%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV155^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n024.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 16:02:02 EDT 2024
% Result : Theorem 1.70s 0.62s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 17
% Syntax : Number of formulae : 372 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 4314 ( 350 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 14689 ( 524 ~; 811 |; 804 &;9315 @)
% ( 16 <=>;1191 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 1166 (1166 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 54 usr; 51 con; 0-2 aty)
% (2028 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2357 (2099 ^ 258 !; 0 ?;2357 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: a ).
thf(func_def_21,type,
sK3: a ).
thf(func_def_22,type,
sK4: a > a > $o ).
thf(func_def_23,type,
sK5: a > a > $o ).
thf(func_def_24,type,
sK6: a > a > $o ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a ).
thf(func_def_27,type,
sK9: a ).
thf(func_def_28,type,
sK10: a ).
thf(func_def_29,type,
sK11: a > a > $o ).
thf(func_def_30,type,
sK12: a ).
thf(func_def_31,type,
sK13: a ).
thf(func_def_32,type,
sK14: a > a > $o ).
thf(func_def_33,type,
sK15: a ).
thf(func_def_34,type,
sK16: a ).
thf(func_def_35,type,
sK17: a ).
thf(func_def_36,type,
sK18: a ).
thf(func_def_37,type,
sK19: a ).
thf(func_def_38,type,
sK20: a ).
thf(func_def_39,type,
sK21: a ).
thf(func_def_40,type,
sK22: a ).
thf(func_def_41,type,
sK23: a ).
thf(func_def_42,type,
sK24: a ).
thf(func_def_43,type,
sK25: a ).
thf(func_def_44,type,
sK26: a ).
thf(func_def_45,type,
sK27: a ).
thf(func_def_46,type,
sK28: a ).
thf(func_def_47,type,
sK29: a ).
thf(func_def_48,type,
sK30: a ).
thf(func_def_49,type,
sK31: a ).
thf(func_def_50,type,
sK32: a ).
thf(func_def_51,type,
sK33: a ).
thf(func_def_52,type,
sK34: a ).
thf(func_def_53,type,
sK35: a ).
thf(func_def_54,type,
sK36: a ).
thf(func_def_55,type,
sK37: a ).
thf(func_def_56,type,
sK38: a ).
thf(f2446,plain,
$false,
inference(avatar_sat_refutation,[],[f51,f67,f242,f302,f375,f410,f522,f825,f1053,f1106,f1246,f1283,f1301,f1651,f1800,f2041,f2445]) ).
thf(f2445,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f2444]) ).
thf(f2444,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f2443]) ).
thf(f2443,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f2428,f2314]) ).
thf(f2314,plain,
( ( ( sK14 @ sK37 @ sK38 )
= $false )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f2310]) ).
thf(f2310,plain,
( ( $false
= ( ( ( sK14 @ sK36 @ sK38 )
& ( sK14 @ sK37 @ sK36 ) )
=> ( sK14 @ sK37 @ sK38 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f2309]) ).
thf(f2309,plain,
( ( ( ^ [Y0: a] :
( ( ( sK14 @ sK36 @ Y0 )
& ( sK14 @ sK37 @ sK36 ) )
=> ( sK14 @ sK37 @ Y0 ) )
@ sK38 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f2305]) ).
thf(f2305,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ sK36 @ Y0 )
& ( sK14 @ sK37 @ sK36 ) )
=> ( sK14 @ sK37 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f2304]) ).
thf(f2304,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ sK36 @ Y1 )
& ( sK14 @ Y0 @ sK36 ) )
=> ( sK14 @ Y0 @ Y1 ) ) )
@ sK37 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f2295]) ).
thf(f2295,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ sK36 @ Y1 )
& ( sK14 @ Y0 @ sK36 ) )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f2291]) ).
thf(f2291,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y2 ) ) ) )
@ sK36 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f409]) ).
thf(f409,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f408]) ).
thf(f408,plain,
( spl0_12
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f2428,plain,
( ( $true
= ( sK14 @ sK37 @ sK38 ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f2425]) ).
thf(f2425,plain,
( ( $true
= ( $true
=> ( sK14 @ sK37 @ sK38 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f2370,f2360]) ).
thf(f2360,plain,
( ( $true
= ( sK14 @ sK37 @ sK36 ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f2315]) ).
thf(f2315,plain,
( ( $true
= ( ( sK14 @ sK36 @ sK38 )
& ( sK14 @ sK37 @ sK36 ) ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f2310]) ).
thf(f2370,plain,
( ! [X0: a] :
( ( ( sK14 @ X0 @ sK36 )
=> ( sK14 @ X0 @ sK38 ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f2366]) ).
thf(f2366,plain,
( ! [X0: a] :
( $true
= ( ( ( sK14 @ X0 @ sK36 )
& $true )
=> ( sK14 @ X0 @ sK38 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f2130,f2363]) ).
thf(f2363,plain,
( ( $true
= ( sK14 @ sK36 @ sK38 ) )
| ~ spl0_12 ),
inference(boolean_simplification,[],[f2362]) ).
thf(f2362,plain,
( ( $true
= ( ( sK14 @ sK36 @ sK38 )
& $true ) )
| ~ spl0_12 ),
inference(backward_demodulation,[],[f2315,f2360]) ).
thf(f2130,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK14 @ X1 @ X2 )
& ( sK14 @ X2 @ X3 ) )
=> ( sK14 @ X1 @ X3 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f2129]) ).
thf(f2129,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK14 @ X1 @ X2 )
& ( sK14 @ X2 @ Y0 ) )
=> ( sK14 @ X1 @ Y0 ) )
@ X3 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f2122]) ).
thf(f2122,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ X1 @ X2 )
& ( sK14 @ X2 @ Y0 ) )
=> ( sK14 @ X1 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f2121]) ).
thf(f2121,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ X1 @ Y0 )
& ( sK14 @ Y0 @ Y1 ) )
=> ( sK14 @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f2092]) ).
thf(f2092,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ X1 @ Y0 )
& ( sK14 @ Y0 @ Y1 ) )
=> ( sK14 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f2091]) ).
thf(f2091,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f2068]) ).
thf(f2068,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f2067]) ).
thf(f2067,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[],[f2062,f2066]) ).
thf(f2066,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f2062]) ).
thf(f2062,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f2052]) ).
thf(f2052,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK14 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f2051]) ).
thf(f2051,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ sK14 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(sigma_clausification,[],[f2044]) ).
thf(f2044,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f2043]) ).
thf(f2043,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f2042]) ).
thf(f2042,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1310,f301]) ).
thf(f301,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f300,plain,
( spl0_8
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f1310,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1309]) ).
thf(f1309,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
@ sK13 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f1308]) ).
thf(f1308,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1307]) ).
thf(f1307,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f66]) ).
thf(f66,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f65,plain,
( spl0_4
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f2041,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2040]) ).
thf(f2040,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f2039]) ).
thf(f2039,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2038]) ).
thf(f2038,plain,
( ( ~ $true = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2037]) ).
thf(f2037,plain,
( ( $true
= ( ~ ( $true
| ( sK5 @ sK35 @ sK34 ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2036,f2032]) ).
thf(f2032,plain,
( ( $true
= ( sK4 @ sK35 @ sK34 ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f2030]) ).
thf(f2030,plain,
( ( $false
= ( ( sK4 @ sK35 @ sK34 )
=> ( sK14 @ sK35 @ sK34 ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f2029]) ).
thf(f2029,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ Y0 @ sK34 )
=> ( sK14 @ Y0 @ sK34 ) )
@ sK35 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f2014]) ).
thf(f2014,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 @ sK34 )
=> ( sK14 @ Y0 @ sK34 ) ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f2012]) ).
thf(f2012,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) )
@ sK34 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f371]) ).
thf(f371,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f370]) ).
thf(f370,plain,
( spl0_9
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f2036,plain,
( ( $true
= ( ~ ( ( sK4 @ sK35 @ sK34 )
| ( sK5 @ sK35 @ sK34 ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2035]) ).
thf(f2035,plain,
( ( $true
= ( ( ( sK4 @ sK35 @ sK34 )
| ( sK5 @ sK35 @ sK34 ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f1871,f2034]) ).
thf(f2034,plain,
( ( $false
= ( sK14 @ sK35 @ sK34 ) )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2033]) ).
thf(f2033,plain,
( ( $false
= ( $true
=> ( sK14 @ sK35 @ sK34 ) ) )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f2030,f2032]) ).
thf(f1871,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK4 @ X2 @ X1 )
| ( sK5 @ X2 @ X1 ) )
=> ( sK14 @ X2 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1870]) ).
thf(f1870,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1858]) ).
thf(f1858,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1857]) ).
thf(f1857,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1834]) ).
thf(f1834,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1833]) ).
thf(f1833,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[],[f1826,f1831]) ).
thf(f1831,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1826]) ).
thf(f1826,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1813]) ).
thf(f1813,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK14 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1812]) ).
thf(f1812,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ sK14 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[],[f1803]) ).
thf(f1803,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1802]) ).
thf(f1802,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1801]) ).
thf(f1801,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[],[f1310,f298]) ).
thf(f298,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f297,plain,
( spl0_7
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f1800,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1799]) ).
thf(f1799,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f1798]) ).
thf(f1798,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1760,f1723]) ).
thf(f1723,plain,
( ( ( sK14 @ sK32 @ sK33 )
= $false )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f1660]) ).
thf(f1660,plain,
( ( $false
= ( ( sK5 @ sK32 @ sK33 )
=> ( sK14 @ sK32 @ sK33 ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f1659]) ).
thf(f1659,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK5 @ sK32 @ Y0 )
=> ( sK14 @ sK32 @ Y0 ) )
@ sK33 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f1656]) ).
thf(f1656,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK32 @ Y0 )
=> ( sK14 @ sK32 @ Y0 ) ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f1655]) ).
thf(f1655,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) )
@ sK32 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f406]) ).
thf(f406,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f405]) ).
thf(f405,plain,
( spl0_11
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f1760,plain,
( ( $true
= ( sK14 @ sK32 @ sK33 ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f1759]) ).
thf(f1759,plain,
( ( $true
= ( $true
=> ( sK14 @ sK32 @ sK33 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f1752]) ).
thf(f1752,plain,
( ( $true
= ( ( ( sK4 @ sK32 @ sK33 )
| $true )
=> ( sK14 @ sK32 @ sK33 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f1732,f1724]) ).
thf(f1724,plain,
( ( $true
= ( sK5 @ sK32 @ sK33 ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f1660]) ).
thf(f1732,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK4 @ X2 @ X1 )
| ( sK5 @ X2 @ X1 ) )
=> ( sK14 @ X2 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1731]) ).
thf(f1731,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1730]) ).
thf(f1730,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
=> ( sK14 @ Y0 @ X1 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1729]) ).
thf(f1729,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1670]) ).
thf(f1670,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1669]) ).
thf(f1669,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[],[f1662,f1667]) ).
thf(f1667,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1662]) ).
thf(f1662,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1658]) ).
thf(f1658,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK14 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1657]) ).
thf(f1657,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ sK14 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(sigma_clausification,[],[f1654]) ).
thf(f1654,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1653]) ).
thf(f1653,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1652]) ).
thf(f1652,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[],[f1310,f301]) ).
thf(f1651,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f1650]) ).
thf(f1650,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f1649]) ).
thf(f1649,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f1648]) ).
thf(f1648,plain,
( ( ~ $true = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1642,f1548]) ).
thf(f1548,plain,
( ( $true
= ( sK14 @ sK29 @ sK31 ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f1542]) ).
thf(f1542,plain,
( ( $true
= ( ( sK14 @ sK29 @ sK31 )
& ( sK14 @ sK31 @ sK28 ) ) )
| ~ spl0_10 ),
inference(not_proxy_clausification,[],[f1537]) ).
thf(f1537,plain,
( ( $false
= ( ~ ( ( sK14 @ sK29 @ sK31 )
& ( sK14 @ sK31 @ sK28 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1536]) ).
thf(f1536,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK14 @ sK29 @ Y0 )
& ( sK14 @ Y0 @ sK28 ) )
@ sK31 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f1530]) ).
thf(f1530,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK14 @ sK29 @ Y0 )
& ( sK14 @ Y0 @ sK28 ) ) ) )
| ~ spl0_10 ),
inference(boolean_simplification,[],[f1529]) ).
thf(f1529,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ sK29 @ Y0 )
& ( sK14 @ Y0 @ sK28 ) )
=> $false ) )
= $false )
| ~ spl0_10 ),
inference(backward_demodulation,[],[f1491,f1526]) ).
thf(f1526,plain,
( ( $false
= ( sK14 @ sK29 @ sK28 ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f1503]) ).
thf(f1503,plain,
( ( ( ( ( sK14 @ sK29 @ sK30 )
& ( sK14 @ sK30 @ sK28 ) )
=> ( sK14 @ sK29 @ sK28 ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1502]) ).
thf(f1502,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK14 @ sK29 @ Y0 )
& ( sK14 @ Y0 @ sK28 ) )
=> ( sK14 @ sK29 @ sK28 ) )
@ sK30 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f1491]) ).
thf(f1491,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ sK29 @ Y0 )
& ( sK14 @ Y0 @ sK28 ) )
=> ( sK14 @ sK29 @ sK28 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1490]) ).
thf(f1490,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ sK28 ) )
=> ( sK14 @ Y0 @ sK28 ) ) )
@ sK29 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f1477]) ).
thf(f1477,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ sK28 ) )
=> ( sK14 @ Y0 @ sK28 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1473]) ).
thf(f1473,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
@ sK28 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f374]) ).
thf(f374,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f373]) ).
thf(f373,plain,
( spl0_10
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f1642,plain,
( ( $true
= ( ~ ( sK14 @ sK29 @ sK31 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f1637]) ).
thf(f1637,plain,
( ( $true
= ( ( sK14 @ sK29 @ sK31 )
=> $false ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f1624,f1526]) ).
thf(f1624,plain,
( ! [X0: a] :
( $true
= ( ( sK14 @ X0 @ sK31 )
=> ( sK14 @ X0 @ sK28 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f1594]) ).
thf(f1594,plain,
( ! [X0: a] :
( $true
= ( ( ( sK14 @ X0 @ sK31 )
& $true )
=> ( sK14 @ X0 @ sK28 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f1562,f1550]) ).
thf(f1550,plain,
( ( $true
= ( sK14 @ sK31 @ sK28 ) )
| ~ spl0_10 ),
inference(boolean_simplification,[],[f1549]) ).
thf(f1549,plain,
( ( $true
= ( $true
& ( sK14 @ sK31 @ sK28 ) ) )
| ~ spl0_10 ),
inference(backward_demodulation,[],[f1542,f1548]) ).
thf(f1562,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK14 @ X1 @ X2 )
& ( sK14 @ X2 @ X3 ) )
=> ( sK14 @ X1 @ X3 ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1561]) ).
thf(f1561,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK14 @ X1 @ X2 )
& ( sK14 @ X2 @ Y0 ) )
=> ( sK14 @ X1 @ Y0 ) )
@ X3 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1558]) ).
thf(f1558,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ X1 @ X2 )
& ( sK14 @ X2 @ Y0 ) )
=> ( sK14 @ X1 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1557]) ).
thf(f1557,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ X1 @ Y0 )
& ( sK14 @ Y0 @ Y1 ) )
=> ( sK14 @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1554]) ).
thf(f1554,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ X1 @ Y0 )
& ( sK14 @ Y0 @ Y1 ) )
=> ( sK14 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1553]) ).
thf(f1553,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1334]) ).
thf(f1334,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1331]) ).
thf(f1331,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1321]) ).
thf(f1321,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK14 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1320]) ).
thf(f1320,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ sK14 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[],[f1313]) ).
thf(f1313,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1312]) ).
thf(f1312,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1311]) ).
thf(f1311,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1310,f298]) ).
thf(f1301,plain,
( ~ spl0_3
| ~ spl0_20
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1300]) ).
thf(f1300,plain,
( $false
| ~ spl0_3
| ~ spl0_20
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f1299]) ).
thf(f1299,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_23 ),
inference(boolean_simplification,[],[f1298]) ).
thf(f1298,plain,
( ( ~ $true = $true )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_23 ),
inference(boolean_simplification,[],[f1297]) ).
thf(f1297,plain,
( ( $true
= ( ~ ( ( sK5 @ sK23 @ sK24 )
| $true ) ) )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1296,f1105]) ).
thf(f1105,plain,
( ( $true
= ( sK4 @ sK23 @ sK24 ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1104]) ).
thf(f1104,plain,
( spl0_23
<=> ( $true
= ( sK4 @ sK23 @ sK24 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f1296,plain,
( ( $true
= ( ~ ( ( sK5 @ sK23 @ sK24 )
| ( sK4 @ sK23 @ sK24 ) ) ) )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_23 ),
inference(boolean_simplification,[],[f1290]) ).
thf(f1290,plain,
( ( $true
= ( ( ( sK5 @ sK23 @ sK24 )
| ( sK4 @ sK23 @ sK24 ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_23 ),
inference(superposition,[],[f704,f1286]) ).
thf(f1286,plain,
( ( $false
= ( sK11 @ sK23 @ sK24 ) )
| ~ spl0_20
| ~ spl0_23 ),
inference(boolean_simplification,[],[f1285]) ).
thf(f1285,plain,
( ( ( $true
=> ( sK11 @ sK23 @ sK24 ) )
= $false )
| ~ spl0_20
| ~ spl0_23 ),
inference(boolean_simplification,[],[f1284]) ).
thf(f1284,plain,
( ( $false
= ( ( $true
| ( sK5 @ sK23 @ sK24 ) )
=> ( sK11 @ sK23 @ sK24 ) ) )
| ~ spl0_20
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1277,f1105]) ).
thf(f1277,plain,
( ( $false
= ( ( ( sK4 @ sK23 @ sK24 )
| ( sK5 @ sK23 @ sK24 ) )
=> ( sK11 @ sK23 @ sK24 ) ) )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f1276]) ).
thf(f1276,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK23 @ Y0 )
| ( sK5 @ sK23 @ Y0 ) )
=> ( sK11 @ sK23 @ Y0 ) )
@ sK24 ) )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f1265]) ).
thf(f1265,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK23 @ Y0 )
| ( sK5 @ sK23 @ Y0 ) )
=> ( sK11 @ sK23 @ Y0 ) ) ) )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f1260]) ).
thf(f1260,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK23 ) )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f1049]) ).
thf(f1049,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f1048]) ).
thf(f1048,plain,
( spl0_20
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f704,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK5 @ X1 @ X2 )
| ( sK4 @ X1 @ X2 ) )
=> ( sK11 @ X1 @ X2 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f703]) ).
thf(f703,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK11 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f696]) ).
thf(f696,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK11 @ X1 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f691]) ).
thf(f691,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f688]) ).
thf(f688,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f627]) ).
thf(f627,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f610]) ).
thf(f610,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) )
=> ( sK11 @ sK8 @ sK7 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f609]) ).
thf(f609,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK11 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f543]) ).
thf(f543,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f536]) ).
thf(f536,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK9 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f535]) ).
thf(f535,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f532]) ).
thf(f532,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f531]) ).
thf(f531,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f528]) ).
thf(f528,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f527]) ).
thf(f527,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f63]) ).
thf(f63,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f62,plain,
( spl0_3
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f1283,plain,
( ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1282]) ).
thf(f1282,plain,
( $false
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f1281]) ).
thf(f1281,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(backward_demodulation,[],[f1259,f1280]) ).
thf(f1280,plain,
( ( $false
= ( sK11 @ sK23 @ sK24 ) )
| ~ spl0_20
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1279]) ).
thf(f1279,plain,
( ( ( $true
=> ( sK11 @ sK23 @ sK24 ) )
= $false )
| ~ spl0_20
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1278]) ).
thf(f1278,plain,
( ( ( ( ( sK4 @ sK23 @ sK24 )
| $true )
=> ( sK11 @ sK23 @ sK24 ) )
= $false )
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1277,f1102]) ).
thf(f1102,plain,
( ( $true
= ( sK5 @ sK23 @ sK24 ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1101]) ).
thf(f1101,plain,
( spl0_22
<=> ( $true
= ( sK5 @ sK23 @ sK24 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f1259,plain,
( ( $true
= ( sK11 @ sK23 @ sK24 ) )
| ~ spl0_3
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1258]) ).
thf(f1258,plain,
( ( ( $true
=> ( sK11 @ sK23 @ sK24 ) )
= $true )
| ~ spl0_3
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1251]) ).
thf(f1251,plain,
( ( $true
= ( ( $true
| ( sK4 @ sK23 @ sK24 ) )
=> ( sK11 @ sK23 @ sK24 ) ) )
| ~ spl0_3
| ~ spl0_22 ),
inference(superposition,[],[f704,f1102]) ).
thf(f1246,plain,
( ~ spl0_3
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1245]) ).
thf(f1245,plain,
( $false
| ~ spl0_3
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f1244]) ).
thf(f1244,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1243]) ).
thf(f1243,plain,
( ( ~ $true = $true )
| ~ spl0_3
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1233,f1138]) ).
thf(f1138,plain,
( ( $true
= ( sK11 @ sK27 @ sK25 ) )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1137]) ).
thf(f1137,plain,
( ( $true
= ( ( sK11 @ sK27 @ sK25 )
& $true ) )
| ~ spl0_21 ),
inference(backward_demodulation,[],[f1122,f1135]) ).
thf(f1135,plain,
( ( $true
= ( sK11 @ sK25 @ sK26 ) )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f1122]) ).
thf(f1122,plain,
( ( $true
= ( ( sK11 @ sK27 @ sK25 )
& ( sK11 @ sK25 @ sK26 ) ) )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f1120]) ).
thf(f1120,plain,
( ( $false
= ( ( ( sK11 @ sK27 @ sK25 )
& ( sK11 @ sK25 @ sK26 ) )
=> ( sK11 @ sK27 @ sK26 ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1119]) ).
thf(f1119,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK11 @ Y0 @ sK25 )
& ( sK11 @ sK25 @ sK26 ) )
=> ( sK11 @ Y0 @ sK26 ) )
@ sK27 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f1118]) ).
thf(f1118,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 @ sK25 )
& ( sK11 @ sK25 @ sK26 ) )
=> ( sK11 @ Y0 @ sK26 ) ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1117]) ).
thf(f1117,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ sK25 )
& ( sK11 @ sK25 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ sK26 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f1116]) ).
thf(f1116,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ sK25 )
& ( sK11 @ sK25 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1109]) ).
thf(f1109,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) )
@ sK25 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f1052]) ).
thf(f1052,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1051]) ).
thf(f1051,plain,
( spl0_21
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f1233,plain,
( ( $true
= ( ~ ( sK11 @ sK27 @ sK25 ) ) )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1232]) ).
thf(f1232,plain,
( ( $true
= ( ~ ( $true
& ( sK11 @ sK27 @ sK25 ) ) ) )
| ~ spl0_3
| ~ spl0_21 ),
inference(superposition,[],[f1130,f1135]) ).
thf(f1130,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK11 @ X0 @ sK26 )
& ( sK11 @ sK27 @ X0 ) ) ) )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1127]) ).
thf(f1127,plain,
( ! [X0: a] :
( $true
= ( ( ( sK11 @ X0 @ sK26 )
& ( sK11 @ sK27 @ X0 ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_21 ),
inference(superposition,[],[f734,f1124]) ).
thf(f1124,plain,
( ( $false
= ( sK11 @ sK27 @ sK26 ) )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1123]) ).
thf(f1123,plain,
( ( ( $true
=> ( sK11 @ sK27 @ sK26 ) )
= $false )
| ~ spl0_21 ),
inference(backward_demodulation,[],[f1120,f1122]) ).
thf(f734,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK11 @ X1 @ X3 )
& ( sK11 @ X2 @ X1 ) )
=> ( sK11 @ X2 @ X3 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f733]) ).
thf(f733,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK11 @ X1 @ Y0 )
& ( sK11 @ X2 @ X1 ) )
=> ( sK11 @ X2 @ Y0 ) )
@ X3 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f706]) ).
thf(f706,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ X1 @ Y0 )
& ( sK11 @ X2 @ X1 ) )
=> ( sK11 @ X2 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f705]) ).
thf(f705,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ X1 @ Y1 )
& ( sK11 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f702]) ).
thf(f702,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ X1 @ Y1 )
& ( sK11 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f701]) ).
thf(f701,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f690]) ).
thf(f690,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f689]) ).
thf(f689,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f627,f688]) ).
thf(f1106,plain,
( spl0_22
| spl0_23
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1093,f1048,f1104,f1101]) ).
thf(f1093,plain,
( ( $true
= ( sK5 @ sK23 @ sK24 ) )
| ( $true
= ( sK4 @ sK23 @ sK24 ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f1067]) ).
thf(f1067,plain,
( ( $true
= ( ( sK4 @ sK23 @ sK24 )
| ( sK5 @ sK23 @ sK24 ) ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f1065]) ).
thf(f1065,plain,
( ( $false
= ( ( ( sK4 @ sK23 @ sK24 )
| ( sK5 @ sK23 @ sK24 ) )
=> ( sK11 @ sK23 @ sK24 ) ) )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f1064]) ).
thf(f1064,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK23 @ Y0 )
| ( sK5 @ sK23 @ Y0 ) )
=> ( sK11 @ sK23 @ Y0 ) )
@ sK24 ) )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f1059]) ).
thf(f1059,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK23 @ Y0 )
| ( sK5 @ sK23 @ Y0 ) )
=> ( sK11 @ sK23 @ Y0 ) ) ) )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f1056]) ).
thf(f1056,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK23 ) )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f1049]) ).
thf(f1053,plain,
( spl0_20
| spl0_21
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f1042,f240,f62,f1051,f1048]) ).
thf(f240,plain,
( spl0_6
<=> ( $true
= ( sK11 @ sK10 @ sK7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f1042,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1039]) ).
thf(f1039,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(not_proxy_clausification,[],[f872]) ).
thf(f872,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f870]) ).
thf(f870,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f633,f842]) ).
thf(f842,plain,
( ( ( sK11 @ sK8 @ sK10 )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f834]) ).
thf(f834,plain,
( ( $false
= ( $true
& ( sK11 @ sK8 @ sK10 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f761,f241]) ).
thf(f241,plain,
( ( $true
= ( sK11 @ sK10 @ sK7 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f240]) ).
thf(f761,plain,
( ! [X0: a] :
( ( ( sK11 @ X0 @ sK7 )
& ( sK11 @ sK8 @ X0 ) )
= $false )
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f751]) ).
thf(f751,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK11 @ X0 @ sK7 )
& ( sK11 @ sK8 @ X0 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f738]) ).
thf(f738,plain,
( ! [X0: a] :
( $true
= ( ( ( sK11 @ X0 @ sK7 )
& ( sK11 @ sK8 @ X0 ) )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[],[f734,f626]) ).
thf(f626,plain,
( ( $false
= ( sK11 @ sK8 @ sK7 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f610]) ).
thf(f633,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK8 @ sK10 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f632]) ).
thf(f632,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f572]) ).
thf(f572,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f560,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f556]) ).
thf(f556,plain,
( ( $false
= ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f555]) ).
thf(f555,plain,
( ( ( ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
@ sK10 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f548]) ).
thf(f548,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f546]) ).
thf(f546,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> $false ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f532,f543]) ).
thf(f825,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f824]) ).
thf(f824,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f821]) ).
thf(f821,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f734,f817]) ).
thf(f817,plain,
( ( ( ( ( sK11 @ sK22 @ sK21 )
& ( sK11 @ sK20 @ sK22 ) )
=> ( sK11 @ sK20 @ sK21 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f816]) ).
thf(f816,plain,
( ( ( ^ [Y0: a] :
( ( ( sK11 @ Y0 @ sK21 )
& ( sK11 @ sK20 @ Y0 ) )
=> ( sK11 @ sK20 @ sK21 ) )
@ sK22 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f815]) ).
thf(f815,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 @ sK21 )
& ( sK11 @ sK20 @ Y0 ) )
=> ( sK11 @ sK20 @ sK21 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f814]) ).
thf(f814,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ Y0 )
& ( sK11 @ sK20 @ Y1 ) )
=> ( sK11 @ sK20 @ Y0 ) ) )
@ sK21 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f799]) ).
thf(f799,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ Y0 )
& ( sK11 @ sK20 @ Y1 ) )
=> ( sK11 @ sK20 @ Y0 ) ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f796]) ).
thf(f796,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
@ sK20 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f238]) ).
thf(f238,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f237,plain,
( spl0_5
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f522,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f521]) ).
thf(f521,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f520]) ).
thf(f520,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f519]) ).
thf(f519,plain,
( ( ~ $true = $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f506,f461]) ).
thf(f461,plain,
( ( $true
= ( sK6 @ sK16 @ sK15 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f445]) ).
thf(f445,plain,
( ( $true
= ( ( sK6 @ sK16 @ sK15 )
& ( sK6 @ sK15 @ sK17 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f443]) ).
thf(f443,plain,
( ( ( ( ( sK6 @ sK16 @ sK15 )
& ( sK6 @ sK15 @ sK17 ) )
=> ( sK6 @ sK16 @ sK17 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f442]) ).
thf(f442,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK16 @ sK15 )
& ( sK6 @ sK15 @ Y0 ) )
=> ( sK6 @ sK16 @ Y0 ) )
@ sK17 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f441]) ).
thf(f441,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK16 @ sK15 )
& ( sK6 @ sK15 @ Y0 ) )
=> ( sK6 @ sK16 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f440]) ).
thf(f440,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ sK15 )
& ( sK6 @ sK15 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK16 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f439]) ).
thf(f439,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ sK15 )
& ( sK6 @ sK15 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f435]) ).
thf(f435,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) )
@ sK15 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f432]) ).
thf(f432,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f427]) ).
thf(f427,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f426]) ).
thf(f426,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f425,f33]) ).
thf(f33,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f32]) ).
thf(f32,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
inference(backward_demodulation,[],[f25,f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ sK2 @ sK3 ) ) ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK6 ) ),
inference(sigma_clausification,[],[f21]) ).
thf(f21,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
= $false ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(backward_demodulation,[],[f17,f19]) ).
thf(f19,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( $false
= ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK2 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ sK3 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK2 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
| ( Y1 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK2 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
| ( Y1 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 @ sK3 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
| ( Y1 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK2 @ sK3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
| ( Y1 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 @ sK3 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ sK2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ sK2 @ Y0 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ sK2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ sK2 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y3 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y3 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y3 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y3 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > a > $o,X2: a,X3: a] :
( ( ( ! [X4: a,X5: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X9: a,X10: a,X11: a] :
( ( ( X6 @ X9 @ X11 )
& ( X6 @ X10 @ X9 ) )
=> ( X6 @ X10 @ X11 ) ) )
=> ( X6 @ X5 @ X4 ) )
| ! [X12: a > a > $o] :
( ( ! [X13: a,X14: a,X15: a] :
( ( ( X12 @ X14 @ X15 )
& ( X12 @ X15 @ X13 ) )
=> ( X12 @ X14 @ X13 ) )
& ! [X16: a,X17: a] :
( ( X0 @ X17 @ X16 )
=> ( X12 @ X17 @ X16 ) ) )
=> ( X12 @ X5 @ X4 ) ) )
=> ! [X18: a > a > $o] :
( ( ! [X19: a,X20: a,X21: a] :
( ( ( X18 @ X20 @ X19 )
& ( X18 @ X21 @ X20 ) )
=> ( X18 @ X21 @ X19 ) )
& ! [X22: a,X23: a] :
( ( ( X0 @ X22 @ X23 )
| ( X1 @ X22 @ X23 ) )
=> ( X18 @ X22 @ X23 ) ) )
=> ( X18 @ X5 @ X4 ) ) )
& ! [X24: a,X25: a,X26: a] :
( ( ! [X27: a > a > $o] :
( ( ! [X28: a,X29: a,X30: a] :
( ( ( X27 @ X30 @ X28 )
& ( X27 @ X28 @ X29 ) )
=> ( X27 @ X30 @ X29 ) )
& ! [X31: a,X32: a] :
( ( ( X1 @ X32 @ X31 )
| ( X0 @ X32 @ X31 ) )
=> ( X27 @ X32 @ X31 ) ) )
=> ( X27 @ X24 @ X26 ) )
& ! [X33: a > a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( X0 @ X35 @ X34 )
| ( X1 @ X35 @ X34 ) )
=> ( X33 @ X35 @ X34 ) )
& ! [X36: a,X37: a,X38: a] :
( ( ( X33 @ X38 @ X37 )
& ( X33 @ X36 @ X38 ) )
=> ( X33 @ X36 @ X37 ) ) )
=> ( X33 @ X25 @ X24 ) ) )
=> ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a,X42: a] :
( ( ( X39 @ X41 @ X42 )
& ( X39 @ X42 @ X40 ) )
=> ( X39 @ X41 @ X40 ) )
& ! [X43: a,X44: a] :
( ( ( X1 @ X44 @ X43 )
| ( X0 @ X44 @ X43 ) )
=> ( X39 @ X44 @ X43 ) ) )
=> ( X39 @ X25 @ X26 ) ) ) )
=> ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a,X48: a] :
( ( ( X45 @ X48 @ X46 )
& ( X45 @ X47 @ X48 ) )
=> ( X45 @ X47 @ X46 ) )
& ! [X49: a,X50: a] :
( ( ( X0 @ X49 @ X50 )
| ( X1 @ X49 @ X50 ) )
=> ( X45 @ X49 @ X50 ) ) )
=> ( X45 @ X3 @ X2 ) ) )
=> ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a] :
( ( ( X0 @ X52 @ X53 )
| ( X1 @ X52 @ X53 ) )
=> ( X51 @ X52 @ X53 ) )
& ! [X54: a,X55: a,X56: a] :
( ( ( X51 @ X54 @ X55 )
& ( X51 @ X55 @ X56 ) )
=> ( X51 @ X54 @ X56 ) ) )
=> ( X51 @ X3 @ X2 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > a > $o,X3: a,X2: a] :
( ( ( ! [X5: a,X4: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X8: a,X7: a,X9: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
| ! [X6: a > a > $o] :
( ( ! [X9: a,X7: a,X8: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
& ! [X8: a,X7: a] :
( ( X0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X9: a,X8: a,X7: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) )
& ! [X7: a,X8: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
& ! [X5: a,X4: a,X9: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X8: a,X10: a,X7: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X8: a,X7: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X5 @ X9 ) )
& ! [X6: a > a > $o] :
( ( ! [X8: a,X7: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
& ! [X7: a,X10: a,X8: a] :
( ( ( X6 @ X8 @ X10 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X10 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X10: a,X7: a,X8: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X8: a,X7: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X9 ) ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X9: a,X4: a,X5: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) )
& ! [X4: a,X5: a] :
( ( ( X0 @ X4 @ X5 )
| ( X1 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X6 @ X2 @ X3 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X4: a,X5: a] :
( ( ( X0 @ X4 @ X5 )
| ( X1 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) )
& ! [X4: a,X5: a,X9: a] :
( ( ( X6 @ X4 @ X5 )
& ( X6 @ X5 @ X9 ) )
=> ( X6 @ X4 @ X9 ) ) )
=> ( X6 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a > a > $o,X3: a,X2: a] :
( ( ( ! [X5: a,X4: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X8: a,X7: a,X9: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
| ! [X6: a > a > $o] :
( ( ! [X9: a,X7: a,X8: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
& ! [X8: a,X7: a] :
( ( X0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X9: a,X8: a,X7: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) )
& ! [X7: a,X8: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
& ! [X5: a,X4: a,X9: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X8: a,X10: a,X7: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X8: a,X7: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X5 @ X9 ) )
& ! [X6: a > a > $o] :
( ( ! [X8: a,X7: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
& ! [X7: a,X10: a,X8: a] :
( ( ( X6 @ X8 @ X10 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X10 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X10: a,X7: a,X8: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X8: a,X7: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X9 ) ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X9: a,X4: a,X5: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) )
& ! [X4: a,X5: a] :
( ( ( X0 @ X4 @ X5 )
| ( X1 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X6 @ X2 @ X3 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X4: a,X5: a] :
( ( ( X0 @ X4 @ X5 )
| ( X1 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) )
& ! [X4: a,X5: a,X9: a] :
( ( ( X6 @ X4 @ X5 )
& ( X6 @ X5 @ X9 ) )
=> ( X6 @ X4 @ X9 ) ) )
=> ( X6 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM250D_pme) ).
thf(f425,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f416]) ).
thf(f416,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[],[f414,f24]) ).
thf(f24,plain,
( $false
= ( sK6 @ sK2 @ sK3 ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f414,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y0 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f413]) ).
thf(f413,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f47]) ).
thf(f47,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f46,plain,
( spl0_1
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f506,plain,
( ( $true
= ( ~ ( sK6 @ sK16 @ sK15 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f499]) ).
thf(f499,plain,
( ( $true
= ( ( sK6 @ sK16 @ sK15 )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[],[f470,f444]) ).
thf(f444,plain,
( ( ( sK6 @ sK16 @ sK17 )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f443]) ).
thf(f470,plain,
( ! [X0: a] :
( ( ( sK6 @ X0 @ sK15 )
=> ( sK6 @ X0 @ sK17 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f464]) ).
thf(f464,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK6 @ X0 @ sK15 ) )
=> ( sK6 @ X0 @ sK17 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f97,f463]) ).
thf(f463,plain,
( ( $true
= ( sK6 @ sK15 @ sK17 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f462]) ).
thf(f462,plain,
( ( $true
= ( $true
& ( sK6 @ sK15 @ sK17 ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f445,f461]) ).
thf(f97,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 @ X1 )
& ( sK6 @ X3 @ X2 ) )
=> ( sK6 @ X3 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f96]) ).
thf(f96,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ X2 @ X1 )
& ( sK6 @ Y0 @ X2 ) )
=> ( sK6 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[],[f87]) ).
thf(f87,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X2 @ X1 )
& ( sK6 @ Y0 @ X2 ) )
=> ( sK6 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f86]) ).
thf(f86,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ X1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f83]) ).
thf(f83,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ X1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f82]) ).
thf(f82,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y2 @ Y1 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f31]) ).
thf(f410,plain,
( spl0_11
| spl0_12
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f401,f300,f65,f408,f405]) ).
thf(f401,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f395]) ).
thf(f395,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f392]) ).
thf(f392,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f388]) ).
thf(f388,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK14 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y2 )
& ( sK14 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y2 ) ) ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f386,f258]) ).
thf(f258,plain,
( ( $false
= ( sK14 @ sK12 @ sK13 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f257]) ).
thf(f257,plain,
( ( ( $true
=> ( sK14 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f254,f256]) ).
thf(f256,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f254]) ).
thf(f254,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y0 @ Y1 )
& ( sK14 @ Y1 @ Y2 ) )
=> ( sK14 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK14 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f253]) ).
thf(f253,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ sK14 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f252]) ).
thf(f252,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f251]) ).
thf(f251,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f248,f250]) ).
thf(f250,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f248]) ).
thf(f248,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f247]) ).
thf(f247,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
@ sK13 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f246]) ).
thf(f246,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK12 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f245]) ).
thf(f245,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f66]) ).
thf(f386,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK12 @ sK13 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f385]) ).
thf(f385,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[],[f301]) ).
thf(f375,plain,
( spl0_9
| spl0_10
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f366,f297,f65,f373,f370]) ).
thf(f366,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f354]) ).
thf(f354,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(not_proxy_clausification,[],[f328]) ).
thf(f328,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f324]) ).
thf(f324,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK14 @ Y1 @ Y2 )
& ( sK14 @ Y2 @ Y0 ) )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK14 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f314,f258]) ).
thf(f314,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK12 @ sK13 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f313]) ).
thf(f313,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[],[f298]) ).
thf(f302,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f295,f65,f300,f297]) ).
thf(f295,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK12 @ sK13 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f250]) ).
thf(f242,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f235,f62,f240,f237]) ).
thf(f235,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $true
= ( sK11 @ sK10 @ sK7 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f157]) ).
thf(f157,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
=> ( sK11 @ sK10 @ sK7 ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f155]) ).
thf(f155,plain,
( ( $true
= ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) )
=> ( sK11 @ sK10 @ sK7 ) ) )
| ~ spl0_3 ),
inference(superposition,[],[f133,f147]) ).
thf(f147,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f138]) ).
thf(f138,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f136]) ).
thf(f136,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y2 )
& ( sK11 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y2 ) ) ) ) ) )
=> ( sK11 @ sK8 @ sK7 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f135]) ).
thf(f135,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK11 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f88]) ).
thf(f88,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f85]) ).
thf(f85,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK9 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f84]) ).
thf(f84,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f81]) ).
thf(f81,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK8 @ sK7 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f80]) ).
thf(f80,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f75]) ).
thf(f75,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK7 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f74]) ).
thf(f74,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f63]) ).
thf(f133,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK10 @ sK7 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f132]) ).
thf(f132,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f124]) ).
thf(f124,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f123]) ).
thf(f123,plain,
( ( $true
= ( $true
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f109,f122]) ).
thf(f122,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f109]) ).
thf(f109,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f99]) ).
thf(f99,plain,
( ( $false
= ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK10 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK7 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f98]) ).
thf(f98,plain,
( ( ( ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
@ sK10 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f92]) ).
thf(f92,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f91]) ).
thf(f91,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> $false ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f81,f88]) ).
thf(f67,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f60,f49,f65,f62]) ).
thf(f49,plain,
( spl0_2
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f60,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f50]) ).
thf(f50,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f51,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f44,f49,f46]) ).
thf(f44,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV155^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12 % Command : run_vampire %s %d THM
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 21 18:45:09 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.35 This is a TH0_THM_NEQ_NAR problem
% 0.11/0.35 Running higher-order theorem proving
% 0.11/0.35 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
% 0.19/0.37 % (3924)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.19/0.37 % (3925)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)
% 0.19/0.37 % (3926)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)
% 0.19/0.37 % (3928)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)
% 0.19/0.37 % (3929)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)
% 0.19/0.37 % (3927)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.37 % (3930)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.37 % (3927)Instruction limit reached!
% 0.19/0.37 % (3927)------------------------------
% 0.19/0.37 % (3927)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.37 % (3927)Termination reason: Unknown
% 0.19/0.37 % (3928)Instruction limit reached!
% 0.19/0.37 % (3928)------------------------------
% 0.19/0.37 % (3928)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.37 % (3927)Termination phase: Property scanning
% 0.19/0.37
% 0.19/0.37 % (3927)Memory used [KB]: 1023
% 0.19/0.37 % (3927)Time elapsed: 0.003 s
% 0.19/0.37 % (3927)Instructions burned: 2 (million)
% 0.19/0.37 % (3927)------------------------------
% 0.19/0.37 % (3927)------------------------------
% 0.19/0.37 % (3928)Termination reason: Unknown
% 0.19/0.37 % (3928)Termination phase: shuffling
% 0.19/0.37
% 0.19/0.37 % (3928)Memory used [KB]: 1023
% 0.19/0.37 % (3928)Time elapsed: 0.004 s
% 0.19/0.37 % (3928)Instructions burned: 3 (million)
% 0.19/0.37 % (3928)------------------------------
% 0.19/0.37 % (3928)------------------------------
% 0.19/0.37 % (3925)Instruction limit reached!
% 0.19/0.37 % (3925)------------------------------
% 0.19/0.37 % (3925)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.37 % (3925)Termination reason: Unknown
% 0.19/0.37 % (3925)Termination phase: Preprocessing 3
% 0.19/0.37
% 0.19/0.37 % (3925)Memory used [KB]: 1023
% 0.19/0.37 % (3925)Time elapsed: 0.006 s
% 0.19/0.37 % (3925)Instructions burned: 5 (million)
% 0.19/0.37 % (3925)------------------------------
% 0.19/0.37 % (3925)------------------------------
% 0.19/0.38 % (3930)Instruction limit reached!
% 0.19/0.38 % (3930)------------------------------
% 0.19/0.38 % (3930)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.38 % (3930)Termination reason: Unknown
% 0.19/0.38 % (3930)Termination phase: Saturation
% 0.19/0.38
% 0.19/0.38 % (3930)Memory used [KB]: 5756
% 0.19/0.38 % (3930)Time elapsed: 0.012 s
% 0.19/0.38 % (3930)Instructions burned: 18 (million)
% 0.19/0.38 % (3930)------------------------------
% 0.19/0.38 % (3930)------------------------------
% 0.19/0.38 % (3926)Instruction limit reached!
% 0.19/0.38 % (3926)------------------------------
% 0.19/0.38 % (3926)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.38 % (3926)Termination reason: Unknown
% 0.19/0.38 % (3926)Termination phase: Saturation
% 0.19/0.38
% 0.19/0.38 % (3926)Memory used [KB]: 5756
% 0.19/0.39 % (3926)Time elapsed: 0.018 s
% 0.19/0.39 % (3926)Instructions burned: 28 (million)
% 0.19/0.39 % (3926)------------------------------
% 0.19/0.39 % (3926)------------------------------
% 0.19/0.39 % (3931)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)
% 0.19/0.39 % (3932)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.39 % (3931)Instruction limit reached!
% 0.19/0.39 % (3931)------------------------------
% 0.19/0.39 % (3931)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (3931)Termination reason: Unknown
% 0.19/0.39 % (3931)Termination phase: Preprocessing 2
% 0.19/0.39
% 0.19/0.39 % (3931)Memory used [KB]: 1023
% 0.19/0.39 % (3931)Time elapsed: 0.004 s
% 0.19/0.39 % (3931)Instructions burned: 3 (million)
% 0.19/0.39 % (3931)------------------------------
% 0.19/0.39 % (3931)------------------------------
% 0.19/0.39 % (3934)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.40 % (3935)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.40 % (3935)Instruction limit reached!
% 0.19/0.40 % (3935)------------------------------
% 0.19/0.40 % (3935)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.40 % (3935)Termination reason: Unknown
% 0.19/0.40 % (3935)Termination phase: Property scanning
% 0.19/0.40
% 0.19/0.40 % (3935)Memory used [KB]: 1023
% 0.19/0.40 % (3935)Time elapsed: 0.004 s
% 0.19/0.40 % (3935)Instructions burned: 3 (million)
% 0.19/0.40 % (3935)------------------------------
% 0.19/0.40 % (3935)------------------------------
% 0.19/0.40 % (3934)Instruction limit reached!
% 0.19/0.40 % (3934)------------------------------
% 0.19/0.40 % (3934)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.40 % (3934)Termination reason: Unknown
% 0.19/0.40 % (3934)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (3934)Memory used [KB]: 5756
% 0.19/0.40 % (3934)Time elapsed: 0.012 s
% 0.19/0.40 % (3934)Instructions burned: 15 (million)
% 0.19/0.40 % (3934)------------------------------
% 0.19/0.40 % (3934)------------------------------
% 0.19/0.40 % (3936)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.19/0.40 % (3937)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.40 % (3932)Instruction limit reached!
% 0.19/0.40 % (3932)------------------------------
% 0.19/0.40 % (3932)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.41 % (3932)Termination reason: Unknown
% 0.19/0.41 % (3932)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (3932)Memory used [KB]: 5628
% 0.19/0.41 % (3932)Time elapsed: 0.021 s
% 0.19/0.41 % (3932)Instructions burned: 37 (million)
% 0.19/0.41 % (3932)------------------------------
% 0.19/0.41 % (3932)------------------------------
% 0.19/0.41 % (3937)Instruction limit reached!
% 0.19/0.41 % (3937)------------------------------
% 0.19/0.41 % (3937)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.41 % (3937)Termination reason: Unknown
% 0.19/0.41 % (3937)Termination phase: Property scanning
% 0.19/0.41
% 0.19/0.41 % (3937)Memory used [KB]: 1151
% 0.19/0.41 % (3937)Time elapsed: 0.007 s
% 0.19/0.41 % (3937)Instructions burned: 8 (million)
% 0.19/0.41 % (3937)------------------------------
% 0.19/0.41 % (3937)------------------------------
% 0.19/0.41 % (3938)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.41 % (3939)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.42 % (3939)Instruction limit reached!
% 0.19/0.42 % (3939)------------------------------
% 0.19/0.42 % (3939)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.42 % (3939)Termination reason: Unknown
% 0.19/0.42 % (3939)Termination phase: Preprocessing 3
% 0.19/0.42
% 0.19/0.42 % (3939)Memory used [KB]: 1023
% 0.19/0.42 % (3939)Time elapsed: 0.005 s
% 0.19/0.42 % (3939)Instructions burned: 4 (million)
% 0.19/0.42 % (3939)------------------------------
% 0.19/0.42 % (3939)------------------------------
% 0.19/0.42 % (3938)Instruction limit reached!
% 0.19/0.42 % (3938)------------------------------
% 0.19/0.42 % (3938)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.42 % (3938)Termination reason: Unknown
% 0.19/0.42 % (3938)Termination phase: Property scanning
% 0.19/0.42
% 0.19/0.42 % (3938)Memory used [KB]: 1151
% 0.19/0.42 % (3938)Time elapsed: 0.010 s
% 0.19/0.42 % (3938)Instructions burned: 16 (million)
% 0.19/0.42 % (3938)------------------------------
% 0.19/0.42 % (3938)------------------------------
% 0.19/0.42 % (3940)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.42 % (3940)Instruction limit reached!
% 0.19/0.42 % (3940)------------------------------
% 0.19/0.42 % (3940)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.42 % (3940)Termination reason: Unknown
% 0.19/0.42 % (3940)Termination phase: shuffling
% 0.19/0.42
% 0.19/0.42 % (3940)Memory used [KB]: 1023
% 0.19/0.42 % (3940)Time elapsed: 0.004 s
% 0.19/0.42 % (3940)Instructions burned: 3 (million)
% 0.19/0.42 % (3940)------------------------------
% 0.19/0.42 % (3940)------------------------------
% 0.19/0.42 % (3941)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.43 % (3941)Instruction limit reached!
% 0.19/0.43 % (3941)------------------------------
% 0.19/0.43 % (3941)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.43 % (3941)Termination reason: Unknown
% 0.19/0.43 % (3941)Termination phase: Property scanning
% 0.19/0.43
% 0.19/0.43 % (3941)Memory used [KB]: 1151
% 0.19/0.43 % (3941)Time elapsed: 0.007 s
% 0.19/0.43 % (3941)Instructions burned: 9 (million)
% 0.19/0.43 % (3941)------------------------------
% 0.19/0.43 % (3941)------------------------------
% 0.19/0.43 % (3942)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.43 % (3942)Instruction limit reached!
% 0.19/0.43 % (3942)------------------------------
% 0.19/0.43 % (3942)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.43 % (3942)Termination reason: Unknown
% 0.19/0.43 % (3942)Termination phase: shuffling
% 0.19/0.43
% 0.19/0.43 % (3942)Memory used [KB]: 1023
% 0.19/0.43 % (3942)Time elapsed: 0.003 s
% 0.19/0.43 % (3942)Instructions burned: 3 (million)
% 0.19/0.43 % (3942)------------------------------
% 0.19/0.43 % (3942)------------------------------
% 0.19/0.44 % (3943)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.44 % (3944)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.44 % (3943)Instruction limit reached!
% 0.19/0.44 % (3943)------------------------------
% 0.19/0.44 % (3943)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.44 % (3943)Termination reason: Unknown
% 0.19/0.44 % (3943)Termination phase: Preprocessing 3
% 0.19/0.44
% 0.19/0.44 % (3943)Memory used [KB]: 1023
% 0.19/0.44 % (3943)Time elapsed: 0.005 s
% 0.19/0.44 % (3943)Instructions burned: 5 (million)
% 0.19/0.44 % (3943)------------------------------
% 0.19/0.44 % (3943)------------------------------
% 0.19/0.44 % (3945)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.19/0.45 % (3944)Instruction limit reached!
% 0.19/0.45 % (3944)------------------------------
% 0.19/0.45 % (3944)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.45 % (3944)Termination reason: Unknown
% 0.19/0.45 % (3944)Termination phase: Saturation
% 0.19/0.45
% 0.19/0.45 % (3944)Memory used [KB]: 5628
% 0.19/0.45 % (3944)Time elapsed: 0.013 s
% 0.19/0.45 % (3944)Instructions burned: 18 (million)
% 0.19/0.45 % (3944)------------------------------
% 0.19/0.45 % (3944)------------------------------
% 0.19/0.45 % (3946)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.45 % (3946)Instruction limit reached!
% 0.19/0.45 % (3946)------------------------------
% 0.19/0.45 % (3946)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.45 % (3946)Termination reason: Unknown
% 0.19/0.45 % (3946)Termination phase: Property scanning
% 0.19/0.45
% 0.19/0.45 % (3946)Memory used [KB]: 1151
% 0.19/0.45 % (3946)Time elapsed: 0.006 s
% 0.19/0.45 % (3946)Instructions burned: 6 (million)
% 0.19/0.45 % (3946)------------------------------
% 0.19/0.45 % (3946)------------------------------
% 0.19/0.46 % (3947)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.19/0.47 % (3949)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.19/0.47 % (3924)Instruction limit reached!
% 0.19/0.47 % (3924)------------------------------
% 0.19/0.47 % (3924)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.47 % (3924)Termination reason: Unknown
% 0.19/0.47 % (3924)Termination phase: Saturation
% 0.19/0.47
% 0.19/0.47 % (3924)Memory used [KB]: 6140
% 0.19/0.47 % (3924)Time elapsed: 0.101 s
% 0.19/0.47 % (3924)Instructions burned: 183 (million)
% 0.19/0.47 % (3924)------------------------------
% 0.19/0.47 % (3924)------------------------------
% 0.19/0.47 % (3950)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2998ds/5Mi)
% 0.19/0.47 % (3950)Instruction limit reached!
% 0.19/0.47 % (3950)------------------------------
% 0.19/0.47 % (3950)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.47 % (3950)Termination reason: Unknown
% 0.19/0.47 % (3950)Termination phase: Property scanning
% 0.19/0.47
% 0.19/0.47 % (3950)Memory used [KB]: 1023
% 0.19/0.47 % (3950)Time elapsed: 0.004 s
% 0.19/0.47 % (3950)Instructions burned: 5 (million)
% 0.19/0.47 % (3950)------------------------------
% 0.19/0.47 % (3950)------------------------------
% 0.19/0.48 % (3949)Instruction limit reached!
% 0.19/0.48 % (3949)------------------------------
% 0.19/0.48 % (3949)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.48 % (3949)Termination reason: Unknown
% 0.19/0.48 % (3949)Termination phase: Saturation
% 0.19/0.48
% 0.19/0.48 % (3949)Memory used [KB]: 5756
% 0.19/0.48 % (3949)Time elapsed: 0.014 s
% 0.19/0.48 % (3949)Instructions burned: 21 (million)
% 0.19/0.48 % (3949)------------------------------
% 0.19/0.48 % (3949)------------------------------
% 0.19/0.48 % (3951)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 (2998ds/6Mi)
% 0.19/0.48 % (3951)Instruction limit reached!
% 0.19/0.48 % (3951)------------------------------
% 0.19/0.48 % (3951)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.48 % (3951)Termination reason: Unknown
% 0.19/0.48 % (3951)Termination phase: Preprocessing 1
% 0.19/0.48
% 0.19/0.48 % (3951)Memory used [KB]: 1023
% 0.19/0.48 % (3951)Time elapsed: 0.003 s
% 0.19/0.48 % (3951)Instructions burned: 6 (million)
% 0.19/0.48 % (3951)------------------------------
% 0.19/0.48 % (3951)------------------------------
% 0.19/0.48 % (3952)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.19/0.49 % (3953)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)
% 0.19/0.49 % (3954)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)
% 0.19/0.50 % (3954)Instruction limit reached!
% 0.19/0.50 % (3954)------------------------------
% 0.19/0.50 % (3954)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.50 % (3954)Termination reason: Unknown
% 0.19/0.50 % (3954)Termination phase: Saturation
% 0.19/0.50
% 0.19/0.50 % (3954)Memory used [KB]: 5500
% 0.19/0.50 % (3954)Time elapsed: 0.007 s
% 0.19/0.50 % (3954)Instructions burned: 21 (million)
% 0.19/0.50 % (3954)------------------------------
% 0.19/0.50 % (3954)------------------------------
% 0.19/0.51 % (3955)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.19/0.51 % (3929)Instruction limit reached!
% 0.19/0.51 % (3929)------------------------------
% 0.19/0.51 % (3929)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.51 % (3929)Termination reason: Unknown
% 0.19/0.51 % (3929)Termination phase: Saturation
% 0.19/0.51
% 0.19/0.51 % (3929)Memory used [KB]: 6396
% 0.19/0.51 % (3929)Time elapsed: 0.144 s
% 0.19/0.51 % (3929)Instructions burned: 276 (million)
% 0.19/0.51 % (3929)------------------------------
% 0.19/0.51 % (3929)------------------------------
% 0.19/0.52 % (3956)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.19/0.53 % (3956)Instruction limit reached!
% 0.19/0.53 % (3956)------------------------------
% 0.19/0.53 % (3956)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.53 % (3956)Termination reason: Unknown
% 0.19/0.53 % (3956)Termination phase: Saturation
% 0.19/0.53
% 0.19/0.53 % (3956)Memory used [KB]: 5756
% 0.19/0.53 % (3956)Time elapsed: 0.009 s
% 0.19/0.53 % (3956)Instructions burned: 19 (million)
% 0.19/0.53 % (3956)------------------------------
% 0.19/0.53 % (3956)------------------------------
% 0.19/0.54 % (3957)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.19/0.54 % (3957)Instruction limit reached!
% 0.19/0.54 % (3957)------------------------------
% 0.19/0.54 % (3957)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.54 % (3957)Termination reason: Unknown
% 0.19/0.54 % (3957)Termination phase: Preprocessing 2
% 0.19/0.54
% 0.19/0.54 % (3957)Memory used [KB]: 1023
% 0.19/0.54 % (3957)Time elapsed: 0.003 s
% 0.19/0.54 % (3957)Instructions burned: 3 (million)
% 0.19/0.54 % (3957)------------------------------
% 0.19/0.54 % (3957)------------------------------
% 0.19/0.55 % (3958)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 1.48/0.56 % (3958)Instruction limit reached!
% 1.48/0.56 % (3958)------------------------------
% 1.48/0.56 % (3958)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.48/0.56 % (3958)Termination reason: Unknown
% 1.48/0.56 % (3958)Termination phase: Saturation
% 1.48/0.56
% 1.48/0.56 % (3958)Memory used [KB]: 5884
% 1.48/0.56 % (3958)Time elapsed: 0.013 s
% 1.48/0.56 % (3958)Instructions burned: 31 (million)
% 1.48/0.56 % (3958)------------------------------
% 1.48/0.56 % (3958)------------------------------
% 1.48/0.57 % (3959)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2997ds/127Mi)
% 1.70/0.60 % (3936)First to succeed.
% 1.70/0.61 % (3959)Instruction limit reached!
% 1.70/0.61 % (3959)------------------------------
% 1.70/0.61 % (3959)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.70/0.61 % (3959)Termination reason: Unknown
% 1.70/0.61 % (3959)Termination phase: Saturation
% 1.70/0.61
% 1.70/0.61 % (3959)Memory used [KB]: 6268
% 1.70/0.61 % (3959)Time elapsed: 0.043 s
% 1.70/0.61 % (3959)Instructions burned: 127 (million)
% 1.70/0.61 % (3959)------------------------------
% 1.70/0.61 % (3959)------------------------------
% 1.70/0.62 % (3952)Instruction limit reached!
% 1.70/0.62 % (3952)------------------------------
% 1.70/0.62 % (3952)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.70/0.62 % (3952)Termination reason: Unknown
% 1.70/0.62 % (3952)Termination phase: Saturation
% 1.70/0.62
% 1.70/0.62 % (3952)Memory used [KB]: 6012
% 1.70/0.62 % (3952)Time elapsed: 0.126 s
% 1.70/0.62 % (3952)Instructions burned: 377 (million)
% 1.70/0.62 % (3952)------------------------------
% 1.70/0.62 % (3952)------------------------------
% 1.70/0.62 % (3936)Refutation found. Thanks to Tanya!
% 1.70/0.62 % SZS status Theorem for theBenchmark
% 1.70/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 1.70/0.62 % (3936)------------------------------
% 1.70/0.62 % (3936)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.70/0.62 % (3936)Termination reason: Refutation
% 1.70/0.62
% 1.70/0.62 % (3936)Memory used [KB]: 7291
% 1.70/0.62 % (3936)Time elapsed: 0.232 s
% 1.70/0.62 % (3936)Instructions burned: 442 (million)
% 1.70/0.62 % (3936)------------------------------
% 1.70/0.62 % (3936)------------------------------
% 1.70/0.62 % (3923)Success in time 0.264 s
%------------------------------------------------------------------------------