%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV156^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n014.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 : Tue May 21 04:12:11 EDT 2024
% Result : Theorem 1.79s 0.55s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 66
% Syntax : Number of formulae : 405 ( 34 unt; 44 typ; 0 def)
% Number of atoms : 4067 ( 336 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 13677 ( 434 ~; 716 |; 760 &;8775 @)
% ( 21 <=>;1084 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 1076 (1076 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 63 usr; 58 con; 0-2 aty)
% (1887 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2229 (1959 ^ 269 !; 0 ?;2229 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a ).
thf(func_def_24,type,
sK5: a > a > $o ).
thf(func_def_25,type,
sK6: a > a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a > a > $o ).
thf(func_def_30,type,
sK11: ( a > a > $o ) > a ).
thf(func_def_31,type,
sK12: ( a > a > $o ) > a ).
thf(func_def_32,type,
sK13: a ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a > a > $o ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a ).
thf(func_def_50,type,
sK31: a ).
thf(func_def_51,type,
sK32: a ).
thf(func_def_52,type,
sK33: a ).
thf(func_def_53,type,
sK34: a ).
thf(func_def_54,type,
sK35: a ).
thf(func_def_55,type,
sK36: a ).
thf(func_def_56,type,
sK37: a ).
thf(func_def_57,type,
sK38: a ).
thf(func_def_58,type,
sK39: a ).
thf(func_def_59,type,
sK40: a ).
thf(func_def_60,type,
sK41: a ).
thf(func_def_61,type,
sK42: a ).
thf(f1764,plain,
$false,
inference(avatar_sat_refutation,[],[f29,f307,f320,f434,f444,f686,f720,f747,f760,f777,f919,f1020,f1101,f1134,f1195,f1243,f1284,f1327,f1650,f1668,f1686,f1761]) ).
thf(f1761,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f1760]) ).
thf(f1760,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f1759]) ).
thf(f1759,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1758]) ).
thf(f1758,plain,
( ( $true = ~ $true )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f1757,f1734]) ).
thf(f1734,plain,
( ( $true
= ( sK10 @ sK40 @ sK41 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1702]) ).
thf(f1702,plain,
( ( $true
= ( ( sK10 @ sK41 @ sK42 )
& ( sK10 @ sK40 @ sK41 ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1700]) ).
thf(f1700,plain,
( ( ( ( ( sK10 @ sK41 @ sK42 )
& ( sK10 @ sK40 @ sK41 ) )
=> ( sK10 @ sK40 @ sK42 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1699]) ).
thf(f1699,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ sK41 @ Y0 )
& ( sK10 @ sK40 @ sK41 ) )
=> ( sK10 @ sK40 @ Y0 ) )
@ sK42 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f1698]) ).
thf(f1698,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK41 @ Y0 )
& ( sK10 @ sK40 @ sK41 ) )
=> ( sK10 @ sK40 @ Y0 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1697]) ).
thf(f1697,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ Y1 )
& ( sK10 @ sK40 @ Y0 ) )
=> ( sK10 @ sK40 @ Y1 ) ) )
@ sK41 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f1694]) ).
thf(f1694,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ Y1 )
& ( sK10 @ sK40 @ Y0 ) )
=> ( sK10 @ sK40 @ Y1 ) ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1692]) ).
thf(f1692,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) )
@ sK40 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f316]) ).
thf(f316,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f315]) ).
thf(f315,plain,
( spl0_5
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f1757,plain,
( ( ( ~ ( sK10 @ sK40 @ sK41 ) )
= $true )
| ~ spl0_2
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1748]) ).
thf(f1748,plain,
( ( ( ~ ( ( sK10 @ sK40 @ sK41 )
& $true ) )
= $true )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f1713,f1737]) ).
thf(f1737,plain,
( ( $true
= ( sK10 @ sK41 @ sK42 ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1736]) ).
thf(f1736,plain,
( ( $true
= ( ( sK10 @ sK41 @ sK42 )
& $true ) )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1702,f1734]) ).
thf(f1713,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK10 @ sK40 @ X0 )
& ( sK10 @ X0 @ sK42 ) ) ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1708]) ).
thf(f1708,plain,
( ! [X0: a] :
( $true
= ( ( ( sK10 @ sK40 @ X0 )
& ( sK10 @ X0 @ sK42 ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f1474,f1704]) ).
thf(f1704,plain,
( ( ( sK10 @ sK40 @ sK42 )
= $false )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1703]) ).
thf(f1703,plain,
( ( ( $true
=> ( sK10 @ sK40 @ sK42 ) )
= $false )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1700,f1702]) ).
thf(f1474,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK10 @ X3 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X3 @ X2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1473]) ).
thf(f1473,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK10 @ Y0 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ Y0 @ X2 ) )
@ X3 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f1459]) ).
thf(f1459,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ Y0 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1458]) ).
thf(f1458,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ X1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f1437]) ).
thf(f1437,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ X1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1436]) ).
thf(f1436,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f1431]) ).
thf(f1431,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f1430]) ).
thf(f1430,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f1400,f1429]) ).
thf(f1429,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f1400]) ).
thf(f1400,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f1395]) ).
thf(f1395,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK10 @ sK8 @ sK9 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1394]) ).
thf(f1394,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f1370]) ).
thf(f1370,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f1364]) ).
thf(f1364,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1363]) ).
thf(f1363,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f1348]) ).
thf(f1348,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1347]) ).
thf(f1347,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f1334]) ).
thf(f1334,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1333]) ).
thf(f1333,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f28]) ).
thf(f28,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f27,plain,
( spl0_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f1686,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f1685]) ).
thf(f1685,plain,
( $false
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f1682]) ).
thf(f1682,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f1531,f1678]) ).
thf(f1678,plain,
( ( $false
= ( ( ( sK3 @ sK38 @ sK39 )
| ( sK5 @ sK38 @ sK39 ) )
=> ( sK10 @ sK38 @ sK39 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1677]) ).
thf(f1677,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK38 @ Y0 )
| ( sK5 @ sK38 @ Y0 ) )
=> ( sK10 @ sK38 @ Y0 ) )
@ sK39 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f1674]) ).
thf(f1674,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK38 @ Y0 )
| ( sK5 @ sK38 @ Y0 ) )
=> ( sK10 @ sK38 @ Y0 ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1672]) ).
thf(f1672,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) )
@ sK38 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f319]) ).
thf(f319,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f318]) ).
thf(f318,plain,
( spl0_6
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f1531,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK3 @ X2 @ X1 )
| ( sK5 @ X2 @ X1 ) )
=> ( sK10 @ X2 @ X1 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1530]) ).
thf(f1530,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK3 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
=> ( sK10 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f1517]) ).
thf(f1517,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
=> ( sK10 @ Y0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f1516]) ).
thf(f1516,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f1429]) ).
thf(f1668,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1667]) ).
thf(f1667,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f1666]) ).
thf(f1666,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1665]) ).
thf(f1665,plain,
( ( $true = ~ $true )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1664]) ).
thf(f1664,plain,
( ( ( ~ ( ( sK3 @ sK16 @ sK15 )
| $true ) )
= $true )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1658,f719]) ).
thf(f719,plain,
( ( $true
= ( sK5 @ sK16 @ sK15 ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f718]) ).
thf(f718,plain,
( spl0_12
<=> ( $true
= ( sK5 @ sK16 @ sK15 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f1658,plain,
( ( $true
= ( ~ ( ( sK3 @ sK16 @ sK15 )
| ( sK5 @ sK16 @ sK15 ) ) ) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1654]) ).
thf(f1654,plain,
( ( $true
= ( ( ( sK3 @ sK16 @ sK15 )
| ( sK5 @ sK16 @ sK15 ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f1531,f1653]) ).
thf(f1653,plain,
( ( $false
= ( sK10 @ sK16 @ sK15 ) )
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1652]) ).
thf(f1652,plain,
( ( $false
= ( $true
=> ( sK10 @ sK16 @ sK15 ) ) )
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1651]) ).
thf(f1651,plain,
( ( ( ( $true
| ( sK3 @ sK16 @ sK15 ) )
=> ( sK10 @ sK16 @ sK15 ) )
= $false )
| ~ spl0_8
| ~ spl0_12 ),
inference(backward_demodulation,[],[f1644,f719]) ).
thf(f1644,plain,
( ( $false
= ( ( ( sK5 @ sK16 @ sK15 )
| ( sK3 @ sK16 @ sK15 ) )
=> ( sK10 @ sK16 @ sK15 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1643]) ).
thf(f1643,plain,
( ( ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK15 )
| ( sK3 @ Y0 @ sK15 ) )
=> ( sK10 @ Y0 @ sK15 ) )
@ sK16 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f1637]) ).
thf(f1637,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK15 )
| ( sK3 @ Y0 @ sK15 ) )
=> ( sK10 @ Y0 @ sK15 ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1635]) ).
thf(f1635,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ sK15 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f433]) ).
thf(f433,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f432]) ).
thf(f432,plain,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f1650,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1649]) ).
thf(f1649,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f1648]) ).
thf(f1648,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_11 ),
inference(backward_demodulation,[],[f1554,f1647]) ).
thf(f1647,plain,
( ( $false
= ( sK10 @ sK16 @ sK15 ) )
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f1646]) ).
thf(f1646,plain,
( ( $false
= ( $true
=> ( sK10 @ sK16 @ sK15 ) ) )
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f1645]) ).
thf(f1645,plain,
( ( ( ( ( sK5 @ sK16 @ sK15 )
| $true )
=> ( sK10 @ sK16 @ sK15 ) )
= $false )
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1644,f716]) ).
thf(f716,plain,
( ( $true
= ( sK3 @ sK16 @ sK15 ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f715]) ).
thf(f715,plain,
( spl0_11
<=> ( $true
= ( sK3 @ sK16 @ sK15 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f1554,plain,
( ( $true
= ( sK10 @ sK16 @ sK15 ) )
| ~ spl0_2
| ~ spl0_11 ),
inference(boolean_simplification,[],[f1553]) ).
thf(f1553,plain,
( ( $true
= ( $true
=> ( sK10 @ sK16 @ sK15 ) ) )
| ~ spl0_2
| ~ spl0_11 ),
inference(boolean_simplification,[],[f1549]) ).
thf(f1549,plain,
( ( $true
= ( ( $true
| ( sK5 @ sK16 @ sK15 ) )
=> ( sK10 @ sK16 @ sK15 ) ) )
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f1531,f716]) ).
thf(f1327,plain,
( ~ spl0_10
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f1326]) ).
thf(f1326,plain,
( $false
| ~ spl0_10
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f1325]) ).
thf(f1325,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_24 ),
inference(boolean_simplification,[],[f1324]) ).
thf(f1324,plain,
( ( $true = ~ $true )
| ~ spl0_10
| ~ spl0_24 ),
inference(boolean_simplification,[],[f1323]) ).
thf(f1323,plain,
( ( $true
= ( ~ ( ( sK3 @ sK36 @ sK37 )
| $true ) ) )
| ~ spl0_10
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1319,f1308]) ).
thf(f1308,plain,
( ( $true
= ( sK5 @ sK36 @ sK37 ) )
| ~ spl0_24 ),
inference(binary_proxy_clausification,[],[f1292]) ).
thf(f1292,plain,
( ( ( ( sK5 @ sK36 @ sK37 )
=> ( sK26 @ sK36 @ sK37 ) )
= $false )
| ~ spl0_24 ),
inference(beta_eta_normalization,[],[f1291]) ).
thf(f1291,plain,
( ( ( ^ [Y0: a] :
( ( sK5 @ sK36 @ Y0 )
=> ( sK26 @ sK36 @ Y0 ) )
@ sK37 )
= $false )
| ~ spl0_24 ),
inference(sigma_clausification,[],[f1288]) ).
thf(f1288,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK36 @ Y0 )
=> ( sK26 @ sK36 @ Y0 ) ) )
= $false )
| ~ spl0_24 ),
inference(beta_eta_normalization,[],[f1287]) ).
thf(f1287,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) )
@ sK36 )
= $false )
| ~ spl0_24 ),
inference(sigma_clausification,[],[f1100]) ).
thf(f1100,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f1099]) ).
thf(f1099,plain,
( spl0_24
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f1319,plain,
( ( $true
= ( ~ ( ( sK3 @ sK36 @ sK37 )
| ( sK5 @ sK36 @ sK37 ) ) ) )
| ~ spl0_10
| ~ spl0_24 ),
inference(boolean_simplification,[],[f1316]) ).
thf(f1316,plain,
( ( $true
= ( ( ( sK3 @ sK36 @ sK37 )
| ( sK5 @ sK36 @ sK37 ) )
=> $false ) )
| ~ spl0_10
| ~ spl0_24 ),
inference(superposition,[],[f993,f1307]) ).
thf(f1307,plain,
( ( ( sK26 @ sK36 @ sK37 )
= $false )
| ~ spl0_24 ),
inference(binary_proxy_clausification,[],[f1292]) ).
thf(f993,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK3 @ X1 @ X2 )
| ( sK5 @ X1 @ X2 ) )
=> ( sK26 @ X1 @ X2 ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f992]) ).
thf(f992,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) )
=> ( sK26 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_10 ),
inference(pi_clausification,[],[f987]) ).
thf(f987,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) )
=> ( sK26 @ X1 @ Y0 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f986]) ).
thf(f986,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK26 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_10 ),
inference(pi_clausification,[],[f981]) ).
thf(f981,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_10 ),
inference(boolean_simplification,[],[f980]) ).
thf(f980,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK26 @ Y0 @ Y1 ) ) ) )
& $true ) )
| ~ spl0_10 ),
inference(backward_demodulation,[],[f973,f978]) ).
thf(f978,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y0 )
& ( sK26 @ Y0 @ Y2 ) )
=> ( sK26 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f973]) ).
thf(f973,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK26 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y0 )
& ( sK26 @ Y0 @ Y2 ) )
=> ( sK26 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f965]) ).
thf(f965,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK26 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y0 )
& ( sK26 @ Y0 @ Y2 ) )
=> ( sK26 @ Y1 @ Y2 ) ) ) ) ) )
=> ( sK26 @ sK25 @ sK24 ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f964]) ).
thf(f964,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) )
@ sK26 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f960]) ).
thf(f960,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) ) )
| ~ spl0_10 ),
inference(boolean_simplification,[],[f959]) ).
thf(f959,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(backward_demodulation,[],[f945,f958]) ).
thf(f958,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f945]) ).
thf(f945,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f944]) ).
thf(f944,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK24 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK24 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK24 ) ) ) )
@ sK25 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f926]) ).
thf(f926,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK24 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK24 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK24 ) ) ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f925]) ).
thf(f925,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK24 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f443]) ).
thf(f443,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f442]) ).
thf(f442,plain,
( spl0_10
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f1284,plain,
( ~ spl0_10
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f1283]) ).
thf(f1283,plain,
( $false
| ~ spl0_10
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f1279]) ).
thf(f1279,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_25 ),
inference(superposition,[],[f1061,f1276]) ).
thf(f1276,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK26 @ sK33 @ sK34 )
& ( sK26 @ sK34 @ Y0 ) )
=> ( sK26 @ sK33 @ Y0 ) ) ) )
| ~ spl0_25 ),
inference(beta_eta_normalization,[],[f1275]) ).
thf(f1275,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK26 @ sK33 @ Y0 )
& ( sK26 @ Y0 @ Y1 ) )
=> ( sK26 @ sK33 @ Y1 ) ) )
@ sK34 )
= $false )
| ~ spl0_25 ),
inference(sigma_clausification,[],[f1256]) ).
thf(f1256,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK26 @ sK33 @ Y0 )
& ( sK26 @ Y0 @ Y1 ) )
=> ( sK26 @ sK33 @ Y1 ) ) ) )
= $false )
| ~ spl0_25 ),
inference(beta_eta_normalization,[],[f1254]) ).
thf(f1254,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y0 @ Y1 )
& ( sK26 @ Y1 @ Y2 ) )
=> ( sK26 @ Y0 @ Y2 ) ) ) )
@ sK33 )
= $false )
| ~ spl0_25 ),
inference(sigma_clausification,[],[f1191]) ).
thf(f1191,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y0 @ Y1 )
& ( sK26 @ Y1 @ Y2 ) )
=> ( sK26 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1190]) ).
thf(f1190,plain,
( spl0_25
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y0 @ Y1 )
& ( sK26 @ Y1 @ Y2 ) )
=> ( sK26 @ Y0 @ Y2 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f1061,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK26 @ X2 @ X1 )
& ( sK26 @ X1 @ Y0 ) )
=> ( sK26 @ X2 @ Y0 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1060]) ).
thf(f1060,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK26 @ Y0 @ X1 )
& ( sK26 @ X1 @ Y1 ) )
=> ( sK26 @ Y0 @ Y1 ) ) )
@ X2 )
= $true )
| ~ spl0_10 ),
inference(pi_clausification,[],[f1049]) ).
thf(f1049,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK26 @ Y0 @ X1 )
& ( sK26 @ X1 @ Y1 ) )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1048]) ).
thf(f1048,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y0 )
& ( sK26 @ Y0 @ Y2 ) )
=> ( sK26 @ Y1 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_10 ),
inference(pi_clausification,[],[f978]) ).
thf(f1243,plain,
( ~ spl0_10
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1242]) ).
thf(f1242,plain,
( $false
| ~ spl0_10
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f1241]) ).
thf(f1241,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_26 ),
inference(boolean_simplification,[],[f1240]) ).
thf(f1240,plain,
( ( $true = ~ $true )
| ~ spl0_10
| ~ spl0_26 ),
inference(boolean_simplification,[],[f1239]) ).
thf(f1239,plain,
( ( ( ~ ( $true
| ( sK5 @ sK31 @ sK32 ) ) )
= $true )
| ~ spl0_10
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1235,f1226]) ).
thf(f1226,plain,
( ( ( sK3 @ sK31 @ sK32 )
= $true )
| ~ spl0_26 ),
inference(binary_proxy_clausification,[],[f1224]) ).
thf(f1224,plain,
( ( ( ( sK3 @ sK31 @ sK32 )
=> ( sK26 @ sK31 @ sK32 ) )
= $false )
| ~ spl0_26 ),
inference(beta_eta_normalization,[],[f1223]) ).
thf(f1223,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK31 @ Y0 )
=> ( sK26 @ sK31 @ Y0 ) )
@ sK32 ) )
| ~ spl0_26 ),
inference(sigma_clausification,[],[f1214]) ).
thf(f1214,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK31 @ Y0 )
=> ( sK26 @ sK31 @ Y0 ) ) ) )
| ~ spl0_26 ),
inference(beta_eta_normalization,[],[f1210]) ).
thf(f1210,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) )
@ sK31 )
= $false )
| ~ spl0_26 ),
inference(sigma_clausification,[],[f1194]) ).
thf(f1194,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1193]) ).
thf(f1193,plain,
( spl0_26
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f1235,plain,
( ( $true
= ( ~ ( ( sK3 @ sK31 @ sK32 )
| ( sK5 @ sK31 @ sK32 ) ) ) )
| ~ spl0_10
| ~ spl0_26 ),
inference(boolean_simplification,[],[f1232]) ).
thf(f1232,plain,
( ( $true
= ( ( ( sK3 @ sK31 @ sK32 )
| ( sK5 @ sK31 @ sK32 ) )
=> $false ) )
| ~ spl0_10
| ~ spl0_26 ),
inference(superposition,[],[f993,f1228]) ).
thf(f1228,plain,
( ( ( sK26 @ sK31 @ sK32 )
= $false )
| ~ spl0_26 ),
inference(boolean_simplification,[],[f1227]) ).
thf(f1227,plain,
( ( ( $true
=> ( sK26 @ sK31 @ sK32 ) )
= $false )
| ~ spl0_26 ),
inference(backward_demodulation,[],[f1224,f1226]) ).
thf(f1195,plain,
( spl0_25
| spl0_26
| ~ spl0_10
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1186,f1018,f442,f1193,f1190]) ).
thf(f1018,plain,
( spl0_22
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f1186,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y0 @ Y1 )
& ( sK26 @ Y1 @ Y2 ) )
=> ( sK26 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_10
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f1175]) ).
thf(f1175,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y0 @ Y1 )
& ( sK26 @ Y1 @ Y2 ) )
=> ( sK26 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_10
| ~ spl0_22 ),
inference(not_proxy_clausification,[],[f1159]) ).
thf(f1159,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y0 @ Y1 )
& ( sK26 @ Y1 @ Y2 ) )
=> ( sK26 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_10
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1156]) ).
thf(f1156,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y0 @ Y1 )
& ( sK26 @ Y1 @ Y2 ) )
=> ( sK26 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_10
| ~ spl0_22 ),
inference(superposition,[],[f1148,f972]) ).
thf(f972,plain,
( ( ( sK26 @ sK25 @ sK24 )
= $false )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f965]) ).
thf(f1148,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK25 @ sK24 ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f1147]) ).
thf(f1147,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) )
@ X1 )
= $true )
| ~ spl0_22 ),
inference(pi_clausification,[],[f1019]) ).
thf(f1019,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) )
= $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1018]) ).
thf(f1134,plain,
( ~ spl0_10
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1133]) ).
thf(f1133,plain,
( $false
| ~ spl0_10
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f1130]) ).
thf(f1130,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f1063,f1122]) ).
thf(f1122,plain,
( ( ( ( ( sK26 @ sK29 @ sK30 )
& ( sK26 @ sK30 @ sK28 ) )
=> ( sK26 @ sK29 @ sK28 ) )
= $false )
| ~ spl0_23 ),
inference(beta_eta_normalization,[],[f1121]) ).
thf(f1121,plain,
( ( ( ^ [Y0: a] :
( ( ( sK26 @ sK29 @ Y0 )
& ( sK26 @ Y0 @ sK28 ) )
=> ( sK26 @ sK29 @ sK28 ) )
@ sK30 )
= $false )
| ~ spl0_23 ),
inference(sigma_clausification,[],[f1116]) ).
thf(f1116,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK26 @ sK29 @ Y0 )
& ( sK26 @ Y0 @ sK28 ) )
=> ( sK26 @ sK29 @ sK28 ) ) )
= $false )
| ~ spl0_23 ),
inference(beta_eta_normalization,[],[f1115]) ).
thf(f1115,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK26 @ Y0 @ Y1 )
& ( sK26 @ Y1 @ sK28 ) )
=> ( sK26 @ Y0 @ sK28 ) ) )
@ sK29 )
= $false )
| ~ spl0_23 ),
inference(sigma_clausification,[],[f1110]) ).
thf(f1110,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK26 @ Y0 @ Y1 )
& ( sK26 @ Y1 @ sK28 ) )
=> ( sK26 @ Y0 @ sK28 ) ) ) )
= $false )
| ~ spl0_23 ),
inference(beta_eta_normalization,[],[f1106]) ).
thf(f1106,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y2 )
& ( sK26 @ Y2 @ Y0 ) )
=> ( sK26 @ Y1 @ Y0 ) ) ) )
@ sK28 )
= $false )
| ~ spl0_23 ),
inference(sigma_clausification,[],[f1097]) ).
thf(f1097,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y2 )
& ( sK26 @ Y2 @ Y0 ) )
=> ( sK26 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1096]) ).
thf(f1096,plain,
( spl0_23
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y2 )
& ( sK26 @ Y2 @ Y0 ) )
=> ( sK26 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f1063,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK26 @ X2 @ X1 )
& ( sK26 @ X1 @ X3 ) )
=> ( sK26 @ X2 @ X3 ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1062]) ).
thf(f1062,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK26 @ X2 @ X1 )
& ( sK26 @ X1 @ Y0 ) )
=> ( sK26 @ X2 @ Y0 ) )
@ X3 ) )
| ~ spl0_10 ),
inference(pi_clausification,[],[f1061]) ).
thf(f1101,plain,
( spl0_23
| spl0_24
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f1092,f1015,f442,f1099,f1096]) ).
thf(f1015,plain,
( spl0_21
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f1092,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y2 )
& ( sK26 @ Y2 @ Y0 ) )
=> ( sK26 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_10
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f1082]) ).
thf(f1082,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y2 )
& ( sK26 @ Y2 @ Y0 ) )
=> ( sK26 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_10
| ~ spl0_21 ),
inference(not_proxy_clausification,[],[f1036]) ).
thf(f1036,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y2 )
& ( sK26 @ Y2 @ Y0 ) )
=> ( sK26 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_10
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1035]) ).
thf(f1035,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK26 @ Y1 @ Y2 )
& ( sK26 @ Y2 @ Y0 ) )
=> ( sK26 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK26 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_10
| ~ spl0_21 ),
inference(superposition,[],[f1027,f972]) ).
thf(f1027,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK25 @ sK24 ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1026]) ).
thf(f1026,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) )
@ X1 ) )
| ~ spl0_21 ),
inference(pi_clausification,[],[f1016]) ).
thf(f1016,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1015]) ).
thf(f1020,plain,
( spl0_21
| spl0_22
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f1013,f442,f1018,f1015]) ).
thf(f1013,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK25 @ sK24 ) ) )
= $true )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f958]) ).
thf(f919,plain,
~ spl0_15,
inference(avatar_contradiction_clause,[],[f918]) ).
thf(f918,plain,
( $false
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f917]) ).
thf(f917,plain,
( ( $true = $false )
| ~ spl0_15 ),
inference(forward_demodulation,[],[f910,f793]) ).
thf(f793,plain,
( ( $false
= ( sK6 @ sK19 @ sK21 ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f792]) ).
thf(f792,plain,
( ( ( ( ( sK6 @ sK20 @ sK21 )
& ( sK6 @ sK19 @ sK20 ) )
=> ( sK6 @ sK19 @ sK21 ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f791]) ).
thf(f791,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK20 @ Y0 )
& ( sK6 @ sK19 @ sK20 ) )
=> ( sK6 @ sK19 @ Y0 ) )
@ sK21 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f790]) ).
thf(f790,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK20 @ Y0 )
& ( sK6 @ sK19 @ sK20 ) )
=> ( sK6 @ sK19 @ Y0 ) ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f789]) ).
thf(f789,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ sK19 @ Y0 ) )
=> ( sK6 @ sK19 @ Y1 ) ) )
@ sK20 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f788]) ).
thf(f788,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ sK19 @ Y0 ) )
=> ( sK6 @ sK19 @ Y1 ) ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f784]) ).
thf(f784,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) )
@ sK19 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f756]) ).
thf(f756,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f755]) ).
thf(f755,plain,
( spl0_15
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f910,plain,
( ( $true
= ( sK6 @ sK19 @ sK21 ) )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f908]) ).
thf(f908,plain,
( ( $true
= ( $true
=> ( sK6 @ sK19 @ sK21 ) ) )
| ~ spl0_15 ),
inference(superposition,[],[f838,f810]) ).
thf(f810,plain,
( ( $true
= ( sK6 @ sK20 @ sK21 ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f794]) ).
thf(f794,plain,
( ( $true
= ( ( sK6 @ sK20 @ sK21 )
& ( sK6 @ sK19 @ sK20 ) ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f792]) ).
thf(f838,plain,
( ! [X0: a] :
( $true
= ( ( sK6 @ sK20 @ X0 )
=> ( sK6 @ sK19 @ X0 ) ) )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f830]) ).
thf(f830,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK6 @ sK20 @ X0 ) )
=> ( sK6 @ sK19 @ X0 ) ) )
| ~ spl0_15 ),
inference(superposition,[],[f140,f812]) ).
thf(f812,plain,
( ( $true
= ( sK6 @ sK19 @ sK20 ) )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f811]) ).
thf(f811,plain,
( ( ( $true
& ( sK6 @ sK19 @ sK20 ) )
= $true )
| ~ spl0_15 ),
inference(backward_demodulation,[],[f794,f810]) ).
thf(f140,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK6 @ X3 @ X2 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ X3 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f139]) ).
thf(f139,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ X2 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[],[f138]) ).
thf(f138,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ X2 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f137]) ).
thf(f137,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f136]) ).
thf(f136,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f135]) ).
thf(f135,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f49]) ).
thf(f49,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f48]) ).
thf(f48,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f37,f47]) ).
thf(f47,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f37]) ).
thf(f37,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f33,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK6 @ sK2 @ sK4 ) )
= $false ),
inference(beta_eta_normalization,[],[f32]) ).
thf(f32,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f18]) ).
thf(f18,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ sK4 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK2 @ sK4 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ sK4 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK2 @ sK4 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
| ( sK3 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
| ( sK3 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ sK2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ sK2 @ Y1 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ sK2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ sK2 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a,X2: a > a > $o,X3: a] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X2 @ X9 @ X8 )
| ( X0 @ X9 @ X8 ) )
=> ( X4 @ X9 @ X8 ) ) )
=> ( X4 @ X3 @ X1 ) )
| ( ! [X10: a,X11: a,X12: a] :
( ( ! [X13: a > a > $o] :
( ( ! [X14: a,X15: a] :
( ( ( X0 @ X15 @ X14 )
| ( X2 @ X15 @ X14 ) )
=> ( X13 @ X15 @ X14 ) )
& ! [X16: a,X17: a,X18: a] :
( ( ( X13 @ X18 @ X17 )
& ( X13 @ X17 @ X16 ) )
=> ( X13 @ X18 @ X16 ) ) )
=> ( X13 @ X11 @ X12 ) )
& ! [X19: a > a > $o] :
( ( ! [X20: a,X21: a] :
( ( ( X2 @ X20 @ X21 )
| ( X0 @ X20 @ X21 ) )
=> ( X19 @ X20 @ X21 ) )
& ! [X22: a,X23: a,X24: a] :
( ( ( X19 @ X23 @ X22 )
& ( X19 @ X22 @ X24 ) )
=> ( X19 @ X23 @ X24 ) ) )
=> ( X19 @ X12 @ X10 ) ) )
=> ! [X25: a > a > $o] :
( ( ! [X26: a,X27: a,X28: a] :
( ( ( X25 @ X28 @ X27 )
& ( X25 @ X26 @ X28 ) )
=> ( X25 @ X26 @ X27 ) )
& ! [X29: a,X30: a] :
( ( ( X0 @ X29 @ X30 )
| ( X2 @ X29 @ X30 ) )
=> ( X25 @ X29 @ X30 ) ) )
=> ( X25 @ X11 @ X10 ) ) )
& ~ ! [X31: a > a > $o] :
( ( ! [X32: a,X33: a] :
( ( ( X2 @ X32 @ X33 )
| ( X0 @ X32 @ X33 ) )
=> ( X31 @ X32 @ X33 ) )
& ! [X34: a,X35: a,X36: a] :
( ( ( X31 @ X36 @ X35 )
& ( X31 @ X35 @ X34 ) )
=> ( X31 @ X36 @ X34 ) ) )
=> ( X31 @ X3 @ X1 ) )
& ! [X37: a,X38: a] :
( ( ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a] :
( ( X0 @ X41 @ X40 )
=> ( X39 @ X41 @ X40 ) )
& ! [X42: a,X43: a,X44: a] :
( ( ( X39 @ X42 @ X44 )
& ( X39 @ X43 @ X42 ) )
=> ( X39 @ X43 @ X44 ) ) )
=> ( X39 @ X37 @ X38 ) )
| ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a] :
( ( X2 @ X47 @ X46 )
=> ( X45 @ X47 @ X46 ) )
& ! [X48: a,X49: a,X50: a] :
( ( ( X45 @ X49 @ X48 )
& ( X45 @ X50 @ X49 ) )
=> ( X45 @ X50 @ X48 ) ) )
=> ( X45 @ X37 @ X38 ) ) )
=> ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a,X54: a] :
( ( ( X51 @ X54 @ X52 )
& ( X51 @ X53 @ X54 ) )
=> ( X51 @ X53 @ X52 ) )
& ! [X55: a,X56: a] :
( ( ( X0 @ X56 @ X55 )
| ( X2 @ X56 @ X55 ) )
=> ( X51 @ X56 @ X55 ) ) )
=> ( X51 @ X37 @ X38 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > $o,X3: a,X0: a > a > $o,X2: a] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
| ( ! [X7: a,X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X10: a,X9: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X8: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X10: a,X9: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X7 ) ) )
& ~ ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
& ! [X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X8: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X7: a,X9: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: a > a > $o,X3: a,X0: a > a > $o,X2: a] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
| ( ! [X7: a,X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X10: a,X9: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X8: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X10: a,X9: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X7 ) ) )
& ~ ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X6: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
& ! [X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X8: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X7: a,X9: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM250H_pme) ).
thf(f777,plain,
~ spl0_16,
inference(avatar_contradiction_clause,[],[f776]) ).
thf(f776,plain,
( $false
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f773]) ).
thf(f773,plain,
( ( $true = $false )
| ~ spl0_16 ),
inference(superposition,[],[f59,f769]) ).
thf(f769,plain,
( ( $false
= ( ( ( sK5 @ sK18 @ sK17 )
| ( sK3 @ sK18 @ sK17 ) )
=> ( sK6 @ sK18 @ sK17 ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f768]) ).
thf(f768,plain,
( ( ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK17 )
| ( sK3 @ Y0 @ sK17 ) )
=> ( sK6 @ Y0 @ sK17 ) )
@ sK18 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f767]) ).
thf(f767,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK17 )
| ( sK3 @ Y0 @ sK17 ) )
=> ( sK6 @ Y0 @ sK17 ) ) )
= $false )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f763]) ).
thf(f763,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK17 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f759]) ).
thf(f759,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f758]) ).
thf(f758,plain,
( spl0_16
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f59,plain,
! [X2: a,X1: a] :
( ( ( ( sK5 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[],[f58]) ).
thf(f58,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[],[f55]) ).
thf(f55,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f54]) ).
thf(f54,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f47]) ).
thf(f760,plain,
( spl0_15
| spl0_16
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f751,f744,f758,f755]) ).
thf(f744,plain,
( spl0_14
<=> ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f751,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f748]) ).
thf(f748,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_14 ),
inference(not_proxy_clausification,[],[f745]) ).
thf(f745,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f744]) ).
thf(f747,plain,
( spl0_14
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f736,f439,f744]) ).
thf(f439,plain,
( spl0_9
<=> ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f736,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f733]) ).
thf(f733,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_9 ),
inference(superposition,[],[f730,f36]) ).
thf(f36,plain,
( $false
= ( sK6 @ sK2 @ sK4 ) ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f730,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK2 @ sK4 ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f729]) ).
thf(f729,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) )
@ X1 ) )
| ~ spl0_9 ),
inference(pi_clausification,[],[f726]) ).
thf(f726,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) )
| ~ spl0_9 ),
inference(not_proxy_clausification,[],[f440]) ).
thf(f440,plain,
( ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f439]) ).
thf(f720,plain,
( spl0_11
| spl0_12
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f711,f432,f718,f715]) ).
thf(f711,plain,
( ( $true
= ( sK3 @ sK16 @ sK15 ) )
| ( $true
= ( sK5 @ sK16 @ sK15 ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f698]) ).
thf(f698,plain,
( ( $true
= ( ( sK5 @ sK16 @ sK15 )
| ( sK3 @ sK16 @ sK15 ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f696]) ).
thf(f696,plain,
( ( $false
= ( ( ( sK5 @ sK16 @ sK15 )
| ( sK3 @ sK16 @ sK15 ) )
=> ( sK10 @ sK16 @ sK15 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f695]) ).
thf(f695,plain,
( ( ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK15 )
| ( sK3 @ Y0 @ sK15 ) )
=> ( sK10 @ Y0 @ sK15 ) )
@ sK16 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f692]) ).
thf(f692,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK15 )
| ( sK3 @ Y0 @ sK15 ) )
=> ( sK10 @ Y0 @ sK15 ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f690]) ).
thf(f690,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ sK15 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f433]) ).
thf(f686,plain,
( ~ spl0_2
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f685]) ).
thf(f685,plain,
( $false
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f684]) ).
thf(f684,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f677,f466]) ).
thf(f466,plain,
( ( $false
= ( sK10 @ ( sK12 @ sK10 ) @ ( sK11 @ sK10 ) ) )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f465]) ).
thf(f465,plain,
( ( $false
= ( $true
=> ( sK10 @ ( sK12 @ sK10 ) @ ( sK11 @ sK10 ) ) ) )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f458,f464]) ).
thf(f464,plain,
( ( $true
= ( ( sK10 @ sK13 @ ( sK11 @ sK10 ) )
& ( sK10 @ ( sK12 @ sK10 ) @ sK13 ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f458]) ).
thf(f458,plain,
( ( $false
= ( ( ( sK10 @ sK13 @ ( sK11 @ sK10 ) )
& ( sK10 @ ( sK12 @ sK10 ) @ sK13 ) )
=> ( sK10 @ ( sK12 @ sK10 ) @ ( sK11 @ sK10 ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f457]) ).
thf(f457,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ Y0 @ ( sK11 @ sK10 ) )
& ( sK10 @ ( sK12 @ sK10 ) @ Y0 ) )
=> ( sK10 @ ( sK12 @ sK10 ) @ ( sK11 @ sK10 ) ) )
@ sK13 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f454]) ).
thf(f454,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 @ ( sK11 @ sK10 ) )
& ( sK10 @ ( sK12 @ sK10 ) @ Y0 ) )
=> ( sK10 @ ( sK12 @ sK10 ) @ ( sK11 @ sK10 ) ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f453]) ).
thf(f453,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ ( sK11 @ sK10 ) )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ ( sK11 @ sK10 ) ) ) )
@ ( sK12 @ sK10 ) )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f450]) ).
thf(f450,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ ( sK11 @ sK10 ) )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ ( sK11 @ sK10 ) ) ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f449]) ).
thf(f449,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
@ ( sK11 @ sK10 ) )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f430]) ).
thf(f430,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f429]) ).
thf(f429,plain,
( spl0_7
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f677,plain,
( ( $true
= ( sK10 @ ( sK12 @ sK10 ) @ ( sK11 @ sK10 ) ) )
| ~ spl0_2
| ~ spl0_7 ),
inference(boolean_simplification,[],[f676]) ).
thf(f676,plain,
( ( $true
= ( $true
=> ( sK10 @ ( sK12 @ sK10 ) @ ( sK11 @ sK10 ) ) ) )
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f527,f481]) ).
thf(f481,plain,
( ( $true
= ( sK10 @ ( sK12 @ sK10 ) @ sK13 ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f464]) ).
thf(f527,plain,
( ! [X0: a] :
( ( ( sK10 @ X0 @ sK13 )
=> ( sK10 @ X0 @ ( sK11 @ sK10 ) ) )
= $true )
| ~ spl0_2
| ~ spl0_7 ),
inference(boolean_simplification,[],[f498]) ).
thf(f498,plain,
( ! [X0: a] :
( $true
= ( ( ( sK10 @ X0 @ sK13 )
& $true )
=> ( sK10 @ X0 @ ( sK11 @ sK10 ) ) ) )
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f490,f484]) ).
thf(f484,plain,
( ( $true
= ( sK10 @ sK13 @ ( sK11 @ sK10 ) ) )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f483]) ).
thf(f483,plain,
( ( ( ( sK10 @ sK13 @ ( sK11 @ sK10 ) )
& $true )
= $true )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f464,f481]) ).
thf(f490,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK10 @ X3 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X3 @ X2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f489]) ).
thf(f489,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK10 @ Y0 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ Y0 @ X2 ) )
@ X3 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f488]) ).
thf(f488,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ Y0 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f487]) ).
thf(f487,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ X1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f486]) ).
thf(f486,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ X1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f485]) ).
thf(f485,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f480]) ).
thf(f480,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f479]) ).
thf(f479,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f472,f478]) ).
thf(f478,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f472]) ).
thf(f472,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f470]) ).
thf(f470,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK10 @ sK8 @ sK9 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f469]) ).
thf(f469,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f462]) ).
thf(f462,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f461]) ).
thf(f461,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f456,f460]) ).
thf(f460,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f456]) ).
thf(f456,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f455]) ).
thf(f455,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f452]) ).
thf(f452,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f451]) ).
thf(f451,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f448]) ).
thf(f448,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f447]) ).
thf(f447,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f28]) ).
thf(f444,plain,
( spl0_9
| spl0_10
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f437,f24,f442,f439]) ).
thf(f24,plain,
( spl0_1
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f437,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f434,plain,
( spl0_7
| spl0_8
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f423,f305,f27,f432,f429]) ).
thf(f305,plain,
( spl0_4
<=> ( ( sK10 @ sK7 @ sK9 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f423,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f413]) ).
thf(f413,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f336]) ).
thf(f336,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f330]) ).
thf(f330,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f108,f306]) ).
thf(f306,plain,
( ( ( sK10 @ sK7 @ sK9 )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f108,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK7 @ sK9 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f107]) ).
thf(f107,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f98]) ).
thf(f98,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f97]) ).
thf(f97,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f51,f95]) ).
thf(f95,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f51]) ).
thf(f51,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f45,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f43]) ).
thf(f43,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f42]) ).
thf(f42,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f35]) ).
thf(f35,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f34]) ).
thf(f34,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f28]) ).
thf(f320,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f311,f302,f318,f315]) ).
thf(f302,plain,
( spl0_3
<=> ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f311,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f308]) ).
thf(f308,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f303]) ).
thf(f303,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f307,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f289,f27,f305,f302]) ).
thf(f289,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( sK10 @ sK7 @ sK9 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f287]) ).
thf(f287,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ( ( sK10 @ sK7 @ sK9 )
= $false )
| ~ spl0_2 ),
inference(superposition,[],[f182,f193]) ).
thf(f193,plain,
( ! [X0: a] :
( ( ( sK10 @ sK8 @ X0 )
= $false )
| ( ( sK10 @ X0 @ sK9 )
= $false ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f183]) ).
thf(f183,plain,
( ! [X0: a] :
( $false
= ( ( sK10 @ sK8 @ X0 )
& ( sK10 @ X0 @ sK9 ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f180,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK10 @ sK8 @ X0 )
& ( sK10 @ X0 @ sK9 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f173]) ).
thf(f173,plain,
( ! [X0: a] :
( $true
= ( ( ( sK10 @ sK8 @ X0 )
& ( sK10 @ X0 @ sK9 ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f171,f63]) ).
thf(f63,plain,
( ( ( sK10 @ sK8 @ sK9 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f62]) ).
thf(f62,plain,
( ( $false
= ( $true
=> ( sK10 @ sK8 @ sK9 ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f57,f61]) ).
thf(f61,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f57]) ).
thf(f57,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK10 @ sK8 @ sK9 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f56]) ).
thf(f56,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f53]) ).
thf(f53,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f52]) ).
thf(f52,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f45,f51]) ).
thf(f171,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK10 @ X3 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X3 @ X2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f170]) ).
thf(f170,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK10 @ Y0 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ Y0 @ X2 ) )
@ X3 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f162]) ).
thf(f162,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 @ X1 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ Y0 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f161]) ).
thf(f161,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ X1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f151]) ).
thf(f151,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 @ X1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f150]) ).
thf(f150,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f64]) ).
thf(f64,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f61]) ).
thf(f182,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK8 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f181]) ).
thf(f181,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f95]) ).
thf(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f22,f27,f24]) ).
thf(f22,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| $false ) ),
inference(backward_demodulation,[],[f17,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV156^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.33 % Computer : n014.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sun May 19 19:10:37 EDT 2024
% 0.14/0.33 % CPUTime :
% 0.14/0.33 This is a TH0_THM_NEQ_NAR problem
% 0.14/0.33 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % (30744)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.34 % (30743)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.34 % (30746)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.34 % (30744)Instruction limit reached!
% 0.14/0.34 % (30744)------------------------------
% 0.14/0.34 % (30744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (30744)Termination reason: Unknown
% 0.14/0.34 % (30744)Termination phase: shuffling
% 0.14/0.34
% 0.14/0.34 % (30744)Memory used [KB]: 1023
% 0.14/0.34 % (30744)Time elapsed: 0.002 s
% 0.14/0.34 % (30744)Instructions burned: 2 (million)
% 0.14/0.34 % (30744)------------------------------
% 0.14/0.34 % (30744)------------------------------
% 0.14/0.35 % (30743)Instruction limit reached!
% 0.14/0.35 % (30743)------------------------------
% 0.14/0.35 % (30743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (30743)Termination reason: Unknown
% 0.14/0.35 % (30743)Termination phase: Preprocessing 3
% 0.14/0.35
% 0.14/0.35 % (30743)Memory used [KB]: 1023
% 0.14/0.35 % (30743)Time elapsed: 0.003 s
% 0.14/0.35 % (30743)Instructions burned: 4 (million)
% 0.14/0.35 % (30743)------------------------------
% 0.14/0.35 % (30743)------------------------------
% 0.14/0.35 % (30740)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.35 % (30741)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 theBenchmark for (2999ds/4Mi)
% 0.14/0.35 % (30742)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 theBenchmark for (2999ds/27Mi)
% 0.14/0.35 % (30745)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.35 % (30747)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.35 % (30746)Instruction limit reached!
% 0.14/0.35 % (30746)------------------------------
% 0.14/0.35 % (30746)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (30746)Termination reason: Unknown
% 0.14/0.35 % (30746)Termination phase: Saturation
% 0.14/0.35
% 0.14/0.35 % (30746)Memory used [KB]: 5756
% 0.14/0.35 % (30746)Time elapsed: 0.008 s
% 0.14/0.35 % (30746)Instructions burned: 20 (million)
% 0.14/0.35 % (30746)------------------------------
% 0.14/0.35 % (30746)------------------------------
% 0.14/0.35 % (30747)Instruction limit reached!
% 0.14/0.35 % (30747)------------------------------
% 0.14/0.35 % (30747)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (30747)Termination reason: Unknown
% 0.14/0.35 % (30747)Termination phase: Naming
% 0.14/0.35
% 0.14/0.35 % (30747)Memory used [KB]: 1023
% 0.14/0.35 % (30747)Time elapsed: 0.004 s
% 0.14/0.35 % (30747)Instructions burned: 3 (million)
% 0.14/0.35 % (30747)------------------------------
% 0.14/0.35 % (30747)------------------------------
% 0.14/0.35 % (30741)Instruction limit reached!
% 0.14/0.35 % (30741)------------------------------
% 0.14/0.35 % (30741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (30741)Termination reason: Unknown
% 0.14/0.35 % (30741)Termination phase: Preprocessing 3
% 0.14/0.35
% 0.14/0.35 % (30741)Memory used [KB]: 1023
% 0.14/0.35 % (30741)Time elapsed: 0.005 s
% 0.14/0.35 % (30741)Instructions burned: 5 (million)
% 0.14/0.35 % (30741)------------------------------
% 0.14/0.35 % (30741)------------------------------
% 0.14/0.35 % (30748)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 theBenchmark for (2999ds/37Mi)
% 0.19/0.35 % (30749)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 theBenchmark for (2999ds/15Mi)
% 0.19/0.36 % (30750)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.36 % (30749)Instruction limit reached!
% 0.19/0.36 % (30749)------------------------------
% 0.19/0.36 % (30749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.36 % (30749)Termination reason: Unknown
% 0.19/0.36 % (30749)Termination phase: Saturation
% 0.19/0.36
% 0.19/0.36 % (30749)Memory used [KB]: 5756
% 0.19/0.36 % (30749)Time elapsed: 0.007 s
% 0.19/0.36 % (30749)Instructions burned: 16 (million)
% 0.19/0.36 % (30749)------------------------------
% 0.19/0.36 % (30749)------------------------------
% 0.19/0.36 % (30750)Instruction limit reached!
% 0.19/0.36 % (30750)------------------------------
% 0.19/0.36 % (30750)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.36 % (30750)Termination reason: Unknown
% 0.19/0.36 % (30750)Termination phase: Property scanning
% 0.19/0.36
% 0.19/0.36 % (30750)Memory used [KB]: 1023
% 0.19/0.36 % (30750)Time elapsed: 0.002 s
% 0.19/0.36 % (30750)Instructions burned: 3 (million)
% 0.19/0.36 % (30750)------------------------------
% 0.19/0.36 % (30750)------------------------------
% 0.19/0.36 % (30748)Instruction limit reached!
% 0.19/0.36 % (30748)------------------------------
% 0.19/0.36 % (30748)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.36 % (30748)Termination reason: Unknown
% 0.19/0.36 % (30748)Termination phase: Saturation
% 0.19/0.36
% 0.19/0.36 % (30748)Memory used [KB]: 5500
% 0.19/0.36 % (30748)Time elapsed: 0.011 s
% 0.19/0.36 % (30748)Instructions burned: 37 (million)
% 0.19/0.36 % (30748)------------------------------
% 0.19/0.36 % (30748)------------------------------
% 0.19/0.37 % (30742)Instruction limit reached!
% 0.19/0.37 % (30742)------------------------------
% 0.19/0.37 % (30742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (30742)Termination reason: Unknown
% 0.19/0.37 % (30742)Termination phase: Saturation
% 0.19/0.37
% 0.19/0.37 % (30742)Memory used [KB]: 5756
% 0.19/0.37 % (30742)Time elapsed: 0.018 s
% 0.19/0.37 % (30742)Instructions burned: 28 (million)
% 0.19/0.37 % (30742)------------------------------
% 0.19/0.37 % (30742)------------------------------
% 0.19/0.37 % (30751)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 theBenchmark for (2999ds/1041Mi)
% 0.19/0.37 % (30752)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.37 % (30753)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.37 % (30754)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 theBenchmark for (2999ds/3Mi)
% 0.19/0.37 % (30754)Instruction limit reached!
% 0.19/0.37 % (30754)------------------------------
% 0.19/0.37 % (30754)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (30754)Termination reason: Unknown
% 0.19/0.37 % (30754)Termination phase: Property scanning
% 0.19/0.37
% 0.19/0.37 % (30754)Memory used [KB]: 1023
% 0.19/0.37 % (30754)Time elapsed: 0.002 s
% 0.19/0.37 % (30754)Instructions burned: 3 (million)
% 0.19/0.37 % (30754)------------------------------
% 0.19/0.37 % (30754)------------------------------
% 0.19/0.37 % (30752)Instruction limit reached!
% 0.19/0.37 % (30752)------------------------------
% 0.19/0.37 % (30752)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (30752)Termination reason: Unknown
% 0.19/0.37 % (30752)Termination phase: Preprocessing 3
% 0.19/0.37
% 0.19/0.37 % (30752)Memory used [KB]: 1151
% 0.19/0.37 % (30752)Time elapsed: 0.006 s
% 0.19/0.37 % (30752)Instructions burned: 7 (million)
% 0.19/0.37 % (30752)------------------------------
% 0.19/0.37 % (30752)------------------------------
% 0.19/0.37 % (30755)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 theBenchmark for (2999ds/3Mi)
% 0.19/0.37 % (30755)Instruction limit reached!
% 0.19/0.37 % (30755)------------------------------
% 0.19/0.37 % (30755)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (30755)Termination reason: Unknown
% 0.19/0.37 % (30755)Termination phase: shuffling
% 0.19/0.37
% 0.19/0.37 % (30755)Memory used [KB]: 1023
% 0.19/0.37 % (30755)Time elapsed: 0.002 s
% 0.19/0.37 % (30755)Instructions burned: 3 (million)
% 0.19/0.37 % (30755)------------------------------
% 0.19/0.37 % (30755)------------------------------
% 0.19/0.37 % (30753)Instruction limit reached!
% 0.19/0.37 % (30753)------------------------------
% 0.19/0.37 % (30753)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (30753)Termination reason: Unknown
% 0.19/0.37 % (30753)Termination phase: Property scanning
% 0.19/0.37
% 0.19/0.37 % (30753)Memory used [KB]: 1151
% 0.19/0.37 % (30753)Time elapsed: 0.006 s
% 0.19/0.37 % (30753)Instructions burned: 18 (million)
% 0.19/0.37 % (30753)------------------------------
% 0.19/0.37 % (30753)------------------------------
% 0.19/0.38 % (30757)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.38 % (30757)Instruction limit reached!
% 0.19/0.38 % (30757)------------------------------
% 0.19/0.38 % (30757)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (30757)Termination reason: Unknown
% 0.19/0.38 % (30757)Termination phase: shuffling
% 0.19/0.38
% 0.19/0.38 % (30757)Memory used [KB]: 1023
% 0.19/0.38 % (30757)Time elapsed: 0.002 s
% 0.19/0.38 % (30757)Instructions burned: 3 (million)
% 0.19/0.38 % (30757)------------------------------
% 0.19/0.38 % (30757)------------------------------
% 0.19/0.38 % (30756)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.38 % (30759)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.38 % (30760)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.19/0.39 % (30756)Instruction limit reached!
% 0.19/0.39 % (30756)------------------------------
% 0.19/0.39 % (30756)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.39 % (30756)Termination reason: Unknown
% 0.19/0.39 % (30756)Termination phase: Property scanning
% 0.19/0.39
% 0.19/0.39 % (30756)Memory used [KB]: 1151
% 0.19/0.39 % (30756)Time elapsed: 0.007 s
% 0.19/0.39 % (30756)Instructions burned: 8 (million)
% 0.19/0.39 % (30756)------------------------------
% 0.19/0.39 % (30756)------------------------------
% 0.19/0.39 % (30758)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.39 % (30761)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.39 % (30759)Instruction limit reached!
% 0.19/0.39 % (30759)------------------------------
% 0.19/0.39 % (30759)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.39 % (30759)Termination reason: Unknown
% 0.19/0.39 % (30759)Termination phase: Saturation
% 0.19/0.39
% 0.19/0.39 % (30759)Memory used [KB]: 5628
% 0.19/0.39 % (30759)Time elapsed: 0.008 s
% 0.19/0.39 % (30759)Instructions burned: 18 (million)
% 0.19/0.39 % (30759)------------------------------
% 0.19/0.39 % (30759)------------------------------
% 0.19/0.39 % (30758)Instruction limit reached!
% 0.19/0.39 % (30758)------------------------------
% 0.19/0.39 % (30758)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.39 % (30758)Termination reason: Unknown
% 0.19/0.39 % (30758)Termination phase: Preprocessing 3
% 0.19/0.39
% 0.19/0.39 % (30758)Memory used [KB]: 1023
% 0.19/0.39 % (30758)Time elapsed: 0.004 s
% 0.19/0.39 % (30758)Instructions burned: 4 (million)
% 0.19/0.39 % (30758)------------------------------
% 0.19/0.39 % (30758)------------------------------
% 0.19/0.39 % (30761)Instruction limit reached!
% 0.19/0.39 % (30761)------------------------------
% 0.19/0.39 % (30761)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.39 % (30761)Termination reason: Unknown
% 0.19/0.39 % (30761)Termination phase: Preprocessing 3
% 0.19/0.39
% 0.19/0.39 % (30761)Memory used [KB]: 1023
% 0.19/0.39 % (30761)Time elapsed: 0.003 s
% 0.19/0.39 % (30761)Instructions burned: 6 (million)
% 0.19/0.39 % (30761)------------------------------
% 0.19/0.39 % (30761)------------------------------
% 0.19/0.40 % (30766)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 theBenchmark for (2999ds/21Mi)
% 0.19/0.40 % (30768)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 theBenchmark for (2999ds/6Mi)
% 0.19/0.41 % (30768)Instruction limit reached!
% 0.19/0.41 % (30768)------------------------------
% 0.19/0.41 % (30768)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (30768)Termination reason: Unknown
% 0.19/0.41 % (30768)Termination phase: SInE selection
% 0.19/0.41
% 0.19/0.41 % (30768)Memory used [KB]: 1023
% 0.19/0.41 % (30768)Time elapsed: 0.004 s
% 0.19/0.41 % (30768)Instructions burned: 6 (million)
% 0.19/0.41 % (30768)------------------------------
% 0.19/0.41 % (30768)------------------------------
% 0.19/0.41 % (30765)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 theBenchmark for (2999ds/902Mi)
% 0.19/0.41 % (30766)Instruction limit reached!
% 0.19/0.41 % (30766)------------------------------
% 0.19/0.41 % (30766)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (30766)Termination reason: Unknown
% 0.19/0.41 % (30766)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (30766)Memory used [KB]: 5756
% 0.19/0.41 % (30766)Time elapsed: 0.012 s
% 0.19/0.41 % (30766)Instructions burned: 21 (million)
% 0.19/0.41 % (30766)------------------------------
% 0.19/0.41 % (30766)------------------------------
% 0.19/0.41 % (30767)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.19/0.42 % (30767)Instruction limit reached!
% 0.19/0.42 % (30767)------------------------------
% 0.19/0.42 % (30767)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (30767)Termination reason: Unknown
% 0.19/0.42 % (30767)Termination phase: Property scanning
% 0.19/0.42
% 0.19/0.42 % (30767)Memory used [KB]: 1023
% 0.19/0.42 % (30767)Time elapsed: 0.006 s
% 0.19/0.42 % (30767)Instructions burned: 5 (million)
% 0.19/0.42 % (30767)------------------------------
% 0.19/0.42 % (30767)------------------------------
% 0.19/0.42 % (30778)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.19/0.42 % (30780)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 theBenchmark for (2999ds/779Mi)
% 0.19/0.43 % (30781)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 theBenchmark for (2999ds/19Mi)
% 0.19/0.44 % (30781)Instruction limit reached!
% 0.19/0.44 % (30781)------------------------------
% 0.19/0.44 % (30781)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.44 % (30781)Termination reason: Unknown
% 0.19/0.44 % (30781)Termination phase: Saturation
% 0.19/0.44
% 0.19/0.44 % (30781)Memory used [KB]: 5500
% 0.19/0.44 % (30781)Time elapsed: 0.011 s
% 0.19/0.44 % (30781)Instructions burned: 20 (million)
% 0.19/0.44 % (30781)------------------------------
% 0.19/0.44 % (30781)------------------------------
% 0.19/0.45 % (30740)Instruction limit reached!
% 0.19/0.45 % (30740)------------------------------
% 0.19/0.45 % (30740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.45 % (30740)Termination reason: Unknown
% 0.19/0.45 % (30740)Termination phase: Saturation
% 0.19/0.45
% 0.19/0.45 % (30740)Memory used [KB]: 6140
% 0.19/0.45 % (30740)Time elapsed: 0.107 s
% 0.19/0.45 % (30740)Instructions burned: 185 (million)
% 0.19/0.45 % (30740)------------------------------
% 0.19/0.45 % (30740)------------------------------
% 0.19/0.46 % (30782)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.19/0.46 % (30783)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.19/0.47 % (30783)Instruction limit reached!
% 0.19/0.47 % (30783)------------------------------
% 0.19/0.47 % (30783)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.47 % (30783)Termination reason: Unknown
% 0.19/0.47 % (30783)Termination phase: Saturation
% 0.19/0.47
% 0.19/0.47 % (30783)Memory used [KB]: 5756
% 0.19/0.47 % (30783)Time elapsed: 0.008 s
% 0.19/0.47 % (30783)Instructions burned: 19 (million)
% 0.19/0.47 % (30783)------------------------------
% 0.19/0.47 % (30783)------------------------------
% 0.19/0.48 % (30784)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.19/0.48 % (30784)Instruction limit reached!
% 0.19/0.48 % (30784)------------------------------
% 0.19/0.48 % (30784)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.48 % (30784)Termination reason: Unknown
% 0.19/0.48 % (30784)Termination phase: Preprocessing 1
% 0.19/0.48
% 0.19/0.48 % (30784)Memory used [KB]: 1023
% 0.19/0.48 % (30784)Time elapsed: 0.002 s
% 0.19/0.48 % (30784)Instructions burned: 3 (million)
% 0.19/0.48 % (30784)------------------------------
% 0.19/0.48 % (30784)------------------------------
% 0.19/0.49 % (30785)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.19/0.49 % (30745)Instruction limit reached!
% 0.19/0.49 % (30745)------------------------------
% 0.19/0.49 % (30745)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.49 % (30745)Termination reason: Unknown
% 0.19/0.49 % (30745)Termination phase: Saturation
% 0.19/0.49
% 0.19/0.49 % (30745)Memory used [KB]: 6396
% 0.19/0.49 % (30745)Time elapsed: 0.143 s
% 0.19/0.49 % (30745)Instructions burned: 277 (million)
% 0.19/0.49 % (30745)------------------------------
% 0.19/0.49 % (30745)------------------------------
% 0.19/0.50 % (30785)Instruction limit reached!
% 0.19/0.50 % (30785)------------------------------
% 0.19/0.50 % (30785)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.50 % (30785)Termination reason: Unknown
% 0.19/0.50 % (30785)Termination phase: Saturation
% 0.19/0.50
% 0.19/0.50 % (30785)Memory used [KB]: 5756
% 0.19/0.50 % (30785)Time elapsed: 0.011 s
% 0.19/0.50 % (30785)Instructions burned: 30 (million)
% 0.19/0.50 % (30785)------------------------------
% 0.19/0.50 % (30785)------------------------------
% 0.19/0.50 % (30789)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.19/0.51 % (30793)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.19/0.53 % (30751)First to succeed.
% 0.19/0.54 % (30789)Instruction limit reached!
% 0.19/0.54 % (30789)------------------------------
% 0.19/0.54 % (30789)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.54 % (30789)Termination reason: Unknown
% 0.19/0.54 % (30789)Termination phase: Saturation
% 0.19/0.54
% 0.19/0.54 % (30789)Memory used [KB]: 6268
% 0.19/0.54 % (30789)Time elapsed: 0.042 s
% 0.19/0.54 % (30789)Instructions burned: 128 (million)
% 0.19/0.54 % (30789)------------------------------
% 0.19/0.54 % (30789)------------------------------
% 0.19/0.54 % (30793)Instruction limit reached!
% 0.19/0.54 % (30793)------------------------------
% 0.19/0.54 % (30793)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.54 % (30793)Termination reason: Unknown
% 0.19/0.54 % (30793)Termination phase: Saturation
% 0.19/0.54
% 0.19/0.54 % (30793)Memory used [KB]: 6012
% 0.19/0.54 % (30793)Time elapsed: 0.037 s
% 0.19/0.54 % (30793)Instructions burned: 102 (million)
% 0.19/0.54 % (30793)------------------------------
% 0.19/0.54 % (30793)------------------------------
% 1.79/0.55 % (30814)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2997ds/3Mi)
% 1.79/0.55 % (30814)Instruction limit reached!
% 1.79/0.55 % (30814)------------------------------
% 1.79/0.55 % (30814)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.79/0.55 % (30816)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2997ds/20Mi)
% 1.79/0.55 % (30814)Termination reason: Unknown
% 1.79/0.55 % (30814)Termination phase: Property scanning
% 1.79/0.55
% 1.79/0.55 % (30814)Memory used [KB]: 1023
% 1.79/0.55 % (30814)Time elapsed: 0.003 s
% 1.79/0.55 % (30814)Instructions burned: 6 (million)
% 1.79/0.55 % (30814)------------------------------
% 1.79/0.55 % (30814)------------------------------
% 1.79/0.55 % (30778)Instruction limit reached!
% 1.79/0.55 % (30778)------------------------------
% 1.79/0.55 % (30778)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.79/0.55 % (30778)Termination reason: Unknown
% 1.79/0.55 % (30778)Termination phase: Saturation
% 1.79/0.55
% 1.79/0.55 % (30778)Memory used [KB]: 6012
% 1.79/0.55 % (30778)Time elapsed: 0.134 s
% 1.79/0.55 % (30778)Instructions burned: 377 (million)
% 1.79/0.55 % (30778)------------------------------
% 1.79/0.55 % (30778)------------------------------
% 1.79/0.55 % (30751)Refutation found. Thanks to Tanya!
% 1.79/0.55 % SZS status Theorem for theBenchmark
% 1.79/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.79/0.56 % (30751)------------------------------
% 1.79/0.56 % (30751)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.79/0.56 % (30751)Termination reason: Refutation
% 1.79/0.56
% 1.79/0.56 % (30751)Memory used [KB]: 7036
% 1.79/0.56 % (30751)Time elapsed: 0.187 s
% 1.79/0.56 % (30751)Instructions burned: 367 (million)
% 1.79/0.56 % (30751)------------------------------
% 1.79/0.56 % (30751)------------------------------
% 1.79/0.56 % (30739)Success in time 0.217 s
% 1.79/0.56 % Vampire---4.8 exiting
%------------------------------------------------------------------------------