f1068,plain,(
% 1.51/1.32 ($true = (sK33 = sK38)) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1042])).
% 1.51/1.32 thf(f1042,plain,(
% 1.51/1.32 ($false != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK38))) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f996,f1005])).
% 1.51/1.32 thf(f1005,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK38))) | ~spl0_29),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f1004])).
% 1.51/1.32 thf(f1004,definition,(
% 1.51/1.32 spl0_29 <=> ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK38)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition])).
% 1.51/1.32 thf(f996,plain,(
% 1.51/1.32 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK38)) != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK38))) | ~spl0_4),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f995])).
% 1.51/1.32 thf(f995,plain,(
% 1.51/1.32 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK33 @ Y2 @ Y1) => (sK33 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK33 @ Y3 @ Y1) & (sK33 @ Y2 @ Y3)) => (sK33 @ Y2 @ Y1))))))))) & (sK33 = Y0))) @ sK38) != ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK33 @ Y2 @ Y1) & (sK33 @ Y1 @ Y3)) => (sK33 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK33 @ Y1 @ Y2) => (sK33 @ Y2 @ Y1))))))) & (sK33 = Y0))) @ sK38)) | ~spl0_4),
% 1.51/1.32 inference(negative_extensionality,[status(thm)],[f901])).
% 1.51/1.32 thf(f1304,plain,(
% 1.51/1.32 ($false = ((sK33 @ sK44 @ sK45) => (sK33 @ sK45 @ sK44))) | ~spl0_33),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1303])).
% 1.51/1.32 thf(f1303,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: ((sK33 @ sK44 @ Y0) => (sK33 @ Y0 @ sK44))) @ sK45)) | ~spl0_33),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f1302])).
% 1.51/1.32 thf(f1302,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: ((sK33 @ sK44 @ Y0) => (sK33 @ Y0 @ sK44))))) | ~spl0_33),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1301])).
% 1.51/1.32 thf(f1301,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))) @ sK44)) | ~spl0_33),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f1166])).
% 1.51/1.32 thf(f1166,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) | ~spl0_33),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f1165])).
% 1.51/1.32 thf(f1165,definition,(
% 1.51/1.32 spl0_33 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0)))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_33])],[avatar_definition])).
% 1.51/1.32 thf(f1306,plain,(
% 1.51/1.32 ($true = (sK33 @ sK44 @ sK45)) | ~spl0_33),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1304])).
% 1.51/1.32 thf(f1298,plain,(
% 1.51/1.32 ~spl0_4 | ~spl0_29 | ~spl0_34),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f1297])).
% 1.51/1.32 thf(f1297,plain,(
% 1.51/1.32 $false | (~spl0_4 | ~spl0_29 | ~spl0_34)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f1296])).
% 1.51/1.32 thf(f1296,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_4 | ~spl0_29 | ~spl0_34)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1295])).
% 1.51/1.32 thf(f1295,plain,(
% 1.51/1.32 ((~ $true) = $true) | (~spl0_4 | ~spl0_29 | ~spl0_34)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f1288,f1202])).
% 1.51/1.32 thf(f1202,plain,(
% 1.51/1.32 ((sK33 @ sK41 @ sK43) = $true) | ~spl0_34),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1182])).
% 1.51/1.32 thf(f1182,plain,(
% 1.51/1.32 ($true = ((sK33 @ sK42 @ sK41) & (sK33 @ sK41 @ sK43))) | ~spl0_34),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1180])).
% 1.51/1.32 thf(f1180,plain,(
% 1.51/1.32 ($false = (((sK33 @ sK42 @ sK41) & (sK33 @ sK41 @ sK43)) => (sK33 @ sK42 @ sK43))) | ~spl0_34),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1179])).
% 1.51/1.32 thf(f1179,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (((sK33 @ sK42 @ sK41) & (sK33 @ sK41 @ Y0)) => (sK33 @ sK42 @ Y0))) @ sK43)) | ~spl0_34),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f1178])).
% 1.51/1.32 thf(f1178,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (((sK33 @ sK42 @ sK41) & (sK33 @ sK41 @ Y0)) => (sK33 @ sK42 @ Y0))))) | ~spl0_34),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1177])).
% 1.51/1.32 thf(f1177,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK33 @ Y0 @ sK41) & (sK33 @ sK41 @ Y1)) => (sK33 @ Y0 @ Y1))))) @ sK42)) | ~spl0_34),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f1176])).
% 1.51/1.32 thf(f1176,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK33 @ Y0 @ sK41) & (sK33 @ sK41 @ Y1)) => (sK33 @ Y0 @ Y1))))))) | ~spl0_34),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1175])).
% 1.51/1.32 thf(f1175,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2))))))) @ sK41)) | ~spl0_34),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f1169])).
% 1.51/1.32 thf(f1169,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2))))))))) | ~spl0_34),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f1168])).
% 1.51/1.32 thf(f1168,definition,(
% 1.51/1.32 spl0_34 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_34])],[avatar_definition])).
% 1.51/1.32 thf(f1288,plain,(
% 1.51/1.32 ($true = (~ (sK33 @ sK41 @ sK43))) | (~spl0_4 | ~spl0_29 | ~spl0_34)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1280])).
% 1.51/1.32 thf(f1280,plain,(
% 1.51/1.32 ($true = ((sK33 @ sK41 @ sK43) => $false)) | (~spl0_4 | ~spl0_29 | ~spl0_34)),
% 1.51/1.32 inference(superposition,[status(thm)],[f1211,f1181])).
% 1.51/1.32 thf(f1181,plain,(
% 1.51/1.32 ($false = (sK33 @ sK42 @ sK43)) | ~spl0_34),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1180])).
% 1.51/1.32 thf(f1211,plain,(
% 1.51/1.32 ( ! [X0 : a] : (($true = ((sK33 @ sK41 @ X0) => (sK33 @ sK42 @ X0)))) ) | (~spl0_4 | ~spl0_29 | ~spl0_34)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1209])).
% 1.51/1.32 thf(f1209,plain,(
% 1.51/1.32 ( ! [X0 : a] : (($true = (((sK33 @ sK41 @ X0) & $true) => (sK33 @ sK42 @ X0)))) ) | (~spl0_4 | ~spl0_29 | ~spl0_34)),
% 1.51/1.32 inference(superposition,[status(thm)],[f1129,f1205])).
% 1.51/1.32 thf(f1205,plain,(
% 1.51/1.32 ($true = (sK33 @ sK42 @ sK41)) | ~spl0_34),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1204])).
% 1.51/1.32 thf(f1204,plain,(
% 1.51/1.32 (((sK33 @ sK42 @ sK41) & $true) = $true) | ~spl0_34),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1182,f1202])).
% 1.51/1.32 thf(f1129,plain,(
% 1.51/1.32 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK33 @ X3 @ X1) & (sK33 @ X2 @ X3)) => (sK33 @ X2 @ X1)))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1128])).
% 1.51/1.32 thf(f1128,plain,(
% 1.51/1.32 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK33 @ Y0 @ X1) & (sK33 @ X2 @ Y0)) => (sK33 @ X2 @ X1))) @ X3))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1124])).
% 1.51/1.32 thf(f1124,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK33 @ Y0 @ X1) & (sK33 @ X2 @ Y0)) => (sK33 @ X2 @ X1)))))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1123])).
% 1.51/1.32 thf(f1123,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK33 @ Y1 @ X1) & (sK33 @ Y0 @ Y1)) => (sK33 @ Y0 @ X1))))) @ X2))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1118])).
% 1.51/1.32 thf(f1118,plain,(
% 1.51/1.32 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK33 @ Y1 @ X1) & (sK33 @ Y0 @ Y1)) => (sK33 @ Y0 @ X1)))))) = $true)) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f1117])).
% 1.51/1.32 thf(f1117,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))) @ X1))) ) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f1111])).
% 1.51/1.32 thf(f1111,plain,(
% 1.51/1.32 ($false != (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1110])).
% 1.51/1.32 thf(f1110,plain,(
% 1.51/1.32 ($false != ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0)))))))))) | (~spl0_4 | ~spl0_29)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1075,f1108])).
% 1.51/1.32 thf(f1170,plain,(
% 1.51/1.32 spl0_33 | spl0_34 | ~spl0_4 | ~spl0_23 | ~spl0_26 | ~spl0_29 | ~spl0_32),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f1163,f1014,f1004,f925,f915,f25,f1168,f1165])).
% 1.51/1.32 thf(f915,definition,(
% 1.51/1.32 spl0_23 <=> ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK35)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])).
% 1.51/1.32 thf(f925,definition,(
% 1.51/1.32 spl0_26 <=> ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition])).
% 1.51/1.32 thf(f1014,definition,(
% 1.51/1.32 spl0_32 <=> ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK38)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_32])],[avatar_definition])).
% 1.51/1.32 thf(f1163,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2))))))))) | (~spl0_4 | ~spl0_23 | ~spl0_26 | ~spl0_29 | ~spl0_32)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1084])).
% 1.51/1.32 thf(f1084,plain,(
% 1.51/1.32 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0)))))))) | (~spl0_4 | ~spl0_23 | ~spl0_26 | ~spl0_29 | ~spl0_32)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1083])).
% 1.51/1.32 thf(f1083,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & $true)) | (~spl0_4 | ~spl0_23 | ~spl0_26 | ~spl0_29 | ~spl0_32)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f926,f1082])).
% 1.51/1.32 thf(f1082,plain,(
% 1.51/1.32 ($true = (sK33 = sK35)) | (~spl0_4 | ~spl0_23 | ~spl0_29 | ~spl0_32)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1077])).
% 1.51/1.32 thf(f1077,plain,(
% 1.51/1.32 ($true = ($true & (sK33 = sK35))) | (~spl0_4 | ~spl0_23 | ~spl0_29 | ~spl0_32)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f916,f1074])).
% 1.51/1.32 thf(f1074,plain,(
% 1.51/1.32 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0)))))))))) | (~spl0_4 | ~spl0_29 | ~spl0_32)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1070])).
% 1.51/1.32 thf(f1070,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & $true)) | (~spl0_4 | ~spl0_29 | ~spl0_32)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1015,f1068])).
% 1.51/1.32 thf(f1015,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK38))) | ~spl0_32),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f1014])).
% 1.51/1.32 thf(f916,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK35))) | ~spl0_23),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f915])).
% 1.51/1.32 thf(f926,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35))) | ~spl0_26),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f925])).
% 1.51/1.32 thf(f1041,plain,(
% 1.51/1.32 ~spl0_29 | ~spl0_31),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f1040])).
% 1.51/1.32 thf(f1040,plain,(
% 1.51/1.32 $false | (~spl0_29 | ~spl0_31)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f1039])).
% 1.51/1.32 thf(f1039,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_29 | ~spl0_31)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1012,f1005])).
% 1.51/1.32 thf(f1012,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK38))) | ~spl0_31),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f1011])).
% 1.51/1.32 thf(f1011,definition,(
% 1.51/1.32 spl0_31 <=> ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK38)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition])).
% 1.51/1.32 thf(f1032,plain,(
% 1.51/1.32 ~spl0_4 | ~spl0_23 | ~spl0_30),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f1031])).
% 1.51/1.32 thf(f1031,plain,(
% 1.51/1.32 $false | (~spl0_4 | ~spl0_23 | ~spl0_30)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f1030])).
% 1.51/1.32 thf(f1030,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_4 | ~spl0_23 | ~spl0_30)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1028])).
% 1.51/1.32 thf(f1028,plain,(
% 1.51/1.32 ($true = ($false & (sK33 = sK35))) | (~spl0_4 | ~spl0_23 | ~spl0_30)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f916,f1027])).
% 1.51/1.32 thf(f1027,plain,(
% 1.51/1.32 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0)))))))))) | (~spl0_4 | ~spl0_30)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f1024])).
% 1.51/1.32 thf(f1024,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & $true)) | (~spl0_4 | ~spl0_30)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f1008,f1020])).
% 1.51/1.32 thf(f1020,plain,(
% 1.51/1.32 ($true = (sK33 = sK38)) | (~spl0_4 | ~spl0_30)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f1017])).
% 1.51/1.32 thf(f1017,plain,(
% 1.51/1.32 ($false != (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK38))) | (~spl0_4 | ~spl0_30)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f996,f1008])).
% 1.51/1.32 thf(f1008,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK38))) | ~spl0_30),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f1007])).
% 1.51/1.32 thf(f1007,definition,(
% 1.51/1.32 spl0_30 <=> ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK38)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition])).
% 1.51/1.32 thf(f1016,plain,(
% 1.51/1.32 spl0_31 | spl0_32 | ~spl0_4),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f1001,f25,f1014,f1011])).
% 1.51/1.32 thf(f1001,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK38))) | ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK38))) | ~spl0_4),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f996])).
% 1.51/1.32 thf(f1009,plain,(
% 1.51/1.32 spl0_29 | spl0_30 | ~spl0_4),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f1002,f25,f1007,f1004])).
% 1.51/1.32 thf(f1002,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK38))) | ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK38))) | ~spl0_4),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f996])).
% 1.51/1.32 thf(f991,plain,(
% 1.51/1.32 ~spl0_23 | ~spl0_25),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f990])).
% 1.51/1.32 thf(f990,plain,(
% 1.51/1.32 $false | (~spl0_23 | ~spl0_25)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f989])).
% 1.51/1.32 thf(f989,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_23 | ~spl0_25)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f916,f923])).
% 1.51/1.32 thf(f923,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK35))) | ~spl0_25),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f922])).
% 1.51/1.32 thf(f922,definition,(
% 1.51/1.32 spl0_25 <=> ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK35)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition])).
% 1.51/1.32 thf(f987,plain,(
% 1.51/1.32 spl0_27 | spl0_28 | ~spl0_24 | ~spl0_25),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f980,f922,f918,f985,f982])).
% 1.51/1.32 thf(f918,definition,(
% 1.51/1.32 spl0_24 <=> ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])).
% 1.51/1.32 thf(f980,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1))))))) | (~spl0_24 | ~spl0_25)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f963])).
% 1.51/1.32 thf(f963,plain,(
% 1.51/1.32 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0)))))))))) | (~spl0_24 | ~spl0_25)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f962])).
% 1.51/1.32 thf(f962,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & $true)) | (~spl0_24 | ~spl0_25)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f923,f961])).
% 1.51/1.32 thf(f961,plain,(
% 1.51/1.32 ($true = (sK33 = sK35)) | ~spl0_24),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f957])).
% 1.51/1.32 thf(f957,plain,(
% 1.51/1.32 ($true = ($true & (sK33 = sK35))) | ~spl0_24),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f919,f956])).
% 1.51/1.32 thf(f956,plain,(
% 1.51/1.32 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0)))))))) | ~spl0_24),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f919])).
% 1.51/1.32 thf(f919,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35))) | ~spl0_24),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f918])).
% 1.51/1.32 thf(f931,plain,(
% 1.51/1.32 ~spl0_24 | ~spl0_26),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f930])).
% 1.51/1.32 thf(f930,plain,(
% 1.51/1.32 $false | (~spl0_24 | ~spl0_26)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f929])).
% 1.51/1.32 thf(f929,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_24 | ~spl0_26)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f919,f926])).
% 1.51/1.32 thf(f927,plain,(
% 1.51/1.32 spl0_25 | spl0_26 | ~spl0_4),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f913,f25,f925,f922])).
% 1.51/1.32 thf(f913,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35))) | ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK35))) | ~spl0_4),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f905])).
% 1.51/1.32 thf(f920,plain,(
% 1.51/1.32 spl0_23 | spl0_24 | ~spl0_4),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f912,f25,f918,f915])).
% 1.51/1.32 thf(f912,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y1 @ Y0) => (sK33 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y2 @ Y0) & (sK33 @ Y1 @ Y2)) => (sK33 @ Y1 @ Y0))))))))) & (sK33 = sK35))) | ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK33 @ Y1 @ Y0) & (sK33 @ Y0 @ Y2)) => (sK33 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK33 @ Y0 @ Y1) => (sK33 @ Y1 @ Y0))))))) & (sK33 = sK35))) | ~spl0_4),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f905])).
% 1.51/1.32 thf(f883,plain,(
% 1.51/1.32 ~spl0_3 | ~spl0_6),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f882])).
% 1.51/1.32 thf(f882,plain,(
% 1.51/1.32 $false | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f881])).
% 1.51/1.32 thf(f881,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f875,f793])).
% 1.51/1.32 thf(f793,plain,(
% 1.51/1.32 ($false = (sK2 @ sK28 @ sK27)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f792])).
% 1.51/1.32 thf(f792,plain,(
% 1.51/1.32 (($true => (sK2 @ sK28 @ sK27)) = $false) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f780,f791])).
% 1.51/1.32 thf(f791,plain,(
% 1.51/1.32 (((sK2 @ sK28 @ sK29) & (sK2 @ sK29 @ sK27)) = $true) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f780])).
% 1.51/1.32 thf(f780,plain,(
% 1.51/1.32 ($false = (((sK2 @ sK28 @ sK29) & (sK2 @ sK29 @ sK27)) => (sK2 @ sK28 @ sK27))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f779,f774])).
% 1.51/1.32 thf(f774,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (((sK2 @ X1 @ X2) = (sK3 @ X1 @ X2))) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(argument_congruence,[status(thm)],[f773])).
% 1.51/1.32 thf(f773,plain,(
% 1.51/1.32 ( ! [X1 : a] : (((sK2 @ X1) = (sK3 @ X1))) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(argument_congruence,[status(thm)],[f770])).
% 1.51/1.32 thf(f770,plain,(
% 1.51/1.32 (sK2 = sK3) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f768])).
% 1.51/1.32 thf(f768,plain,(
% 1.51/1.32 ((sK2 = sK3) = $true) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f767])).
% 1.51/1.32 thf(f767,plain,(
% 1.51/1.32 (($true & (sK2 = sK3)) = $true) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f762,f766])).
% 1.51/1.32 thf(f766,plain,(
% 1.51/1.32 (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) = $true) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f762])).
% 1.51/1.32 thf(f762,plain,(
% 1.51/1.32 ($true = (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK2 = sK3))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f760,f761])).
% 1.51/1.32 thf(f761,plain,(
% 1.51/1.32 (sK2 = sK23) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f757])).
% 1.51/1.32 thf(f757,plain,(
% 1.51/1.32 ($true = (sK23 = sK2)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f752])).
% 1.51/1.32 thf(f752,plain,(
% 1.51/1.32 ($true = ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3)) & (sK23 = sK2))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(not_proxy_clausification,[status(thm)],[f749])).
% 1.51/1.32 thf(f749,plain,(
% 1.51/1.32 ($false = (~ ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3)) & (sK23 = sK2)))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f748])).
% 1.51/1.32 thf(f748,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: (~ ((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)))) @ sK23)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f747])).
% 1.51/1.32 thf(f747,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (~ ((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)))))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f746])).
% 1.51/1.32 thf(f746,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => $false)))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f745])).
% 1.51/1.32 thf(f745,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK3 @ Y2 @ Y1)))))) & (sK3 = sK2)) & $false))))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f629,f50])).
% 1.51/1.32 thf(f50,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y1 @ Y0))))))))) | ~spl0_6),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.51/1.32 thf(f49,definition,(
% 1.51/1.32 spl0_6 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y1 @ Y0)))))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.51/1.32 thf(f629,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK3 @ Y2 @ Y1)))))) & (sK3 = sK2)) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y2 @ Y1))))))))))))) | ~spl0_3),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f628])).
% 1.51/1.32 thf(f628,plain,(
% 1.51/1.32 (((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y4 @ Y2)) => (Y0 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3))))))) & (Y1 = Y0)) & (Y1 = sK2)) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2)))))) & (Y0 = sK2)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y4 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))))) @ sK3) = $false) | ~spl0_3),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f617])).
% 1.51/1.32 thf(f617,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y4 @ Y2)) => (Y0 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3))))))) & (Y1 = Y0)) & (Y1 = sK2)) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2)))))) & (Y0 = sK2)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y4 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))))))) | ~spl0_3),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f616])).
% 1.51/1.32 thf(f616,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3))))))))))))))) @ sK2)) | ~spl0_3),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f23])).
% 1.51/1.32 thf(f23,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3))))))))))))))))) | ~spl0_3),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.51/1.32 thf(f22,definition,(
% 1.51/1.32 spl0_3 <=> ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3)))))))))))))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.51/1.32 thf(f760,plain,(
% 1.51/1.32 ($true = (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f759])).
% 1.51/1.32 thf(f759,plain,(
% 1.51/1.32 ($true = ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3)) & $true)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f752,f757])).
% 1.51/1.32 thf(f779,plain,(
% 1.51/1.32 ($false = (((sK2 @ sK28 @ sK29) & (sK3 @ sK29 @ sK27)) => (sK2 @ sK28 @ sK27))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f778,f774])).
% 1.51/1.32 thf(f778,plain,(
% 1.51/1.32 ($false = (((sK3 @ sK28 @ sK29) & (sK3 @ sK29 @ sK27)) => (sK2 @ sK28 @ sK27))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f777])).
% 1.51/1.32 thf(f777,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (((sK3 @ sK28 @ Y0) & (sK3 @ Y0 @ sK27)) => (sK2 @ sK28 @ sK27))) @ sK29)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f775])).
% 1.51/1.32 thf(f775,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (((sK3 @ sK28 @ Y0) & (sK3 @ Y0 @ sK27)) => (sK2 @ sK28 @ sK27))))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f756,f774])).
% 1.51/1.32 thf(f756,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (((sK3 @ sK28 @ Y0) & (sK3 @ Y0 @ sK27)) => (sK3 @ sK28 @ sK27))))) | ~spl0_6),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f755])).
% 1.51/1.32 thf(f755,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y1 @ sK27)) => (sK3 @ Y0 @ sK27))))) @ sK28)) | ~spl0_6),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f751])).
% 1.51/1.32 thf(f751,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y1 @ sK27)) => (sK3 @ Y0 @ sK27))))))) | ~spl0_6),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f750])).
% 1.51/1.32 thf(f750,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y1 @ Y0))))))) @ sK27)) | ~spl0_6),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f50])).
% 1.51/1.32 thf(f875,plain,(
% 1.51/1.32 ($true = (sK2 @ sK28 @ sK27)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f872])).
% 1.51/1.32 thf(f872,plain,(
% 1.51/1.32 (($true => (sK2 @ sK28 @ sK27)) = $true) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(superposition,[status(thm)],[f851,f805])).
% 1.51/1.32 thf(f805,plain,(
% 1.51/1.32 ($true = (sK2 @ sK30 @ sK27)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f800])).
% 1.51/1.32 thf(f800,plain,(
% 1.51/1.32 ($true = ((sK2 @ sK28 @ sK30) & (sK2 @ sK30 @ sK27))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(not_proxy_clausification,[status(thm)],[f799])).
% 1.51/1.32 thf(f799,plain,(
% 1.51/1.32 ($false = (~ ((sK2 @ sK28 @ sK30) & (sK2 @ sK30 @ sK27)))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f798,f774])).
% 1.51/1.32 thf(f798,plain,(
% 1.51/1.32 ($false = (~ ((sK2 @ sK28 @ sK30) & (sK3 @ sK30 @ sK27)))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f797,f774])).
% 1.51/1.32 thf(f797,plain,(
% 1.51/1.32 ($false = (~ ((sK3 @ sK28 @ sK30) & (sK3 @ sK30 @ sK27)))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f796])).
% 1.51/1.32 thf(f796,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (~ ((sK3 @ sK28 @ Y0) & (sK3 @ Y0 @ sK27)))) @ sK30)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f795])).
% 1.51/1.32 thf(f795,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK3 @ sK28 @ Y0) & (sK3 @ Y0 @ sK27)))))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f794])).
% 1.51/1.32 thf(f794,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (((sK3 @ sK28 @ Y0) & (sK3 @ Y0 @ sK27)) => $false)))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f775,f793])).
% 1.51/1.32 thf(f851,plain,(
% 1.51/1.32 ( ! [X0 : a] : (($true = ((sK2 @ sK30 @ X0) => (sK2 @ sK28 @ X0)))) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f842])).
% 1.51/1.32 thf(f842,plain,(
% 1.51/1.32 ( ! [X0 : a] : (($true = (($true & (sK2 @ sK30 @ X0)) => (sK2 @ sK28 @ X0)))) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(superposition,[status(thm)],[f826,f808])).
% 1.51/1.32 thf(f808,plain,(
% 1.51/1.32 ($true = (sK2 @ sK28 @ sK30)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f807])).
% 1.51/1.32 thf(f807,plain,(
% 1.51/1.32 ($true = ((sK2 @ sK28 @ sK30) & $true)) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f800,f805])).
% 1.51/1.32 thf(f826,plain,(
% 1.51/1.32 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK2 @ X2 @ X1) & (sK2 @ X1 @ X3)) => (sK2 @ X2 @ X3)))) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f825])).
% 1.51/1.32 thf(f825,plain,(
% 1.51/1.32 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK2 @ X2 @ X1) & (sK2 @ X1 @ Y0)) => (sK2 @ X2 @ Y0))) @ X3))) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f824])).
% 1.51/1.32 thf(f824,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK2 @ X2 @ X1) & (sK2 @ X1 @ Y0)) => (sK2 @ X2 @ Y0)))))) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f823])).
% 1.51/1.32 thf(f823,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ X1) & (sK2 @ X1 @ Y1)) => (sK2 @ Y0 @ Y1))))) @ X2) = $true)) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f822])).
% 1.51/1.32 thf(f822,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ X1) & (sK2 @ X1 @ Y1)) => (sK2 @ Y0 @ Y1)))))))) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f821])).
% 1.51/1.32 thf(f821,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y1 @ Y2))))))) @ X1))) ) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f816])).
% 1.51/1.32 thf(f816,plain,(
% 1.51/1.32 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y1 @ Y2))))))))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f815])).
% 1.51/1.32 thf(f815,plain,(
% 1.51/1.32 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y1 @ Y2)))))))))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f812,f814])).
% 1.51/1.32 thf(f814,plain,(
% 1.51/1.32 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) = $true) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f812])).
% 1.51/1.32 thf(f812,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y1 @ Y2)))))))))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f811])).
% 1.51/1.32 thf(f811,plain,(
% 1.51/1.32 (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y1 @ Y2))))))))) & $true) = $true) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f766,f809])).
% 1.51/1.32 thf(f809,plain,(
% 1.51/1.32 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) | (~spl0_3 | ~spl0_6)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f766])).
% 1.51/1.32 thf(f744,plain,(
% 1.51/1.32 ~spl0_3 | ~spl0_17),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f743])).
% 1.51/1.32 thf(f743,plain,(
% 1.51/1.32 $false | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f742])).
% 1.51/1.32 thf(f742,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f740,f621])).
% 1.51/1.32 thf(f621,plain,(
% 1.51/1.32 ($false = (sK3 = sK2)) | ~spl0_17),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f620])).
% 1.51/1.32 thf(f620,definition,(
% 1.51/1.32 spl0_17 <=> ($false = (sK3 = sK2))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.51/1.32 thf(f740,plain,(
% 1.51/1.32 ((sK3 = sK2) = $true) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f712,f738])).
% 1.51/1.32 thf(f738,plain,(
% 1.51/1.32 (sK3 = sK23) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f737])).
% 1.51/1.32 thf(f737,plain,(
% 1.51/1.32 ((sK23 = sK3) = $true) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f736])).
% 1.51/1.32 thf(f736,plain,(
% 1.51/1.32 ($true = ($true & (sK23 = sK3))) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f715,f735])).
% 1.51/1.32 thf(f735,plain,(
% 1.51/1.32 ($true = ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1)))))))) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f715])).
% 1.51/1.32 thf(f715,plain,(
% 1.51/1.32 ($true = (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3))) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f714])).
% 1.51/1.32 thf(f714,plain,(
% 1.51/1.32 ($true = ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3)) & $true)) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f708,f712])).
% 1.51/1.32 thf(f708,plain,(
% 1.51/1.32 ($true = ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3)) & (sK23 = sK2))) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(not_proxy_clausification,[status(thm)],[f706])).
% 1.51/1.32 thf(f706,plain,(
% 1.51/1.32 ($false = (~ ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3)) & (sK23 = sK2)))) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f705])).
% 1.51/1.32 thf(f705,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: (~ ((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)))) @ sK23)) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f703])).
% 1.51/1.32 thf(f703,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (~ ((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)))))) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f702])).
% 1.51/1.32 thf(f702,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => $false)))) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f701])).
% 1.51/1.32 thf(f701,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => ($false & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y2 @ Y1))))))))))))) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f700])).
% 1.51/1.32 thf(f700,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK3 @ Y2 @ Y1)))))) & $false) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y2 @ Y1))))))))))))) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f629,f621])).
% 1.51/1.32 thf(f712,plain,(
% 1.51/1.32 ($true = (sK23 = sK2)) | (~spl0_3 | ~spl0_17)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f708])).
% 1.51/1.32 thf(f697,plain,(
% 1.51/1.32 ~spl0_3 | ~spl0_18),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f696])).
% 1.51/1.32 thf(f696,plain,(
% 1.51/1.32 $false | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f695])).
% 1.51/1.32 thf(f695,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f687,f643])).
% 1.51/1.32 thf(f643,plain,(
% 1.51/1.32 ($false = (sK3 @ sK24 @ sK22)) | ~spl0_18),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f639])).
% 1.51/1.32 thf(f639,plain,(
% 1.51/1.32 ($false = ((sK3 @ sK22 @ sK24) => (sK3 @ sK24 @ sK22))) | ~spl0_18),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f638])).
% 1.51/1.32 thf(f638,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: ((sK3 @ sK22 @ Y0) => (sK3 @ Y0 @ sK22))) @ sK24)) | ~spl0_18),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f635])).
% 1.51/1.32 thf(f635,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK22 @ Y0) => (sK3 @ Y0 @ sK22))))) | ~spl0_18),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f634])).
% 1.51/1.32 thf(f634,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0))))) @ sK22)) | ~spl0_18),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f624])).
% 1.51/1.32 thf(f624,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0))))))) | ~spl0_18),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f623])).
% 1.51/1.32 thf(f623,definition,(
% 1.51/1.32 spl0_18 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0)))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 1.51/1.32 thf(f687,plain,(
% 1.51/1.32 ($true = (sK3 @ sK24 @ sK22)) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f685])).
% 1.51/1.32 thf(f685,plain,(
% 1.51/1.32 ($true = ($true => (sK3 @ sK24 @ sK22))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(superposition,[status(thm)],[f669,f644])).
% 1.51/1.32 thf(f644,plain,(
% 1.51/1.32 ($true = (sK3 @ sK22 @ sK24)) | ~spl0_18),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f639])).
% 1.51/1.32 thf(f669,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((sK3 @ X2 @ X1) => (sK3 @ X1 @ X2)))) ) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f668])).
% 1.51/1.32 thf(f668,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK3 @ Y0 @ X1) => (sK3 @ X1 @ Y0))) @ X2))) ) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f666])).
% 1.51/1.32 thf(f666,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK3 @ Y0 @ X1) => (sK3 @ X1 @ Y0)))))) ) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f665])).
% 1.51/1.32 thf(f665,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))) @ X1))) ) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f660])).
% 1.51/1.32 thf(f660,plain,(
% 1.51/1.32 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f659])).
% 1.51/1.32 thf(f659,plain,(
% 1.51/1.32 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1)))))))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f656,f658])).
% 1.51/1.32 thf(f658,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2)))))))))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f656])).
% 1.51/1.32 thf(f656,plain,(
% 1.51/1.32 ($true = ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1)))))))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f655])).
% 1.51/1.32 thf(f655,plain,(
% 1.51/1.32 ($true = (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & $true)) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f652,f653])).
% 1.51/1.32 thf(f653,plain,(
% 1.51/1.32 ((sK23 = sK3) = $true) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f652])).
% 1.51/1.32 thf(f652,plain,(
% 1.51/1.32 ($true = (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f651])).
% 1.51/1.32 thf(f651,plain,(
% 1.51/1.32 ($true = ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3)) & $true)) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f640,f649])).
% 1.51/1.32 thf(f649,plain,(
% 1.51/1.32 ($true = (sK23 = sK2)) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f640])).
% 1.51/1.32 thf(f640,plain,(
% 1.51/1.32 ($true = ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3)) & (sK23 = sK2))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(not_proxy_clausification,[status(thm)],[f637])).
% 1.51/1.32 thf(f637,plain,(
% 1.51/1.32 ($false = (~ ((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK23 @ Y0 @ Y1) => (sK23 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK23 @ Y1 @ Y0) & (sK23 @ Y0 @ Y2)) => (sK23 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK23 = sK3)) & (sK23 = sK2)))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f636])).
% 1.51/1.32 thf(f636,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: (~ ((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)))) @ sK23)) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f633])).
% 1.51/1.32 thf(f633,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (~ ((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)))))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f632])).
% 1.51/1.32 thf(f632,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => $false)))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f631])).
% 1.51/1.32 thf(f631,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => ($false & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y2 @ Y1))))))))))))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f630])).
% 1.51/1.32 thf(f630,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => (($false & (sK3 = sK2)) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y2 @ Y1))))))))))))) | (~spl0_3 | ~spl0_18)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f629,f624])).
% 1.51/1.32 thf(f625,plain,(
% 1.51/1.32 spl0_17 | spl0_18 | ~spl0_5),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f618,f46,f623,f620])).
% 1.51/1.32 thf(f46,definition,(
% 1.51/1.32 spl0_5 <=> ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0)))))) & (sK3 = sK2)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.51/1.32 thf(f618,plain,(
% 1.51/1.32 ($false = (sK3 = sK2)) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0))))))) | ~spl0_5),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.51/1.32 thf(f47,plain,(
% 1.51/1.32 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0)))))) & (sK3 = sK2))) | ~spl0_5),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.51/1.32 thf(f610,plain,(
% 1.51/1.32 ~spl0_1 | ~spl0_16),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f609])).
% 1.51/1.32 thf(f609,plain,(
% 1.51/1.32 $false | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f608])).
% 1.51/1.32 thf(f608,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f607])).
% 1.51/1.32 thf(f607,plain,(
% 1.51/1.32 ((~ $true) = $true) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f599,f505])).
% 1.51/1.32 thf(f505,plain,(
% 1.51/1.32 ($true = (sK14 @ sK21 @ sK19)) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f502])).
% 1.51/1.32 thf(f502,plain,(
% 1.51/1.32 ($true = ((sK14 @ sK18 @ sK21) & (sK14 @ sK21 @ sK19))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(not_proxy_clausification,[status(thm)],[f487])).
% 1.51/1.32 thf(f487,plain,(
% 1.51/1.32 ($false = (~ ((sK14 @ sK18 @ sK21) & (sK14 @ sK21 @ sK19)))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f486])).
% 1.51/1.32 thf(f486,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (~ ((sK14 @ sK18 @ Y0) & (sK14 @ Y0 @ sK19)))) @ sK21)) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f470])).
% 1.51/1.32 thf(f470,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK14 @ sK18 @ Y0) & (sK14 @ Y0 @ sK19)))))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f469])).
% 1.51/1.32 thf(f469,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (((sK14 @ sK18 @ Y0) & (sK14 @ Y0 @ sK19)) => $false)))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f461,f468])).
% 1.51/1.32 thf(f468,plain,(
% 1.51/1.32 ($false = (sK14 @ sK18 @ sK19)) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f467])).
% 1.51/1.32 thf(f467,plain,(
% 1.51/1.32 ($false = ($true => (sK14 @ sK18 @ sK19))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f464,f466])).
% 1.51/1.32 thf(f466,plain,(
% 1.51/1.32 (((sK14 @ sK18 @ sK20) & (sK14 @ sK20 @ sK19)) = $true) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f464])).
% 1.51/1.32 thf(f464,plain,(
% 1.51/1.32 ($false = (((sK14 @ sK18 @ sK20) & (sK14 @ sK20 @ sK19)) => (sK14 @ sK18 @ sK19))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f463])).
% 1.51/1.32 thf(f463,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (((sK14 @ sK18 @ Y0) & (sK14 @ Y0 @ sK19)) => (sK14 @ sK18 @ sK19))) @ sK20)) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f461])).
% 1.51/1.32 thf(f461,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (((sK14 @ sK18 @ Y0) & (sK14 @ Y0 @ sK19)) => (sK14 @ sK18 @ sK19))))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f460])).
% 1.51/1.32 thf(f460,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ sK18 @ Y1) & (sK14 @ Y1 @ Y0)) => (sK14 @ sK18 @ Y0))))) @ sK19)) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f457])).
% 1.51/1.32 thf(f457,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ sK18 @ Y1) & (sK14 @ Y1 @ Y0)) => (sK14 @ sK18 @ Y0))))))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f456])).
% 1.51/1.32 thf(f456,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK14 @ Y0 @ Y2) & (sK14 @ Y2 @ Y1)) => (sK14 @ Y0 @ Y1))))))) @ sK18)) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f450])).
% 1.51/1.32 thf(f450,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK14 @ Y0 @ Y2) & (sK14 @ Y2 @ Y1)) => (sK14 @ Y0 @ Y1))))))))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f449])).
% 1.51/1.32 thf(f449,plain,(
% 1.51/1.32 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK14 @ Y0 @ Y2) & (sK14 @ Y2 @ Y1)) => (sK14 @ Y0 @ Y1)))))))) & $true) = $false) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f448])).
% 1.51/1.32 thf(f448,plain,(
% 1.51/1.32 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK14 @ Y0 @ Y2) & (sK14 @ Y2 @ Y1)) => (sK14 @ Y0 @ Y1)))))))) & (sK14 = sK14))) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f398,f425])).
% 1.51/1.32 thf(f425,plain,(
% 1.51/1.32 (sK15 = sK14) | ~spl0_1),
% 1.51/1.32 inference(equality_proxy_clausification,[status(thm)],[f424])).
% 1.51/1.32 thf(f424,plain,(
% 1.51/1.32 ($true = (sK15 = sK14)) | ~spl0_1),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f423])).
% 1.51/1.32 thf(f423,plain,(
% 1.51/1.32 ($true = ($true & (sK15 = sK14))) | ~spl0_1),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f413,f422])).
% 1.51/1.32 thf(f422,plain,(
% 1.51/1.32 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK14 @ Y1 @ Y2) & (sK14 @ Y0 @ Y1)) => (sK14 @ Y0 @ Y2))))))))) | ~spl0_1),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f413])).
% 1.51/1.32 thf(f413,plain,(
% 1.51/1.32 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK14 @ Y1 @ Y2) & (sK14 @ Y0 @ Y1)) => (sK14 @ Y0 @ Y2)))))))) & (sK15 = sK14))) | ~spl0_1),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f389])).
% 1.51/1.32 thf(f389,plain,(
% 1.51/1.32 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK14 @ Y1 @ Y2) & (sK14 @ Y0 @ Y1)) => (sK14 @ Y0 @ Y2)))))))) & (sK15 = sK14)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK14 @ Y0 @ Y1) => (sK14 @ Y1 @ Y0)))))))) | ~spl0_1),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f387])).
% 1.51/1.32 thf(f387,plain,(
% 1.51/1.32 ($false = ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK14 @ Y1 @ Y2) & (sK14 @ Y0 @ Y1)) => (sK14 @ Y0 @ Y2)))))))) & (sK15 = sK14)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK14 @ Y0 @ Y1) => (sK14 @ Y1 @ Y0))))))) => (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) & (sK15 = sK14)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ Y0 @ Y1) => (sK15 @ Y1 @ Y0))))))))) | ~spl0_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f386])).
% 1.51/1.32 thf(f386,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK14 @ Y2 @ Y3) & (sK14 @ Y1 @ Y2)) => (sK14 @ Y1 @ Y3)))))))) & (Y0 = sK14)) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK14 @ Y1 @ Y2) => (sK14 @ Y2 @ Y1))))))) => (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (Y0 = sK14)) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))) @ sK15)) | ~spl0_1),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f385])).
% 1.51/1.32 thf(f385,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK14 @ Y2 @ Y3) & (sK14 @ Y1 @ Y2)) => (sK14 @ Y1 @ Y3)))))))) & (Y0 = sK14)) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK14 @ Y1 @ Y2) => (sK14 @ Y2 @ Y1))))))) => (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (Y0 = sK14)) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))))) | ~spl0_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f384])).
% 1.51/1.32 thf(f384,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y4)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))))))) @ sK14)) | ~spl0_1),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f13])).
% 1.51/1.32 thf(f13,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y4)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))))))))) | ~spl0_1),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f12])).
% 1.51/1.32 thf(f12,definition,(
% 1.51/1.32 spl0_1 <=> ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y4)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2)))))))))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.51/1.32 thf(f398,plain,(
% 1.51/1.32 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) & (sK15 = sK14))) | ~spl0_16),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f397])).
% 1.51/1.32 thf(f397,definition,(
% 1.51/1.32 spl0_16 <=> ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) & (sK15 = sK14)))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.51/1.32 thf(f599,plain,(
% 1.51/1.32 ((~ (sK14 @ sK21 @ sK19)) = $true) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f594])).
% 1.51/1.32 thf(f594,plain,(
% 1.51/1.32 (((sK14 @ sK21 @ sK19) => $false) = $true) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(superposition,[status(thm)],[f517,f468])).
% 1.51/1.32 thf(f517,plain,(
% 1.51/1.32 ( ! [X0 : a] : (($true = ((sK14 @ sK21 @ X0) => (sK14 @ sK18 @ X0)))) ) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f510])).
% 1.51/1.32 thf(f510,plain,(
% 1.51/1.32 ( ! [X0 : a] : (($true = (((sK14 @ sK21 @ X0) & $true) => (sK14 @ sK18 @ X0)))) ) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(superposition,[status(thm)],[f459,f508])).
% 1.51/1.32 thf(f508,plain,(
% 1.51/1.32 ((sK14 @ sK18 @ sK21) = $true) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f507])).
% 1.51/1.32 thf(f507,plain,(
% 1.51/1.32 ($true = ((sK14 @ sK18 @ sK21) & $true)) | (~spl0_1 | ~spl0_16)),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f502,f505])).
% 1.51/1.32 thf(f459,plain,(
% 1.51/1.32 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (((sK14 @ X2 @ X3) & (sK14 @ X1 @ X2)) => (sK14 @ X1 @ X3)))) ) | ~spl0_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f458])).
% 1.51/1.32 thf(f458,plain,(
% 1.51/1.32 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK14 @ X2 @ Y0) & (sK14 @ X1 @ X2)) => (sK14 @ X1 @ Y0))) @ X3))) ) | ~spl0_1),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f439])).
% 1.51/1.32 thf(f439,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK14 @ X2 @ Y0) & (sK14 @ X1 @ X2)) => (sK14 @ X1 @ Y0)))))) ) | ~spl0_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f438])).
% 1.51/1.32 thf(f438,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y0 @ Y1) & (sK14 @ X1 @ Y0)) => (sK14 @ X1 @ Y1))))) @ X2) = $true)) ) | ~spl0_1),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f431])).
% 1.51/1.32 thf(f431,plain,(
% 1.51/1.32 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y0 @ Y1) & (sK14 @ X1 @ Y0)) => (sK14 @ X1 @ Y1)))))) = $true)) ) | ~spl0_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f430])).
% 1.51/1.32 thf(f430,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK14 @ Y1 @ Y2) & (sK14 @ Y0 @ Y1)) => (sK14 @ Y0 @ Y2))))))) @ X1))) ) | ~spl0_1),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f422])).
% 1.51/1.32 thf(f447,plain,(
% 1.51/1.32 ~spl0_1 | ~spl0_15),
% 1.51/1.32 inference(avatar_contradiction_clause,[status(thm)],[f446])).
% 1.51/1.32 thf(f446,plain,(
% 1.51/1.32 $false | (~spl0_1 | ~spl0_15)),
% 1.51/1.32 inference(trivial_inequality_removal,[status(thm)],[f445])).
% 1.51/1.32 thf(f445,plain,(
% 1.51/1.32 ($false = $true) | (~spl0_1 | ~spl0_15)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f444])).
% 1.51/1.32 thf(f444,plain,(
% 1.51/1.32 ((~ $true) = $true) | (~spl0_1 | ~spl0_15)),
% 1.51/1.32 inference(forward_demodulation,[status(thm)],[f443,f437])).
% 1.51/1.32 thf(f437,plain,(
% 1.51/1.32 ((sK14 @ sK16 @ sK17) = $true) | (~spl0_1 | ~spl0_15)),
% 1.51/1.32 inference(superposition,[status(thm)],[f407,f429])).
% 1.51/1.32 thf(f429,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (((sK15 @ X1 @ X2) = (sK14 @ X1 @ X2))) ) | ~spl0_1),
% 1.51/1.32 inference(argument_congruence,[status(thm)],[f428])).
% 1.51/1.32 thf(f428,plain,(
% 1.51/1.32 ( ! [X1 : a] : (((sK15 @ X1) = (sK14 @ X1))) ) | ~spl0_1),
% 1.51/1.32 inference(argument_congruence,[status(thm)],[f425])).
% 1.51/1.32 thf(f407,plain,(
% 1.51/1.32 ($true = (sK15 @ sK16 @ sK17)) | ~spl0_15),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f405])).
% 1.51/1.32 thf(f405,plain,(
% 1.51/1.32 ($false = ((sK15 @ sK16 @ sK17) => (sK15 @ sK17 @ sK16))) | ~spl0_15),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f404])).
% 1.51/1.32 thf(f404,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: ((sK15 @ sK16 @ Y0) => (sK15 @ Y0 @ sK16))) @ sK17)) | ~spl0_15),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f403])).
% 1.51/1.32 thf(f403,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: ((sK15 @ sK16 @ Y0) => (sK15 @ Y0 @ sK16))))) | ~spl0_15),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f402])).
% 1.51/1.32 thf(f402,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ Y0 @ Y1) => (sK15 @ Y1 @ Y0))))) @ sK16)) | ~spl0_15),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f395])).
% 1.51/1.32 thf(f395,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ Y0 @ Y1) => (sK15 @ Y1 @ Y0))))))) | ~spl0_15),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f394])).
% 1.51/1.32 thf(f394,definition,(
% 1.51/1.32 spl0_15 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ Y0 @ Y1) => (sK15 @ Y1 @ Y0)))))))),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.51/1.32 thf(f443,plain,(
% 1.51/1.32 ((~ (sK14 @ sK16 @ sK17)) = $true) | (~spl0_1 | ~spl0_15)),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f441])).
% 1.51/1.32 thf(f441,plain,(
% 1.51/1.32 ($true = ((sK14 @ sK16 @ sK17) => $false)) | (~spl0_1 | ~spl0_15)),
% 1.51/1.32 inference(superposition,[status(thm)],[f419,f436])).
% 1.51/1.32 thf(f436,plain,(
% 1.51/1.32 ($false = (sK14 @ sK17 @ sK16)) | (~spl0_1 | ~spl0_15)),
% 1.51/1.32 inference(superposition,[status(thm)],[f406,f429])).
% 1.51/1.32 thf(f406,plain,(
% 1.51/1.32 ($false = (sK15 @ sK17 @ sK16)) | ~spl0_15),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f405])).
% 1.51/1.32 thf(f419,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((sK14 @ X1 @ X2) => (sK14 @ X2 @ X1)))) ) | ~spl0_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f418])).
% 1.51/1.32 thf(f418,plain,(
% 1.51/1.32 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK14 @ X1 @ Y0) => (sK14 @ Y0 @ X1))) @ X2))) ) | ~spl0_1),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f417])).
% 1.51/1.32 thf(f417,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK14 @ X1 @ Y0) => (sK14 @ Y0 @ X1)))))) ) | ~spl0_1),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f416])).
% 1.51/1.32 thf(f416,plain,(
% 1.51/1.32 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK14 @ Y0 @ Y1) => (sK14 @ Y1 @ Y0))))) @ X1))) ) | ~spl0_1),
% 1.51/1.32 inference(pi_clausification,[status(thm)],[f415])).
% 1.51/1.32 thf(f415,plain,(
% 1.51/1.32 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK14 @ Y0 @ Y1) => (sK14 @ Y1 @ Y0))))))) | ~spl0_1),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f414])).
% 1.51/1.32 thf(f414,plain,(
% 1.51/1.32 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK14 @ Y0 @ Y1) => (sK14 @ Y1 @ Y0))))))) = $true) | ~spl0_1),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f389,f413])).
% 1.51/1.32 thf(f399,plain,(
% 1.51/1.32 spl0_15 | spl0_16 | ~spl0_1),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f392,f12,f397,f394])).
% 1.51/1.32 thf(f392,plain,(
% 1.51/1.32 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) & (sK15 = sK14))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ Y0 @ Y1) => (sK15 @ Y1 @ Y0))))))) | ~spl0_1),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f391])).
% 1.51/1.32 thf(f391,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) & (sK15 = sK14)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ Y0 @ Y1) => (sK15 @ Y1 @ Y0)))))))) | ~spl0_1),
% 1.51/1.32 inference(boolean_simplification,[status(thm)],[f390])).
% 1.51/1.32 thf(f390,plain,(
% 1.51/1.32 ($false = ($true => (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) & (sK15 = sK14)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK15 @ Y0 @ Y1) => (sK15 @ Y1 @ Y0))))))))) | ~spl0_1),
% 1.51/1.32 inference(backward_demodulation,[status(thm)],[f387,f389])).
% 1.51/1.32 thf(f51,plain,(
% 1.51/1.32 spl0_5 | spl0_6 | ~spl0_3),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f44,f22,f49,f46])).
% 1.51/1.32 thf(f44,plain,(
% 1.51/1.32 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y1 @ Y0))))))))) | ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0)))))) & (sK3 = sK2))) | ~spl0_3),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.51/1.32 thf(f36,plain,(
% 1.51/1.32 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0)))))) & (sK3 = sK2)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y1 @ Y0)))))))))) | ~spl0_3),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.51/1.32 thf(f35,plain,(
% 1.51/1.32 ($false = (((((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y1) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y2 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK4 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y1 @ Y0) & (sK4 @ Y0 @ Y2)) => (sK4 @ Y1 @ Y2))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y1 @ Y0) => (sK3 @ Y0 @ Y1))))))) & (sK4 = sK3)) & (sK4 = sK2)) => (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK3 @ Y1 @ Y0)))))) & (sK3 = sK2)) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y2 @ Y0)) => (sK3 @ Y1 @ Y0))))))))))) | ~spl0_3),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.51/1.32 thf(f34,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK3 @ Y2 @ Y1)))))) & (sK3 = sK2)) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y2 @ Y1))))))))))) @ sK4)) | ~spl0_3),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f33])).
% 1.51/1.32 thf(f33,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y2) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y3 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y2 @ Y1) => (sK3 @ Y1 @ Y2))))))) & (Y0 = sK3)) & (Y0 = sK2)) => (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (sK3 @ Y2 @ Y1)))))) & (sK3 = sK2)) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (sK3 @ Y3 @ Y1)) => (sK3 @ Y2 @ Y1))))))))))))) | ~spl0_3),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.51/1.32 thf(f32,plain,(
% 1.51/1.32 (((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y4 @ Y2)) => (Y0 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3))))))) & (Y1 = Y0)) & (Y1 = sK2)) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2)))))) & (Y0 = sK2)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y4 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))))) @ sK3) = $false) | ~spl0_3),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f31])).
% 1.51/1.32 thf(f31,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y4 @ Y2)) => (Y0 @ Y4 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y3 @ Y4))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3))))))) & (Y1 = Y0)) & (Y1 = sK2)) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2)))))) & (Y0 = sK2)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y4 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))))))) | ~spl0_3),
% 1.51/1.32 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.51/1.32 thf(f30,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3))))))))))))))) @ sK2)) | ~spl0_3),
% 1.51/1.32 inference(sigma_clausification,[status(thm)],[f23])).
% 1.51/1.32 thf(f27,plain,(
% 1.51/1.32 spl0_3 | spl0_4 | ~spl0_2),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f20,f15,f25,f22])).
% 1.51/1.32 thf(f15,definition,(
% 1.51/1.32 spl0_2 <=> (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3)))))))))))))))) & ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1))))))) = $false)),
% 1.51/1.32 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.51/1.32 thf(f20,plain,(
% 1.51/1.32 ($false = ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1))))))) | ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3))))))))))))))))) | ~spl0_2),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.51/1.32 thf(f16,plain,(
% 1.51/1.32 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3)))))))))))))))) & ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1))))))) = $false) | ~spl0_2),
% 1.51/1.32 inference(avatar_component_clause,[status(thm)],[f15])).
% 1.51/1.32 thf(f17,plain,(
% 1.51/1.32 spl0_1 | spl0_2),
% 1.51/1.32 inference(avatar_split_clause,[status(thm)],[f10,f15,f12])).
% 1.51/1.32 thf(f10,plain,(
% 1.51/1.32 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y4)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))))))))) | (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3)))))))))))))))) & ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1))))))) = $false)),
% 1.51/1.32 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.51/1.32 thf(f7,plain,(
% 1.51/1.32 ($false = (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3)))))))))))))))) & ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1))))))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y4)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))))))))))),
% 1.51/1.32 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.51/1.32 thf(f6,plain,(
% 1.51/1.32 ((~ (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3)))))))))))))))) & ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1))))))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y4)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2)))))))))))))) = $true)),
% 1.51/1.32 inference(cnf_transformation,[status(thm)],[f5])).
% 1.51/1.32 thf(f5,plain,(
% 1.51/1.32 ((~ (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y5 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y4 @ Y5))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4 @ Y3) => (Y1 @ Y3 @ Y4))))))) & (Y2 = Y1)) & (Y2 = Y0)) => (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y1 @ Y3 @ Y4) => (Y1 @ Y4 @ Y3)))))) & (Y1 = Y0)) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y1 @ Y4 @ Y5) & (Y1 @ Y5 @ Y3)) => (Y1 @ Y4 @ Y3)))))))))))))))) & ((^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y4)) => (Y0 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) & (Y0 = Y1))))) = (^[Y0 : a > a > $o]: ((^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3 @ Y2) => (Y0 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y4 @ Y2) & (Y0 @ Y3 @ Y4)) => (Y0 @ Y3 @ Y2))))))))) & (Y0 = Y1))))))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y0 @ Y3 @ Y4) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y4)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y3 @ Y2))))))) => (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (Y1 = Y0)) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2)))))))))))))) = $true)),
% 1.51/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.32 thf(f4,plain,(
% 1.51/1.32 ~(! [X0 : a > a > $o,X1 : a > a > $o] : ((! [X2 : a,X3 : a] : ((X1 @ X3 @ X2) => (X1 @ X2 @ X3)) & (X0 = X1) & ! [X4 : a,X5 : a,X6 : a] : (((X1 @ X6 @ X5) & (X1 @ X5 @ X4)) => (X1 @ X6 @ X4))) => (! [X7 : a,X8 : a] : ((X0 @ X8 @ X7) => (X0 @ X7 @ X8)) & (X0 = X1) & ! [X9 : a,X10 : a,X11 : a] : (((X0 @ X9 @ X10) & (X0 @ X11 @ X9)) => (X0 @ X11 @ X10)))) & ((^[X12 : a > a > $o, X13 : a > a > $o] : ((X12 = X13) & ! [X14 : a,X15 : a] : ((X12 @ X15 @ X14) => (X12 @ X14 @ X15)) & ! [X16 : a,X17 : a,X18 : a] : (((X12 @ X18 @ X16) & (X12 @ X17 @ X18)) => (X12 @ X17 @ X16)))) = (^[X19 : a > a > $o, X20 : a > a > $o] : ((X19 = X20) & ! [X21 : a,X22 : a,X23 : a] : (((X19 @ X22 @ X21) & (X19 @ X21 @ X23)) => (X19 @ X22 @ X23)) & ! [X24 : a,X25 : a] : ((X19 @ X24 @ X25) => (X19 @ X25 @ X24))))) & ! [X26 : a > a > $o,X27 : a > a > $o,X28 : a > a > $o] : (((X26 = X28) & (X26 = X27) & ! [X29 : a,X30 : a] : ((X27 @ X29 @ X30) => (X27 @ X30 @ X29)) & ! [X31 : a,X32 : a,X33 : a] : (((X26 @ X33 @ X31) & (X26 @ X32 @ X33)) => (X26 @ X32 @ X31)) & ! [X34 : a,X35 : a] : ((X26 @ X35 @ X34) => (X26 @ X34 @ X35)) & ! [X36 : a,X37 : a,X38 : a] : (((X27 @ X36 @ X38) & (X27 @ X38 @ X37)) => (X27 @ X36 @ X37))) => (! [X39 : a,X40 : a,X41 : a] : (((X27 @ X39 @ X41) & (X27 @ X40 @ X39)) => (X27 @ X40 @ X41)) & (X27 = X28) & ! [X42 : a,X43 : a] : ((X27 @ X43 @ X42) => (X27 @ X42 @ X43)))))),
% 1.51/1.32 inference(rectify,[status(thm)],[f2])).
% 1.51/1.32 thf(f2,negated_conjecture,(
% 1.51/1.32 ~(! [X1 : a > a > $o,X0 : a > a > $o] : ((! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2)) & (X0 = X1) & ! [X4 : a,X3 : a,X2 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4))) => (! [X3 : a,X2 : a] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & (X0 = X1) & ! [X3 : a,X4 : a,X2 : a] : (((X1 @ X3 @ X4) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X4)))) & ((^[X6 : a > a > $o, X7 : a > a > $o] : ((X6 = X7) & ! [X1 : a,X0 : a] : ((X6 @ X0 @ X1) => (X6 @ X1 @ X0)) & ! [X4 : a,X0 : a,X1 : a] : (((X6 @ X1 @ X4) & (X6 @ X0 @ X1)) => (X6 @ X0 @ X4)))) = (^[X6 : a > a > $o, X7 : a > a > $o] : ((X6 = X7) & ! [X1 : a,X0 : a,X4 : a] : (((X6 @ X0 @ X1) & (X6 @ X1 @ X4)) => (X6 @ X0 @ X4)) & ! [X0 : a,X1 : a] : ((X6 @ X0 @ X1) => (X6 @ X1 @ X0))))) & ! [X1 : a > a > $o,X0 : a > a > $o,X4 : a > a > $o] : (((X1 = X4) & (X0 = X1) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2)) & ! [X5 : a,X2 : a,X3 : a] : (((X1 @ X3 @ X5) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X5)) & ! [X3 : a,X2 : a] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X2 : a,X5 : a,X3 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X2 @ X5))) => (! [X3 : a,X2 : a,X5 : a] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)) & (X0 = X4) & ! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2)))))),
% 1.51/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.32 thf(f1,conjecture,(
% 1.51/1.32 ! [X1 : a > a > $o,X0 : a > a > $o] : ((! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2)) & (X0 = X1) & ! [X4 : a,X3 : a,X2 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X4)) => (X0 @ X2 @ X4))) => (! [X3 : a,X2 : a] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & (X0 = X1) & ! [X3 : a,X4 : a,X2 : a] : (((X1 @ X3 @ X4) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X4)))) & ((^[X6 : a > a > $o, X7 : a > a > $o] : ((X6 = X7) & ! [X1 : a,X0 : a] : ((X6 @ X0 @ X1) => (X6 @ X1 @ X0)) & ! [X4 : a,X0 : a,X1 : a] : (((X6 @ X1 @ X4) & (X6 @ X0 @ X1)) => (X6 @ X0 @ X4)))) = (^[X6 : a > a > $o, X7 : a > a > $o] : ((X6 = X7) & ! [X1 : a,X0 : a,X4 : a] : (((X6 @ X0 @ X1) & (X6 @ X1 @ X4)) => (X6 @ X0 @ X4)) & ! [X0 : a,X1 : a] : ((X6 @ X0 @ X1) => (X6 @ X1 @ X0))))) & ! [X1 : a > a > $o,X0 : a > a > $o,X4 : a > a > $o] : (((X1 = X4) & (X0 = X1) & ! [X2 : a,X3 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2)) & ! [X5 : a,X2 : a,X3 : a] : (((X1 @ X3 @ X5) & (X1 @ X2 @ X3)) => (X1 @ X2 @ X5)) & ! [X3 : a,X2 : a] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X2 : a,X5 : a,X3 : a] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X2 @ X5))) => (! [X3 : a,X2 : a,X5 : a] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)) & (X0 = X4) & ! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X0 @ X3 @ X2))))),
% 1.51/1.32 file('/export/starexec/sandbox/tmp/tmp.2qyIePZdi7/DTF2THF_19242.p',cTHM515_pme)).
% 1.51/1.32 % SZS output end Proof for DTF2THF_19242
% 1.51/1.32 % (19524)------------------------------
% 1.51/1.32 % (19524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.32 % (19524)Termination reason: Refutation
% 1.51/1.32
% 1.51/1.32 % (19524)Memory used [KB]: 6780
% 1.51/1.32 % (19524)Time elapsed: 0.131 s
% 1.51/1.32 % (19524)Instructions burned: 366 (million)
% 1.51/1.32 % (19524)------------------------------
% 1.51/1.32 % (19524)------------------------------
% 1.51/1.32 % (19512)Success in time 0.154 s
%------------------------------------------------------------------------------