%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV153^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n027.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 : Mon Jun 24 16:02:01 EDT 2024
% Result : Theorem 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 13
% Syntax : Number of formulae : 249 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 2875 ( 231 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 8876 ( 333 ~; 741 |; 621 &;5241 @)
% ( 12 <=>; 886 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 475 ( 475 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 36 usr; 33 con; 0-2 aty)
% (1042 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1243 (1082 ^ 161 !; 0 ?;1243 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_21,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK2: a > a > $o ).
thf(func_def_23,type,
sK3: a > a > $o ).
thf(func_def_24,type,
sK4: a ).
thf(func_def_25,type,
sK5: a ).
thf(func_def_26,type,
sK6: a > $o ).
thf(func_def_27,type,
sK7: a ).
thf(func_def_28,type,
sK8: a ).
thf(func_def_29,type,
sK9: a ).
thf(func_def_30,type,
sK10: a > $o ).
thf(func_def_31,type,
sK11: a ).
thf(func_def_32,type,
sK12: a ).
thf(func_def_33,type,
sK13: a ).
thf(func_def_34,type,
sK14: a > $o ).
thf(func_def_35,type,
sK15: a ).
thf(func_def_36,type,
sK16: a ).
thf(func_def_37,type,
sK17: a ).
thf(func_def_38,type,
sK18: a ).
thf(func_def_39,type,
sK19: a ).
thf(func_def_40,type,
sK20: a ).
thf(func_def_41,type,
sK21: a ).
thf(func_def_42,type,
sK22: a ).
thf(func_def_43,type,
sK23: a ).
thf(func_def_44,type,
sK24: a ).
thf(f1074,plain,
$false,
inference(avatar_sat_refutation,[],[f59,f231,f275,f294,f304,f334,f456,f479,f546,f631,f957,f982,f1066]) ).
thf(f1066,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1065]) ).
thf(f1065,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f1064]) ).
thf(f1064,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1063,f1019]) ).
thf(f1019,plain,
( ( $false
= ( sK14 @ sK22 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f1018]) ).
thf(f1018,plain,
( ( ( ( ( sK3 @ sK23 @ sK22 )
& ( sK14 @ sK23 ) )
=> ( sK14 @ sK22 ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f1017]) ).
thf(f1017,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK22 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ sK22 ) )
@ sK23 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f989]) ).
thf(f989,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK22 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ sK22 ) ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f985]) ).
thf(f985,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) )
@ sK22 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f953]) ).
thf(f953,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f952]) ).
thf(f952,plain,
( spl0_14
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f1063,plain,
( ( ( sK14 @ sK22 )
= $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1062]) ).
thf(f1062,plain,
( ( ( $true
=> ( sK14 @ sK22 ) )
= $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1061,f1044]) ).
thf(f1044,plain,
( ( ( sK14 @ sK24 )
= $true )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1043]) ).
thf(f1043,plain,
( ( ( $true
& ( sK14 @ sK24 ) )
= $true )
| ~ spl0_14 ),
inference(backward_demodulation,[],[f1038,f1042]) ).
thf(f1042,plain,
( ( ( sK3 @ sK24 @ sK22 )
= $true )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f1038]) ).
thf(f1038,plain,
( ( ( ( sK3 @ sK24 @ sK22 )
& ( sK14 @ sK24 ) )
= $true )
| ~ spl0_14 ),
inference(not_proxy_clausification,[],[f1028]) ).
thf(f1028,plain,
( ( $false
= ( ~ ( ( sK3 @ sK24 @ sK22 )
& ( sK14 @ sK24 ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f1027]) ).
thf(f1027,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK3 @ Y0 @ sK22 )
& ( sK14 @ Y0 ) )
@ sK24 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f1024]) ).
thf(f1024,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK3 @ Y0 @ sK22 )
& ( sK14 @ Y0 ) ) )
= $false )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1022]) ).
thf(f1022,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK22 )
& ( sK14 @ Y0 ) )
=> $false ) ) )
| ~ spl0_14 ),
inference(backward_demodulation,[],[f989,f1019]) ).
thf(f1061,plain,
( ( ( ( sK14 @ sK24 )
=> ( sK14 @ sK22 ) )
= $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1060]) ).
thf(f1060,plain,
( ( $true
= ( ( ( sK14 @ sK24 )
& $true )
=> ( sK14 @ sK22 ) ) )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1054]) ).
thf(f1054,plain,
( ( ( ( ( sK14 @ sK24 )
& ( $true
| ( sK2 @ sK24 @ sK22 ) ) )
=> ( sK14 @ sK22 ) )
= $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_14 ),
inference(superposition,[],[f792,f1042]) ).
thf(f792,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK14 @ X2 )
& ( ( sK3 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) ) )
=> ( sK14 @ X1 ) )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f791]) ).
thf(f791,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK14 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) ) )
=> ( sK14 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(pi_clausification,[],[f765]) ).
thf(f765,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) ) )
=> ( sK14 @ X1 ) ) )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f764]) ).
thf(f764,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(pi_clausification,[],[f713]) ).
thf(f713,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f682]) ).
thf(f682,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f675]) ).
thf(f675,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
=> ( sK14 @ sK13 ) )
= $false )
| ~ spl0_6
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f674]) ).
thf(f674,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) )
@ sK14 ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(sigma_clausification,[],[f662]) ).
thf(f662,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $false )
| ~ spl0_6
| ~ spl0_7 ),
inference(boolean_simplification,[],[f661]) ).
thf(f661,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_7 ),
inference(boolean_simplification,[],[f660]) ).
thf(f660,plain,
( ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f659,f330]) ).
thf(f330,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f329]) ).
thf(f329,plain,
( spl0_7
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f659,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f658]) ).
thf(f658,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK12 @ Y2 )
| ( sK3 @ sK12 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK13 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f646]) ).
thf(f646,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK12 @ Y2 )
| ( sK3 @ sK12 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f645]) ).
thf(f645,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK12 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f303]) ).
thf(f303,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f302,plain,
( spl0_6
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f982,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f981]) ).
thf(f981,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f980]) ).
thf(f980,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_15 ),
inference(boolean_simplification,[],[f979]) ).
thf(f979,plain,
( ( ~ $true = $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_15 ),
inference(boolean_simplification,[],[f978]) ).
thf(f978,plain,
( ( ( ~ ( ( sK2 @ sK12 @ sK21 )
| $true ) )
= $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_15 ),
inference(forward_demodulation,[],[f977,f966]) ).
thf(f966,plain,
( ( ( sK3 @ sK12 @ sK21 )
= $true )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f962]) ).
thf(f962,plain,
( ( ( ( sK3 @ sK12 @ sK21 )
=> ( sK14 @ sK21 ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f960]) ).
thf(f960,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) )
@ sK21 )
= $false )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f956]) ).
thf(f956,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $false )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f955]) ).
thf(f955,plain,
( spl0_15
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f977,plain,
( ( ( ~ ( ( sK2 @ sK12 @ sK21 )
| ( sK3 @ sK12 @ sK21 ) ) )
= $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_15 ),
inference(boolean_simplification,[],[f972]) ).
thf(f972,plain,
( ( ( ( ( sK2 @ sK12 @ sK21 )
| ( sK3 @ sK12 @ sK21 ) )
=> $false )
= $true )
| ~ spl0_6
| ~ spl0_7
| ~ spl0_15 ),
inference(superposition,[],[f728,f968]) ).
thf(f968,plain,
( ( $false
= ( sK14 @ sK21 ) )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f967]) ).
thf(f967,plain,
( ( ( $true
=> ( sK14 @ sK21 ) )
= $false )
| ~ spl0_15 ),
inference(backward_demodulation,[],[f962,f966]) ).
thf(f728,plain,
( ! [X1: a] :
( ( ( ( sK2 @ sK12 @ X1 )
| ( sK3 @ sK12 @ X1 ) )
=> ( sK14 @ X1 ) )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f727]) ).
thf(f727,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(pi_clausification,[],[f715]) ).
thf(f715,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(boolean_simplification,[],[f714]) ).
thf(f714,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(backward_demodulation,[],[f682,f713]) ).
thf(f957,plain,
( spl0_14
| spl0_15
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f948,f329,f302,f955,f952]) ).
thf(f948,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f930]) ).
thf(f930,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(not_proxy_clausification,[],[f700]) ).
thf(f700,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(boolean_simplification,[],[f699]) ).
thf(f699,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f688,f681]) ).
thf(f681,plain,
( ( $false
= ( sK14 @ sK13 ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f675]) ).
thf(f688,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK13 ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f687]) ).
thf(f687,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f330]) ).
thf(f631,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f630]) ).
thf(f630,plain,
( $false
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f626]) ).
thf(f626,plain,
( ( $false = $true )
| ~ spl0_5 ),
inference(superposition,[],[f618,f39]) ).
thf(f39,plain,
! [X2: a,X1: a] :
( ( ( ( sK6 @ X2 )
& ( ( sK3 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) ) )
=> ( sK6 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f38]) ).
thf(f38,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f35]) ).
thf(f35,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f34]) ).
thf(f34,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f33]) ).
thf(f33,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f32]) ).
thf(f32,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[],[f25,f30]) ).
thf(f30,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK2 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK2 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK2 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK5 ) )
= $false ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f21]) ).
thf(f21,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $false ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
| $false )
= $false ),
inference(backward_demodulation,[],[f17,f18]) ).
thf(f18,plain,
( $false
= ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK4 @ Y2 )
| ( sK2 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK4 @ Y2 )
| ( sK2 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK2 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y1 @ Y5 )
| ( sK3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK2 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK2 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK4 @ Y2 )
| ( sK2 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK4 @ Y2 )
| ( sK2 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK2 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y1 @ Y5 )
| ( sK3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK2 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK2 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK3 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK2 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y2 @ Y6 )
| ( sK3 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK2 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y3 @ Y6 )
| ( sK3 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK2 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y3 @ Y6 )
| ( sK3 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK3 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK2 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y2 @ Y6 )
| ( sK3 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK2 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y3 @ Y6 )
| ( sK3 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK2 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y3 @ Y6 )
| ( sK3 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( Y0 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y0 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( sK2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y3 @ Y7 )
| ( Y0 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( sK2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( sK2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( Y0 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y0 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( sK2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y3 @ Y7 )
| ( Y0 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( sK2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( sK2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y4 @ Y8 )
| ( Y1 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y4 @ Y8 )
| ( Y1 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y4 @ Y8 )
| ( Y1 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( ~ ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y4 @ Y8 )
| ( Y1 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a > a > $o,X3: a > a > $o] :
( ( ! [X4: a,X5: a,X6: a] :
( ( ! [X7: a > $o] :
( ( ! [X8: a] :
( ( ( X2 @ X5 @ X8 )
| ( X3 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
& ! [X9: a,X10: a] :
( ( ( X7 @ X10 )
& ( ( X2 @ X10 @ X9 )
| ( X3 @ X10 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
& ! [X11: a > $o] :
( ( ! [X12: a] :
( ( ( X2 @ X6 @ X12 )
| ( X3 @ X6 @ X12 ) )
=> ( X11 @ X12 ) )
& ! [X13: a,X14: a] :
( ( ( X11 @ X14 )
& ( ( X2 @ X14 @ X13 )
| ( X3 @ X14 @ X13 ) ) )
=> ( X11 @ X13 ) ) )
=> ( X11 @ X4 ) ) )
=> ! [X15: a > $o] :
( ( ! [X16: a] :
( ( ( X2 @ X5 @ X16 )
| ( X3 @ X5 @ X16 ) )
=> ( X15 @ X16 ) )
& ! [X17: a,X18: a] :
( ( ( X15 @ X18 )
& ( ( X2 @ X18 @ X17 )
| ( X3 @ X18 @ X17 ) ) )
=> ( X15 @ X17 ) ) )
=> ( X15 @ X4 ) ) )
& ! [X19: a,X20: a] :
( ( ! [X21: a > $o] :
( ( ! [X22: a] :
( ( X3 @ X20 @ X22 )
=> ( X21 @ X22 ) )
& ! [X23: a,X24: a] :
( ( ( X21 @ X23 )
& ( X3 @ X23 @ X24 ) )
=> ( X21 @ X24 ) ) )
=> ( X21 @ X19 ) )
| ! [X25: a > $o] :
( ( ! [X26: a] :
( ( X2 @ X20 @ X26 )
=> ( X25 @ X26 ) )
& ! [X27: a,X28: a] :
( ( ( X25 @ X27 )
& ( X2 @ X27 @ X28 ) )
=> ( X25 @ X28 ) ) )
=> ( X25 @ X19 ) ) )
=> ! [X29: a > $o] :
( ( ! [X30: a] :
( ( ( X2 @ X20 @ X30 )
| ( X3 @ X20 @ X30 ) )
=> ( X29 @ X30 ) )
& ! [X31: a,X32: a] :
( ( ( ( X3 @ X31 @ X32 )
| ( X2 @ X31 @ X32 ) )
& ( X29 @ X31 ) )
=> ( X29 @ X32 ) ) )
=> ( X29 @ X19 ) ) )
& ~ ! [X33: a > $o] :
( ( ! [X34: a] :
( ( ( X3 @ X1 @ X34 )
| ( X2 @ X1 @ X34 ) )
=> ( X33 @ X34 ) )
& ! [X35: a,X36: a] :
( ( ( ( X3 @ X36 @ X35 )
| ( X2 @ X36 @ X35 ) )
& ( X33 @ X36 ) )
=> ( X33 @ X35 ) ) )
=> ( X33 @ X0 ) ) )
| ! [X37: a > $o] :
( ( ! [X38: a] :
( ( ( X3 @ X1 @ X38 )
| ( X2 @ X1 @ X38 ) )
=> ( X37 @ X38 ) )
& ! [X39: a,X40: a] :
( ( ( ( X3 @ X39 @ X40 )
| ( X2 @ X39 @ X40 ) )
& ( X37 @ X39 ) )
=> ( X37 @ X40 ) ) )
=> ( X37 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X2: a,X1: a > a > $o,X0: a > a > $o] :
( ( ! [X10: a,X8: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
& ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X9 @ X5 )
| ( X0 @ X9 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X1 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) ) )
& ~ ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X3: a,X2: a,X1: a > a > $o,X0: a > a > $o] :
( ( ! [X10: a,X8: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
& ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X9 @ X5 )
| ( X0 @ X9 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X1 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) ) )
& ~ ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM251H_pme) ).
thf(f618,plain,
( ( $false
= ( ( ( sK6 @ sK19 )
& ( ( sK3 @ sK19 @ sK20 )
| ( sK2 @ sK19 @ sK20 ) ) )
=> ( sK6 @ sK20 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f617]) ).
thf(f617,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK19 )
& ( ( sK3 @ sK19 @ Y0 )
| ( sK2 @ sK19 @ Y0 ) ) )
=> ( sK6 @ Y0 ) )
@ sK20 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f607]) ).
thf(f607,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK19 )
& ( ( sK3 @ sK19 @ Y0 )
| ( sK2 @ sK19 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f603]) ).
thf(f603,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) )
@ sK19 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f593]) ).
thf(f593,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(not_proxy_clausification,[],[f583]) ).
thf(f583,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f582]) ).
thf(f582,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
=> $false )
= $true )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f581,f24]) ).
thf(f24,plain,
( ( sK6 @ sK5 )
= $false ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f581,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
=> ( sK6 @ sK5 ) )
= $true )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f577]) ).
thf(f577,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
& $true )
=> ( sK6 @ sK5 ) )
= $true )
| ~ spl0_5 ),
inference(superposition,[],[f563,f30]) ).
thf(f563,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK2 @ sK4 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK5 ) )
= $true )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f562]) ).
thf(f562,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[],[f549]) ).
thf(f549,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $true )
| ~ spl0_5 ),
inference(not_proxy_clausification,[],[f300]) ).
thf(f300,plain,
( ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f299]) ).
thf(f299,plain,
( spl0_5
<=> ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f546,plain,
( ~ spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f545]) ).
thf(f545,plain,
( $false
| ~ spl0_6
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f544]) ).
thf(f544,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f543,f507]) ).
thf(f507,plain,
( ( ( sK14 @ sK16 )
= $false )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f506]) ).
thf(f506,plain,
( ( $false
= ( $true
=> ( sK14 @ sK16 ) ) )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f503,f505]) ).
thf(f505,plain,
( ( ( ( sK2 @ sK17 @ sK16 )
& ( sK14 @ sK17 ) )
= $true )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f503]) ).
thf(f503,plain,
( ( ( ( ( sK2 @ sK17 @ sK16 )
& ( sK14 @ sK17 ) )
=> ( sK14 @ sK16 ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f502]) ).
thf(f502,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK16 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ sK16 ) )
@ sK17 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f484]) ).
thf(f484,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK16 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ sK16 ) ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f482]) ).
thf(f482,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) )
@ sK16 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f452]) ).
thf(f452,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f451]) ).
thf(f451,plain,
( spl0_9
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f543,plain,
( ( ( sK14 @ sK16 )
= $true )
| ~ spl0_6
| ~ spl0_9 ),
inference(boolean_simplification,[],[f542]) ).
thf(f542,plain,
( ( $true
= ( $true
=> ( sK14 @ sK16 ) ) )
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f541,f522]) ).
thf(f522,plain,
( ( ( sK14 @ sK17 )
= $true )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f521]) ).
thf(f521,plain,
( ( ( $true
& ( sK14 @ sK17 ) )
= $true )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f505,f520]) ).
thf(f520,plain,
( ( ( sK2 @ sK17 @ sK16 )
= $true )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f505]) ).
thf(f541,plain,
( ( $true
= ( ( sK14 @ sK17 )
=> ( sK14 @ sK16 ) ) )
| ~ spl0_6
| ~ spl0_9 ),
inference(boolean_simplification,[],[f540]) ).
thf(f540,plain,
( ( $true
= ( ( ( sK14 @ sK17 )
& $true )
=> ( sK14 @ sK16 ) ) )
| ~ spl0_6
| ~ spl0_9 ),
inference(boolean_simplification,[],[f536]) ).
thf(f536,plain,
( ( ( ( ( sK14 @ sK17 )
& ( ( sK3 @ sK17 @ sK16 )
| $true ) )
=> ( sK14 @ sK16 ) )
= $true )
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f372,f520]) ).
thf(f372,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK14 @ X2 )
& ( ( sK3 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) ) )
=> ( sK14 @ X1 ) )
= $true )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f371]) ).
thf(f371,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK14 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) ) )
=> ( sK14 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_6 ),
inference(pi_clausification,[],[f364]) ).
thf(f364,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) ) )
=> ( sK14 @ X1 ) ) )
= $true )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f363]) ).
thf(f363,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_6 ),
inference(pi_clausification,[],[f326]) ).
thf(f326,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) ) )
= $true )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f325]) ).
thf(f325,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) ) )
& $true )
= $true )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f320,f323]) ).
thf(f323,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f320]) ).
thf(f320,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f318]) ).
thf(f318,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
=> ( sK14 @ sK13 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f317]) ).
thf(f317,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) )
@ sK14 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f311]) ).
thf(f311,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $false )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f310]) ).
thf(f310,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f309]) ).
thf(f309,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK12 @ Y2 )
| ( sK3 @ sK12 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK13 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f308]) ).
thf(f308,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK12 @ Y2 )
| ( sK3 @ sK12 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f307]) ).
thf(f307,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK12 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f303]) ).
thf(f479,plain,
( ~ spl0_6
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f478]) ).
thf(f478,plain,
( $false
| ~ spl0_6
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f477]) ).
thf(f477,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_10 ),
inference(boolean_simplification,[],[f476]) ).
thf(f476,plain,
( ( ~ $true = $true )
| ~ spl0_6
| ~ spl0_10 ),
inference(boolean_simplification,[],[f475]) ).
thf(f475,plain,
( ( ( ~ ( $true
| ( sK3 @ sK12 @ sK15 ) ) )
= $true )
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_demodulation,[],[f471,f465]) ).
thf(f465,plain,
( ( ( sK2 @ sK12 @ sK15 )
= $true )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f461]) ).
thf(f461,plain,
( ( $false
= ( ( sK2 @ sK12 @ sK15 )
=> ( sK14 @ sK15 ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f459]) ).
thf(f459,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) )
@ sK15 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f455]) ).
thf(f455,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f454]) ).
thf(f454,plain,
( spl0_10
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f471,plain,
( ( $true
= ( ~ ( ( sK2 @ sK12 @ sK15 )
| ( sK3 @ sK12 @ sK15 ) ) ) )
| ~ spl0_6
| ~ spl0_10 ),
inference(boolean_simplification,[],[f470]) ).
thf(f470,plain,
( ( ( ( ( sK2 @ sK12 @ sK15 )
| ( sK3 @ sK12 @ sK15 ) )
=> $false )
= $true )
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f338,f467]) ).
thf(f467,plain,
( ( ( sK14 @ sK15 )
= $false )
| ~ spl0_10 ),
inference(boolean_simplification,[],[f466]) ).
thf(f466,plain,
( ( ( $true
=> ( sK14 @ sK15 ) )
= $false )
| ~ spl0_10 ),
inference(backward_demodulation,[],[f461,f465]) ).
thf(f338,plain,
( ! [X1: a] :
( ( ( ( sK2 @ sK12 @ X1 )
| ( sK3 @ sK12 @ X1 ) )
=> ( sK14 @ X1 ) )
= $true )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f337]) ).
thf(f337,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_6 ),
inference(pi_clausification,[],[f323]) ).
thf(f456,plain,
( spl0_9
| spl0_10
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f447,f332,f302,f454,f451]) ).
thf(f332,plain,
( spl0_8
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f447,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f425]) ).
thf(f425,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f346]) ).
thf(f346,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) ) ) )
| ~ spl0_6
| ~ spl0_8 ),
inference(boolean_simplification,[],[f345]) ).
thf(f345,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f340,f322]) ).
thf(f322,plain,
( ( $false
= ( sK14 @ sK13 ) )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f321]) ).
thf(f321,plain,
( ( ( $true
=> ( sK14 @ sK13 ) )
= $false )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f318,f320]) ).
thf(f340,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK13 ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f339]) ).
thf(f339,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) )
@ X1 )
= $true )
| ~ spl0_8 ),
inference(pi_clausification,[],[f333]) ).
thf(f333,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f332]) ).
thf(f334,plain,
( spl0_7
| spl0_8
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f327,f302,f332,f329]) ).
thf(f327,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f312]) ).
thf(f312,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f310]) ).
thf(f304,plain,
( spl0_5
| spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f297,f54,f302,f299]) ).
thf(f54,plain,
( spl0_1
<=> ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f297,plain,
( ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f55]) ).
thf(f55,plain,
( ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f294,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f293]) ).
thf(f293,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f292]) ).
thf(f292,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f291,f211]) ).
thf(f211,plain,
( ( ( sK10 @ sK11 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f210]) ).
thf(f210,plain,
( ( ( $true
=> ( sK10 @ sK11 ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f205,f209]) ).
thf(f209,plain,
( ( ( ( sK2 @ sK7 @ sK11 )
| ( sK3 @ sK7 @ sK11 ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f205]) ).
thf(f205,plain,
( ( $false
= ( ( ( sK2 @ sK7 @ sK11 )
| ( sK3 @ sK7 @ sK11 ) )
=> ( sK10 @ sK11 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f203]) ).
thf(f203,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK3 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) )
@ sK11 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f200]) ).
thf(f200,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK3 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f171,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK3 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f170]) ).
thf(f170,plain,
( ( ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK3 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f169,f145]) ).
thf(f145,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f133]) ).
thf(f133,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f131]) ).
thf(f131,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> ( sK10 @ sK9 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f130]) ).
thf(f130,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f111]) ).
thf(f111,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f94]) ).
thf(f94,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK3 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f93]) ).
thf(f93,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK7 @ Y2 )
| ( sK3 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK8 @ Y2 )
| ( sK3 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK8 @ Y2 )
| ( sK3 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f83]) ).
thf(f83,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK7 @ Y2 )
| ( sK3 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK8 @ Y2 )
| ( sK3 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK8 @ Y2 )
| ( sK3 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f82]) ).
thf(f82,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK7 @ Y3 )
| ( sK3 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f72]) ).
thf(f72,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK7 @ Y3 )
| ( sK3 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f71]) ).
thf(f71,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f58]) ).
thf(f58,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f57,plain,
( spl0_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f169,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK3 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f168]) ).
thf(f168,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK3 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[],[f163,f132]) ).
thf(f132,plain,
( ( ( sK10 @ sK9 )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f131]) ).
thf(f163,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK3 @ sK7 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK9 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f162]) ).
thf(f162,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK3 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f139]) ).
thf(f139,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK3 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f112]) ).
thf(f112,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK3 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f94]) ).
thf(f291,plain,
( ( ( sK10 @ sK11 )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f290]) ).
thf(f290,plain,
( ( ( $true
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f287,f154]) ).
thf(f154,plain,
( ( ( sK10 @ sK7 )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f153]) ).
thf(f153,plain,
( ( ( $true
=> ( sK10 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f151,f145]) ).
thf(f151,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
=> ( sK10 @ sK7 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f150]) ).
thf(f150,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
& $true )
=> ( sK10 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[],[f143,f147]) ).
thf(f147,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f146]) ).
thf(f146,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f133,f145]) ).
thf(f143,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f142]) ).
thf(f142,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f141]) ).
thf(f141,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f140]) ).
thf(f140,plain,
( ( ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f112,f139]) ).
thf(f287,plain,
( ( ( ( sK10 @ sK7 )
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f286]) ).
thf(f286,plain,
( ( ( ( $true
& ( sK10 @ sK7 ) )
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f284]) ).
thf(f284,plain,
( ( ( ( ( $true
| ( sK3 @ sK7 @ sK11 ) )
& ( sK10 @ sK7 ) )
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f235,f230]) ).
thf(f230,plain,
( ( ( sK2 @ sK7 @ sK11 )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f229,plain,
( spl0_4
<=> ( ( sK2 @ sK7 @ sK11 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f235,plain,
( ! [X2: a,X1: a] :
( ( ( ( ( sK2 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) )
& ( sK10 @ X1 ) )
=> ( sK10 @ X2 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f234]) ).
thf(f234,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
& ( sK10 @ X1 ) )
=> ( sK10 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f219]) ).
thf(f219,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
& ( sK10 @ X1 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f214]) ).
thf(f214,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f145]) ).
thf(f275,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f274]) ).
thf(f274,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f273,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f272,f211]) ).
thf(f272,plain,
( ( ( sK10 @ sK11 )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f271]) ).
thf(f271,plain,
( ( ( $true
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f256,f154]) ).
thf(f256,plain,
( ( ( ( sK10 @ sK7 )
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f255]) ).
thf(f255,plain,
( ( ( ( $true
& ( sK10 @ sK7 ) )
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f248]) ).
thf(f248,plain,
( ( ( ( ( ( sK2 @ sK7 @ sK11 )
| $true )
& ( sK10 @ sK7 ) )
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f235,f227]) ).
thf(f227,plain,
( ( ( sK3 @ sK7 @ sK11 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f226,plain,
( spl0_3
<=> ( ( sK3 @ sK7 @ sK11 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f231,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f224,f57,f229,f226]) ).
thf(f224,plain,
( ( ( sK2 @ sK7 @ sK11 )
= $true )
| ( ( sK3 @ sK7 @ sK11 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f209]) ).
thf(f59,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f52,f57,f54]) ).
thf(f52,plain,
( ( ( ~ ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK2 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV153^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 21 19:10:54 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.34 This is a TH0_THM_NEQ_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.36 % (12429)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)
% 0.12/0.37 % (12427)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37 % (12428)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)
% 0.12/0.37 % (12431)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)
% 0.12/0.37 % (12430)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (12432)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)
% 0.12/0.37 % (12433)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.37 % (12430)Instruction limit reached!
% 0.12/0.37 % (12430)------------------------------
% 0.12/0.37 % (12430)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (12430)Termination reason: Unknown
% 0.12/0.37 % (12430)Termination phase: Preprocessing 1
% 0.12/0.37
% 0.12/0.37 % (12430)Memory used [KB]: 1023
% 0.12/0.37 % (12430)Time elapsed: 0.004 s
% 0.12/0.37 % (12430)Instructions burned: 2 (million)
% 0.12/0.37 % (12430)------------------------------
% 0.12/0.37 % (12430)------------------------------
% 0.12/0.37 % (12431)Instruction limit reached!
% 0.12/0.37 % (12431)------------------------------
% 0.12/0.37 % (12431)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (12431)Termination reason: Unknown
% 0.12/0.37 % (12431)Termination phase: shuffling
% 0.12/0.37
% 0.12/0.37 % (12431)Memory used [KB]: 1023
% 0.12/0.37 % (12431)Time elapsed: 0.004 s
% 0.12/0.37 % (12431)Instructions burned: 3 (million)
% 0.12/0.37 % (12431)------------------------------
% 0.12/0.37 % (12431)------------------------------
% 0.12/0.37 % (12428)Instruction limit reached!
% 0.12/0.37 % (12428)------------------------------
% 0.12/0.37 % (12428)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (12428)Termination reason: Unknown
% 0.12/0.37 % (12428)Termination phase: Preprocessing 3
% 0.12/0.37
% 0.12/0.37 % (12428)Memory used [KB]: 1023
% 0.12/0.37 % (12428)Time elapsed: 0.005 s
% 0.12/0.37 % (12428)Instructions burned: 4 (million)
% 0.12/0.37 % (12428)------------------------------
% 0.12/0.37 % (12428)------------------------------
% 0.12/0.37 % (12429)Instruction limit reached!
% 0.12/0.37 % (12429)------------------------------
% 0.12/0.37 % (12429)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (12429)Termination reason: Unknown
% 0.12/0.37 % (12429)Termination phase: Saturation
% 0.12/0.37
% 0.12/0.37 % (12429)Memory used [KB]: 5756
% 0.12/0.37 % (12429)Time elapsed: 0.012 s
% 0.12/0.37 % (12429)Instructions burned: 29 (million)
% 0.12/0.37 % (12429)------------------------------
% 0.12/0.37 % (12429)------------------------------
% 0.12/0.38 % (12433)Instruction limit reached!
% 0.12/0.38 % (12433)------------------------------
% 0.12/0.38 % (12433)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (12433)Termination reason: Unknown
% 0.12/0.38 % (12433)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (12433)Memory used [KB]: 5628
% 0.12/0.38 % (12433)Time elapsed: 0.013 s
% 0.12/0.38 % (12433)Instructions burned: 18 (million)
% 0.12/0.38 % (12433)------------------------------
% 0.12/0.38 % (12433)------------------------------
% 0.12/0.38 % (12437)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)
% 0.12/0.38 % (12437)Instruction limit reached!
% 0.12/0.38 % (12437)------------------------------
% 0.12/0.38 % (12437)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (12437)Termination reason: Unknown
% 0.12/0.38 % (12437)Termination phase: Preprocessing 3
% 0.12/0.38
% 0.12/0.38 % (12437)Memory used [KB]: 1023
% 0.12/0.38 % (12437)Time elapsed: 0.003 s
% 0.12/0.38 % (12437)Instructions burned: 3 (million)
% 0.12/0.38 % (12437)------------------------------
% 0.12/0.38 % (12437)------------------------------
% 0.12/0.38 % (12434)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)
% 0.12/0.38 % (12435)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)
% 0.12/0.38 % (12436)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)
% 0.12/0.39 % (12434)Instruction limit reached!
% 0.12/0.39 % (12434)------------------------------
% 0.12/0.39 % (12434)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (12434)Termination reason: Unknown
% 0.12/0.39 % (12434)Termination phase: Preprocessing 3
% 0.12/0.39
% 0.12/0.39 % (12434)Memory used [KB]: 1023
% 0.12/0.39 % (12434)Time elapsed: 0.004 s
% 0.12/0.39 % (12434)Instructions burned: 3 (million)
% 0.12/0.39 % (12434)------------------------------
% 0.12/0.39 % (12434)------------------------------
% 0.12/0.39 % (12439)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.12/0.39 % (12439)Instruction limit reached!
% 0.12/0.39 % (12439)------------------------------
% 0.12/0.39 % (12439)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (12439)Termination reason: Unknown
% 0.12/0.39 % (12439)Termination phase: Property scanning
% 0.12/0.39
% 0.12/0.39 % (12439)Memory used [KB]: 1151
% 0.12/0.39 % (12439)Time elapsed: 0.004 s
% 0.12/0.39 % (12439)Instructions burned: 7 (million)
% 0.12/0.39 % (12439)------------------------------
% 0.12/0.39 % (12439)------------------------------
% 0.12/0.39 % (12438)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)
% 0.21/0.39 % (12436)Instruction limit reached!
% 0.21/0.39 % (12436)------------------------------
% 0.21/0.39 % (12436)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (12436)Termination reason: Unknown
% 0.21/0.39 % (12436)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (12436)Memory used [KB]: 5756
% 0.21/0.39 % (12436)Time elapsed: 0.012 s
% 0.21/0.39 % (12436)Instructions burned: 15 (million)
% 0.21/0.39 % (12436)------------------------------
% 0.21/0.39 % (12436)------------------------------
% 0.21/0.40 % (12440)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.40 % (12441)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)
% 0.21/0.40 % (12441)Instruction limit reached!
% 0.21/0.40 % (12441)------------------------------
% 0.21/0.40 % (12441)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (12441)Termination reason: Unknown
% 0.21/0.40 % (12441)Termination phase: Preprocessing 3
% 0.21/0.40
% 0.21/0.40 % (12441)Memory used [KB]: 1023
% 0.21/0.40 % (12441)Time elapsed: 0.003 s
% 0.21/0.40 % (12441)Instructions burned: 3 (million)
% 0.21/0.40 % (12441)------------------------------
% 0.21/0.40 % (12441)------------------------------
% 0.21/0.40 % (12435)Instruction limit reached!
% 0.21/0.40 % (12435)------------------------------
% 0.21/0.40 % (12435)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (12435)Termination reason: Unknown
% 0.21/0.40 % (12435)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (12435)Memory used [KB]: 5628
% 0.21/0.40 % (12435)Time elapsed: 0.022 s
% 0.21/0.40 % (12435)Instructions burned: 37 (million)
% 0.21/0.40 % (12435)------------------------------
% 0.21/0.40 % (12435)------------------------------
% 0.21/0.41 % (12442)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)
% 0.21/0.41 % (12440)Instruction limit reached!
% 0.21/0.41 % (12440)------------------------------
% 0.21/0.41 % (12440)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (12440)Termination reason: Unknown
% 0.21/0.41 % (12440)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (12440)Memory used [KB]: 5628
% 0.21/0.41 % (12440)Time elapsed: 0.011 s
% 0.21/0.41 % (12440)Instructions burned: 17 (million)
% 0.21/0.41 % (12440)------------------------------
% 0.21/0.41 % (12440)------------------------------
% 0.21/0.41 % (12442)Instruction limit reached!
% 0.21/0.41 % (12442)------------------------------
% 0.21/0.41 % (12442)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (12442)Termination reason: Unknown
% 0.21/0.41 % (12442)Termination phase: Naming
% 0.21/0.41
% 0.21/0.41 % (12442)Memory used [KB]: 1023
% 0.21/0.41 % (12442)Time elapsed: 0.004 s
% 0.21/0.41 % (12442)Instructions burned: 3 (million)
% 0.21/0.41 % (12442)------------------------------
% 0.21/0.41 % (12442)------------------------------
% 0.21/0.41 % (12443)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)
% 0.21/0.41 % (12443)Instruction limit reached!
% 0.21/0.41 % (12443)------------------------------
% 0.21/0.41 % (12443)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (12443)Termination reason: Unknown
% 0.21/0.41 % (12443)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (12443)Memory used [KB]: 1151
% 0.21/0.41 % (12443)Time elapsed: 0.004 s
% 0.21/0.41 % (12443)Instructions burned: 7 (million)
% 0.21/0.41 % (12443)------------------------------
% 0.21/0.41 % (12443)------------------------------
% 0.21/0.42 % (12444)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)
% 0.21/0.42 % (12444)Instruction limit reached!
% 0.21/0.42 % (12444)------------------------------
% 0.21/0.42 % (12444)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (12444)Termination reason: Unknown
% 0.21/0.42 % (12444)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (12444)Memory used [KB]: 1023
% 0.21/0.42 % (12444)Time elapsed: 0.004 s
% 0.21/0.42 % (12444)Instructions burned: 4 (million)
% 0.21/0.42 % (12444)------------------------------
% 0.21/0.42 % (12444)------------------------------
% 0.21/0.42 % (12447)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.43 % (12445)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.43 % (12446)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)
% 0.21/0.43 % (12445)Instruction limit reached!
% 0.21/0.43 % (12445)------------------------------
% 0.21/0.43 % (12445)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (12445)Termination reason: Unknown
% 0.21/0.43 % (12445)Termination phase: Preprocessing 3
% 0.21/0.43
% 0.21/0.43 % (12445)Memory used [KB]: 1023
% 0.21/0.43 % (12445)Time elapsed: 0.005 s
% 0.21/0.43 % (12445)Instructions burned: 5 (million)
% 0.21/0.43 % (12445)------------------------------
% 0.21/0.43 % (12445)------------------------------
% 0.21/0.44 % (12448)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.44 % (12446)Instruction limit reached!
% 0.21/0.44 % (12446)------------------------------
% 0.21/0.44 % (12446)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.44 % (12446)Termination reason: Unknown
% 0.21/0.44 % (12446)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (12446)Memory used [KB]: 5756
% 0.21/0.44 % (12446)Time elapsed: 0.013 s
% 0.21/0.44 % (12446)Instructions burned: 18 (million)
% 0.21/0.44 % (12446)------------------------------
% 0.21/0.44 % (12446)------------------------------
% 0.21/0.44 % (12448)Instruction limit reached!
% 0.21/0.44 % (12448)------------------------------
% 0.21/0.44 % (12448)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.44 % (12448)Termination reason: Unknown
% 0.21/0.44 % (12448)Termination phase: Property scanning
% 0.21/0.44
% 0.21/0.44 % (12448)Memory used [KB]: 1151
% 0.21/0.44 % (12448)Time elapsed: 0.005 s
% 0.21/0.44 % (12448)Instructions burned: 7 (million)
% 0.21/0.44 % (12448)------------------------------
% 0.21/0.44 % (12448)------------------------------
% 0.21/0.44 % (12449)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)
% 0.21/0.45 % (12451)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.45 % (12451)Instruction limit reached!
% 0.21/0.45 % (12451)------------------------------
% 0.21/0.45 % (12451)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.45 % (12451)Termination reason: Unknown
% 0.21/0.45 % (12451)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (12451)Memory used [KB]: 1023
% 0.21/0.45 % (12451)Time elapsed: 0.003 s
% 0.21/0.45 % (12451)Instructions burned: 6 (million)
% 0.21/0.45 % (12451)------------------------------
% 0.21/0.45 % (12451)------------------------------
% 0.21/0.45 % (12450)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)
% 0.21/0.46 % (12452)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)
% 0.21/0.46 % (12452)Instruction limit reached!
% 0.21/0.46 % (12452)------------------------------
% 0.21/0.46 % (12452)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.46 % (12452)Termination reason: Unknown
% 0.21/0.46 % (12452)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (12452)Memory used [KB]: 5500
% 0.21/0.46 % (12452)Time elapsed: 0.004 s
% 0.21/0.46 % (12452)Instructions burned: 8 (million)
% 0.21/0.46 % (12452)------------------------------
% 0.21/0.46 % (12452)------------------------------
% 0.21/0.47 % (12450)Instruction limit reached!
% 0.21/0.47 % (12450)------------------------------
% 0.21/0.47 % (12450)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.47 % (12450)Termination reason: Unknown
% 0.21/0.47 % (12450)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (12450)Memory used [KB]: 5756
% 0.21/0.47 % (12450)Time elapsed: 0.013 s
% 0.21/0.47 % (12450)Instructions burned: 21 (million)
% 0.21/0.47 % (12450)------------------------------
% 0.21/0.47 % (12450)------------------------------
% 0.21/0.47 % (12453)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.21/0.47 % (12427)Instruction limit reached!
% 0.21/0.47 % (12427)------------------------------
% 0.21/0.47 % (12427)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.47 % (12427)Termination reason: Unknown
% 0.21/0.47 % (12427)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (12427)Memory used [KB]: 6652
% 0.21/0.47 % (12427)Time elapsed: 0.109 s
% 0.21/0.47 % (12427)Instructions burned: 185 (million)
% 0.21/0.47 % (12427)------------------------------
% 0.21/0.47 % (12427)------------------------------
% 0.21/0.48 % (12454)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 (2998ds/779Mi)
% 0.21/0.48 % (12455)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 (2998ds/19Mi)
% 0.21/0.49 % (12438)First to succeed.
% 0.21/0.49 % (12455)Instruction limit reached!
% 0.21/0.49 % (12455)------------------------------
% 0.21/0.49 % (12455)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.49 % (12455)Termination reason: Unknown
% 0.21/0.49 % (12455)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (12455)Memory used [KB]: 5628
% 0.21/0.49 % (12455)Time elapsed: 0.008 s
% 0.21/0.49 % (12455)Instructions burned: 21 (million)
% 0.21/0.49 % (12455)------------------------------
% 0.21/0.49 % (12455)------------------------------
% 0.21/0.50 % (12456)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)
% 0.21/0.50 % (12432)Instruction limit reached!
% 0.21/0.50 % (12432)------------------------------
% 0.21/0.50 % (12432)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.50 % (12438)Refutation found. Thanks to Tanya!
% 0.21/0.50 % SZS status Theorem for theBenchmark
% 0.21/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50 % (12438)------------------------------
% 0.21/0.50 % (12438)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.50 % (12438)Termination reason: Refutation
% 0.21/0.50
% 0.21/0.50 % (12438)Memory used [KB]: 6524
% 0.21/0.50 % (12438)Time elapsed: 0.108 s
% 0.21/0.50 % (12438)Instructions burned: 179 (million)
% 0.21/0.50 % (12438)------------------------------
% 0.21/0.50 % (12438)------------------------------
% 0.21/0.50 % (12426)Success in time 0.138 s
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