TSTP Solution File: SEV154^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV154^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n018.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 : Sun May 5 09:41:32 EDT 2024
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 56
% Syntax : Number of formulae : 447 ( 27 unt; 31 typ; 0 def)
% Number of atoms : 4348 ( 393 equ; 0 cnn)
% Maximal formula atoms : 5 ( 10 avg)
% Number of connectives : 12214 ( 626 ~;1220 |; 811 &;7031 @)
% ( 24 <=>;1152 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 604 ( 604 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 50 con; 0-2 aty)
% (1350 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1577 (1409 ^ 167 !; 0 ?;1577 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a > a > $o ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a > $o ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a > $o ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(f2366,plain,
$false,
inference(avatar_sat_refutation,[],[f34,f50,f239,f272,f392,f435,f513,f523,f581,f619,f636,f841,f916,f937,f994,f1001,f1008,f1032,f1033,f1076,f1206,f1428,f1784,f2298,f2365]) ).
thf(f2365,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f2364]) ).
thf(f2364,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f2363]) ).
thf(f2363,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f2362]) ).
thf(f2362,plain,
( ( ~ $true = $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f2361]) ).
thf(f2361,plain,
( ( ( ~ ( ( sK4 @ sK11 @ sK25 )
| $true ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f2358,f2349]) ).
thf(f2349,plain,
( ( $true
= ( sK3 @ sK11 @ sK25 ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f2325]) ).
thf(f2325,plain,
( ( $false
= ( ( sK3 @ sK11 @ sK25 )
=> ( sK13 @ sK25 ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f2323]) ).
thf(f2323,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) )
@ sK25 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f431]) ).
thf(f431,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f430]) ).
thf(f430,plain,
( spl0_11
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f2358,plain,
( ( ( ~ ( ( sK4 @ sK11 @ sK25 )
| ( sK3 @ sK11 @ sK25 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f2352]) ).
thf(f2352,plain,
( ( ( ( ( sK4 @ sK11 @ sK25 )
| ( sK3 @ sK11 @ sK25 ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f2161,f2351]) ).
thf(f2351,plain,
( ( ( sK13 @ sK25 )
= $false )
| ~ spl0_11 ),
inference(boolean_simplification,[],[f2350]) ).
thf(f2350,plain,
( ( $false
= ( $true
=> ( sK13 @ sK25 ) ) )
| ~ spl0_11 ),
inference(backward_demodulation,[],[f2325,f2349]) ).
thf(f2161,plain,
( ! [X1: a] :
( ( ( ( sK4 @ sK11 @ X1 )
| ( sK3 @ sK11 @ X1 ) )
=> ( sK13 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f2160]) ).
thf(f2160,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1932]) ).
thf(f1932,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1813]) ).
thf(f1813,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1800]) ).
thf(f1800,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1799]) ).
thf(f1799,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(sigma_clausification,[],[f1787]) ).
thf(f1787,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1786]) ).
thf(f1786,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1785]) ).
thf(f1785,plain,
( ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1234,f271]) ).
thf(f271,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f270,plain,
( spl0_8
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f1234,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1233]) ).
thf(f1233,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK3 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f1223]) ).
thf(f1223,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK3 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1222]) ).
thf(f1222,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f49]) ).
thf(f49,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f48,plain,
( spl0_4
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f2298,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f2297]) ).
thf(f2297,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f2296]) ).
thf(f2296,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f2295,f2258]) ).
thf(f2258,plain,
( ( ( sK13 @ sK29 )
= $false )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f2233]) ).
thf(f2233,plain,
( ( ( ( ( sK3 @ sK28 @ sK29 )
& ( sK13 @ sK28 ) )
=> ( sK13 @ sK29 ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f2232]) ).
thf(f2232,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK28 @ Y0 )
& ( sK13 @ sK28 ) )
=> ( sK13 @ Y0 ) )
@ sK29 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f2207]) ).
thf(f2207,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK28 @ Y0 )
& ( sK13 @ sK28 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f2203]) ).
thf(f2203,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) )
@ sK28 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f434]) ).
thf(f434,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f433]) ).
thf(f433,plain,
( spl0_12
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f2295,plain,
( ( ( sK13 @ sK29 )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f2294]) ).
thf(f2294,plain,
( ( $true
= ( $true
=> ( sK13 @ sK29 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f2291,f2273]) ).
thf(f2273,plain,
( ( $true
= ( sK13 @ sK28 ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f2259]) ).
thf(f2259,plain,
( ( ( ( sK3 @ sK28 @ sK29 )
& ( sK13 @ sK28 ) )
= $true )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f2233]) ).
thf(f2291,plain,
( ( ( ( sK13 @ sK28 )
=> ( sK13 @ sK29 ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f2290]) ).
thf(f2290,plain,
( ( ( ( $true
& ( sK13 @ sK28 ) )
=> ( sK13 @ sK29 ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f2285]) ).
thf(f2285,plain,
( ( $true
= ( ( ( ( sK4 @ sK28 @ sK29 )
| $true )
& ( sK13 @ sK28 ) )
=> ( sK13 @ sK29 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f1968,f2276]) ).
thf(f2276,plain,
( ( ( sK3 @ sK28 @ sK29 )
= $true )
| ~ spl0_12 ),
inference(boolean_simplification,[],[f2275]) ).
thf(f2275,plain,
( ( ( ( sK3 @ sK28 @ sK29 )
& $true )
= $true )
| ~ spl0_12 ),
inference(backward_demodulation,[],[f2259,f2273]) ).
thf(f1968,plain,
( ! [X2: a,X1: a] :
( ( ( ( ( sK4 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
& ( sK13 @ X2 ) )
=> ( sK13 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1967]) ).
thf(f1967,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1951]) ).
thf(f1951,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1950]) ).
thf(f1950,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1934]) ).
thf(f1934,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1933]) ).
thf(f1933,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[],[f1813,f1932]) ).
thf(f1784,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1783]) ).
thf(f1783,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f1782]) ).
thf(f1782,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1781,f1747]) ).
thf(f1747,plain,
( ( ( sK13 @ sK27 )
= $false )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f1740]) ).
thf(f1740,plain,
( ( ( ( ( sK13 @ sK26 )
& ( sK4 @ sK26 @ sK27 ) )
=> ( sK13 @ sK27 ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f1739]) ).
thf(f1739,plain,
( ( ( ^ [Y0: a] :
( ( ( sK13 @ sK26 )
& ( sK4 @ sK26 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ sK27 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f1728]) ).
thf(f1728,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ sK26 )
& ( sK4 @ sK26 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f1726]) ).
thf(f1726,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) )
@ sK26 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f388]) ).
thf(f388,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f387]) ).
thf(f387,plain,
( spl0_9
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f1781,plain,
( ( ( sK13 @ sK27 )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1780]) ).
thf(f1780,plain,
( ( ( $true
=> ( sK13 @ sK27 ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1779,f1763]) ).
thf(f1763,plain,
( ( ( sK13 @ sK26 )
= $true )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f1748]) ).
thf(f1748,plain,
( ( ( ( sK13 @ sK26 )
& ( sK4 @ sK26 @ sK27 ) )
= $true )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f1740]) ).
thf(f1779,plain,
( ( ( ( sK13 @ sK26 )
=> ( sK13 @ sK27 ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1778]) ).
thf(f1778,plain,
( ( ( ( $true
& ( sK13 @ sK26 ) )
=> ( sK13 @ sK27 ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1774]) ).
thf(f1774,plain,
( ( $true
= ( ( ( $true
| ( sK3 @ sK26 @ sK27 ) )
& ( sK13 @ sK26 ) )
=> ( sK13 @ sK27 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f1568,f1765]) ).
thf(f1765,plain,
( ( ( sK4 @ sK26 @ sK27 )
= $true )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1764]) ).
thf(f1764,plain,
( ( $true
= ( $true
& ( sK4 @ sK26 @ sK27 ) ) )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f1748,f1763]) ).
thf(f1568,plain,
( ! [X2: a,X1: a] :
( ( ( ( ( sK4 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
& ( sK13 @ X2 ) )
=> ( sK13 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1567]) ).
thf(f1567,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1557]) ).
thf(f1557,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1556]) ).
thf(f1556,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1548]) ).
thf(f1548,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1547]) ).
thf(f1547,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[],[f1529,f1546]) ).
thf(f1546,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1529]) ).
thf(f1529,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1523]) ).
thf(f1523,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1522]) ).
thf(f1522,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[],[f1519]) ).
thf(f1519,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1518]) ).
thf(f1518,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1517]) ).
thf(f1517,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| $true )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[],[f1234,f268]) ).
thf(f268,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f267,plain,
( spl0_7
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f1428,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f1427]) ).
thf(f1427,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f1426]) ).
thf(f1426,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f1425]) ).
thf(f1425,plain,
( ( ~ $true = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f1424]) ).
thf(f1424,plain,
( ( ( ~ ( $true
| ( sK3 @ sK11 @ sK24 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1416,f1300]) ).
thf(f1300,plain,
( ( ( sK4 @ sK11 @ sK24 )
= $true )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f1294]) ).
thf(f1294,plain,
( ( ( ( sK4 @ sK11 @ sK24 )
=> ( sK13 @ sK24 ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1292]) ).
thf(f1292,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) )
@ sK24 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f391]) ).
thf(f391,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f390]) ).
thf(f390,plain,
( spl0_10
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f1416,plain,
( ( $true
= ( ~ ( ( sK4 @ sK11 @ sK24 )
| ( sK3 @ sK11 @ sK24 ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f1413]) ).
thf(f1413,plain,
( ( ( ( ( sK4 @ sK11 @ sK24 )
| ( sK3 @ sK11 @ sK24 ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f1400,f1299]) ).
thf(f1299,plain,
( ( ( sK13 @ sK24 )
= $false )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f1294]) ).
thf(f1400,plain,
( ! [X1: a] :
( ( ( ( sK4 @ sK11 @ X1 )
| ( sK3 @ sK11 @ X1 ) )
=> ( sK13 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1399]) ).
thf(f1399,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1289]) ).
thf(f1289,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1259]) ).
thf(f1259,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1248]) ).
thf(f1248,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1247]) ).
thf(f1247,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[],[f1237]) ).
thf(f1237,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1236]) ).
thf(f1236,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1235]) ).
thf(f1235,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| $true )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1234,f268]) ).
thf(f1206,plain,
( ~ spl0_1
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1205]) ).
thf(f1205,plain,
( $false
| ~ spl0_1
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f1204]) ).
thf(f1204,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(backward_demodulation,[],[f1197,f1203]) ).
thf(f1203,plain,
( ( ( ~ ( sK6 @ sK16 ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1202]) ).
thf(f1202,plain,
( ( ( ~ ( ( sK6 @ sK16 )
& $true ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1201]) ).
thf(f1201,plain,
( ( $false
= ( ~ ( ( sK6 @ sK16 )
& ( $true
| ( sK4 @ sK16 @ sK14 ) ) ) ) )
| ~ spl0_1
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1190,f512]) ).
thf(f512,plain,
( ( $true
= ( sK3 @ sK16 @ sK14 ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f511]) ).
thf(f511,plain,
( spl0_14
<=> ( $true
= ( sK3 @ sK16 @ sK14 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f1190,plain,
( ( ( ~ ( ( sK6 @ sK16 )
& ( ( sK3 @ sK16 @ sK14 )
| ( sK4 @ sK16 @ sK14 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1189]) ).
thf(f1189,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) )
@ sK16 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1179]) ).
thf(f1179,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f1178]) ).
thf(f1178,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) )
=> $false ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f1154,f1177]) ).
thf(f1177,plain,
( ( ( sK6 @ sK14 )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f1176]) ).
thf(f1176,plain,
( ( ( $true
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f1164,f1175]) ).
thf(f1175,plain,
( ( $true
= ( ( sK6 @ sK15 )
& ( ( sK3 @ sK15 @ sK14 )
| ( sK4 @ sK15 @ sK14 ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f1164]) ).
thf(f1164,plain,
( ( ( ( ( sK6 @ sK15 )
& ( ( sK3 @ sK15 @ sK14 )
| ( sK4 @ sK15 @ sK14 ) ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1163]) ).
thf(f1163,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) )
=> ( sK6 @ sK14 ) )
@ sK15 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1154]) ).
thf(f1154,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) )
=> ( sK6 @ sK14 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1150]) ).
thf(f1150,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1135]) ).
thf(f1135,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f1097]) ).
thf(f1097,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f1096]) ).
thf(f1096,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1093,f37]) ).
thf(f37,plain,
( ( sK6 @ sK2 )
= $false ),
inference(binary_proxy_clausification,[],[f26]) ).
thf(f26,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK2 ) )
= $false ),
inference(beta_eta_normalization,[],[f25]) ).
thf(f25,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f19]) ).
thf(f19,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK4 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK4 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK3 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK4 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK4 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK3 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK4 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK4 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK4 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK3 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK4 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK4 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK3 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK4 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( Y0 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y0 @ Y7 @ Y6 )
| ( sK3 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y3 @ Y6 )
| ( sK3 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK3 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( Y0 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( Y0 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK3 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( Y0 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y0 @ Y7 @ Y6 )
| ( sK3 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y3 @ Y6 )
| ( sK3 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK3 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( Y0 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( Y0 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK3 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( Y1 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( Y1 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( Y1 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ sK2 ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( Y1 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ sK2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y1 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( Y1 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( Y1 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ sK2 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y2 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y2 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y2 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y2 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y5 @ Y8 )
| ( Y1 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a > a > $o,X3: a] :
( ~ ( ( ! [X4: a,X5: a,X6: a] :
( ( ! [X7: a > $o] :
( ( ! [X8: a] :
( ( ( X1 @ X6 @ X8 )
| ( X2 @ X6 @ X8 ) )
=> ( X7 @ X8 ) )
& ! [X9: a,X10: a] :
( ( ( X7 @ X10 )
& ( ( X1 @ X10 @ X9 )
| ( X2 @ X10 @ X9 ) ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X5 ) )
& ! [X11: a > $o] :
( ( ! [X12: a] :
( ( ( X2 @ X5 @ X12 )
| ( X1 @ X5 @ X12 ) )
=> ( X11 @ X12 ) )
& ! [X13: a,X14: a] :
( ( ( ( X2 @ X13 @ X14 )
| ( X1 @ X13 @ X14 ) )
& ( X11 @ X13 ) )
=> ( X11 @ X14 ) ) )
=> ( X11 @ X4 ) ) )
=> ! [X15: a > $o] :
( ( ! [X16: a,X17: a] :
( ( ( ( X1 @ X17 @ X16 )
| ( X2 @ X17 @ X16 ) )
& ( X15 @ X17 ) )
=> ( X15 @ X16 ) )
& ! [X18: a] :
( ( ( X1 @ X6 @ X18 )
| ( X2 @ X6 @ X18 ) )
=> ( X15 @ X18 ) ) )
=> ( X15 @ X4 ) ) )
& ! [X19: a,X20: a] :
( ( ! [X21: a > $o] :
( ( ! [X22: a,X23: a] :
( ( ( X1 @ X23 @ X22 )
& ( X21 @ X23 ) )
=> ( X21 @ X22 ) )
& ! [X24: a] :
( ( X1 @ X20 @ X24 )
=> ( X21 @ X24 ) ) )
=> ( X21 @ X19 ) )
| ! [X25: a > $o] :
( ( ! [X26: a] :
( ( X2 @ X20 @ X26 )
=> ( X25 @ X26 ) )
& ! [X27: a,X28: a] :
( ( ( X25 @ X28 )
& ( X2 @ X28 @ X27 ) )
=> ( X25 @ X27 ) ) )
=> ( X25 @ X19 ) ) )
=> ! [X29: a > $o] :
( ( ! [X30: a,X31: a] :
( ( ( X29 @ X30 )
& ( ( X2 @ X30 @ X31 )
| ( X1 @ X30 @ X31 ) ) )
=> ( X29 @ X31 ) )
& ! [X32: a] :
( ( ( X2 @ X20 @ X32 )
| ( X1 @ X20 @ X32 ) )
=> ( X29 @ X32 ) ) )
=> ( X29 @ X19 ) ) ) )
=> ! [X33: a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( ( X1 @ X34 @ X35 )
| ( X2 @ X34 @ X35 ) )
& ( X33 @ X34 ) )
=> ( X33 @ X35 ) )
& ! [X36: a] :
( ( ( X1 @ X0 @ X36 )
| ( X2 @ X0 @ X36 ) )
=> ( X33 @ X36 ) ) )
=> ( X33 @ X3 ) ) )
| ! [X37: a > $o] :
( ( ! [X38: a] :
( ( ( X1 @ X0 @ X38 )
| ( X2 @ X0 @ X38 ) )
=> ( X37 @ X38 ) )
& ! [X39: a,X40: a] :
( ( ( X37 @ X40 )
& ( ( X2 @ X40 @ X39 )
| ( X1 @ X40 @ X39 ) ) )
=> ( X37 @ X39 ) ) )
=> ( X37 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X0: a > a > $o,X1: a > a > $o,X3: a] :
( ~ ( ( ! [X10: a,X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X8 @ X5 )
| ( X1 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
& ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X9 @ X5 )
| ( X0 @ X9 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
=> ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X8 @ X5 )
| ( X1 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X0 @ X6 @ X7 )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X1 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X2: a,X0: a > a > $o,X1: a > a > $o,X3: a] :
( ~ ( ( ! [X10: a,X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X8 @ X5 )
| ( X1 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
& ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X9 @ X5 )
| ( X0 @ X9 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
=> ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X8 @ X5 )
| ( X1 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X0 @ X6 @ X7 )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X1 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mmAN5JKWoX/Vampire---4.8_23399',cTHM251G_pme) ).
thf(f1093,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK2 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f1091]) ).
thf(f1091,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> ( sK6 @ sK2 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f1086,f55]) ).
thf(f55,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f38]) ).
thf(f38,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f26]) ).
thf(f1086,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK2 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1085]) ).
thf(f1085,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f30]) ).
thf(f30,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f29,plain,
( spl0_1
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f1197,plain,
( ( ( ~ ( sK6 @ sK16 ) )
= $true )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1196]) ).
thf(f1196,plain,
( ( $true
= ( ( sK6 @ sK16 )
=> $false ) )
| ~ spl0_1
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1102,f1177]) ).
thf(f1102,plain,
( ( ( ( sK6 @ sK16 )
=> ( sK6 @ sK14 ) )
= $true )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1101]) ).
thf(f1101,plain,
( ( ( ( $true
& ( sK6 @ sK16 ) )
=> ( sK6 @ sK14 ) )
= $true )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1100]) ).
thf(f1100,plain,
( ( ( ( ( ( sK4 @ sK16 @ sK14 )
| $true )
& ( sK6 @ sK16 ) )
=> ( sK6 @ sK14 ) )
= $true )
| ~ spl0_14 ),
inference(superposition,[],[f109,f512]) ).
thf(f109,plain,
! [X2: a,X1: a] :
( ( ( ( ( sK4 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) )
& ( sK6 @ X1 ) )
=> ( sK6 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[],[f108]) ).
thf(f108,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
& ( sK6 @ X1 ) )
=> ( sK6 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[],[f107]) ).
thf(f107,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
& ( sK6 @ X1 ) )
=> ( sK6 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f106]) ).
thf(f106,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f58]) ).
thf(f58,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f57]) ).
thf(f57,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& $true ) ),
inference(backward_demodulation,[],[f38,f55]) ).
thf(f1076,plain,
( ~ spl0_20
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1075]) ).
thf(f1075,plain,
( $false
| ~ spl0_20
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f1074]) ).
thf(f1074,plain,
( ( $true = $false )
| ~ spl0_20
| ~ spl0_23 ),
inference(boolean_simplification,[],[f1073]) ).
thf(f1073,plain,
( ( ~ $false = $false )
| ~ spl0_20
| ~ spl0_23 ),
inference(boolean_simplification,[],[f1072]) ).
thf(f1072,plain,
( ( $false
= ( ~ ( $false
& ( ( sK4 @ sK21 @ sK19 )
| ( sK3 @ sK21 @ sK19 ) ) ) ) )
| ~ spl0_20
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1071,f942]) ).
thf(f942,plain,
( ( $false
= ( sK10 @ sK21 ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f941]) ).
thf(f941,plain,
( spl0_23
<=> ( $false
= ( sK10 @ sK21 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f1071,plain,
( ( ( ~ ( ( sK10 @ sK21 )
& ( ( sK4 @ sK21 @ sK19 )
| ( sK3 @ sK21 @ sK19 ) ) ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f1070]) ).
thf(f1070,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) )
@ sK21 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f1056]) ).
thf(f1056,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) ) )
= $false )
| ~ spl0_20 ),
inference(boolean_simplification,[],[f1055]) ).
thf(f1055,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) )
=> $false ) )
= $false )
| ~ spl0_20 ),
inference(backward_demodulation,[],[f1024,f1054]) ).
thf(f1054,plain,
( ( $false
= ( sK10 @ sK19 ) )
| ~ spl0_20 ),
inference(boolean_simplification,[],[f1053]) ).
thf(f1053,plain,
( ( ( $true
=> ( sK10 @ sK19 ) )
= $false )
| ~ spl0_20 ),
inference(backward_demodulation,[],[f1037,f1052]) ).
thf(f1052,plain,
( ( $true
= ( ( sK10 @ sK20 )
& ( ( sK4 @ sK20 @ sK19 )
| ( sK3 @ sK20 @ sK19 ) ) ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f1037]) ).
thf(f1037,plain,
( ( ( ( ( sK10 @ sK20 )
& ( ( sK4 @ sK20 @ sK19 )
| ( sK3 @ sK20 @ sK19 ) ) )
=> ( sK10 @ sK19 ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f1036]) ).
thf(f1036,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) )
=> ( sK10 @ sK19 ) )
@ sK20 ) )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f1024]) ).
thf(f1024,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) )
=> ( sK10 @ sK19 ) ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f1022]) ).
thf(f1022,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) )
@ sK19 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f840]) ).
thf(f840,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f839]) ).
thf(f839,plain,
( spl0_20
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f1033,plain,
( spl0_23
| spl0_24
| ~ spl0_3
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f1017,f911,f45,f944,f941]) ).
thf(f944,plain,
( spl0_24
<=> ( $true
= ( sK10 @ sK19 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f45,plain,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f911,plain,
( spl0_21
<=> ( $true
= ( sK3 @ sK21 @ sK19 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f1017,plain,
( ( $true
= ( sK10 @ sK19 ) )
| ( $false
= ( sK10 @ sK21 ) )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1016]) ).
thf(f1016,plain,
( ( $true
= ( sK10 @ sK19 ) )
| ( ( ( sK10 @ sK21 )
& $true )
= $false )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1011]) ).
thf(f1011,plain,
( ( $true
= ( sK10 @ sK19 ) )
| ( $false
= ( ( sK10 @ sK21 )
& ( $true
| ( sK4 @ sK21 @ sK19 ) ) ) )
| ~ spl0_3
| ~ spl0_21 ),
inference(superposition,[],[f584,f912]) ).
thf(f912,plain,
( ( $true
= ( sK3 @ sK21 @ sK19 ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f911]) ).
thf(f584,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK10 @ X1 )
& ( ( sK3 @ X1 @ X2 )
| ( sK4 @ X1 @ X2 ) ) )
= $false )
| ( ( sK10 @ X2 )
= $true ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f573]) ).
thf(f573,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK10 @ X1 )
& ( ( sK3 @ X1 @ X2 )
| ( sK4 @ X1 @ X2 ) ) )
=> ( sK10 @ X2 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f572]) ).
thf(f572,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK3 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ X2 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f571]) ).
thf(f571,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK3 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f570]) ).
thf(f570,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f565]) ).
thf(f565,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f564]) ).
thf(f564,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f559,f563]) ).
thf(f563,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f559]) ).
thf(f559,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f557]) ).
thf(f557,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
=> ( sK10 @ sK9 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f556]) ).
thf(f556,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) )
@ sK10 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f549]) ).
thf(f549,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f548]) ).
thf(f548,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f543,f547]) ).
thf(f547,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f543]) ).
thf(f543,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f542]) ).
thf(f542,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK8 @ Y2 )
| ( sK3 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK9 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f539]) ).
thf(f539,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK8 @ Y2 )
| ( sK3 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f538]) ).
thf(f538,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f529]) ).
thf(f529,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f528]) ).
thf(f528,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f46]) ).
thf(f46,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f1032,plain,
( ~ spl0_20
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f1031]) ).
thf(f1031,plain,
( $false
| ~ spl0_20
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f1030]) ).
thf(f1030,plain,
( ( $true = $false )
| ~ spl0_20
| ~ spl0_24 ),
inference(beta_eta_normalization,[],[f1029]) ).
thf(f1029,plain,
( ( ( ^ [Y0: a] : $true
@ sK23 )
= $false )
| ~ spl0_20
| ~ spl0_24 ),
inference(sigma_clausification,[],[f1028]) ).
thf(f1028,plain,
( ( ( !! @ a
@ ^ [Y0: a] : $true )
= $false )
| ~ spl0_20
| ~ spl0_24 ),
inference(boolean_simplification,[],[f1027]) ).
thf(f1027,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) )
=> $true ) )
= $false )
| ~ spl0_20
| ~ spl0_24 ),
inference(forward_demodulation,[],[f1024,f945]) ).
thf(f945,plain,
( ( $true
= ( sK10 @ sK19 ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f944]) ).
thf(f1008,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1007]) ).
thf(f1007,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f1006]) ).
thf(f1006,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_26 ),
inference(boolean_simplification,[],[f1005]) ).
thf(f1005,plain,
( ( ~ $true = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_26 ),
inference(boolean_simplification,[],[f1004]) ).
thf(f1004,plain,
( ( ( ~ ( $true
| ( sK4 @ sK8 @ sK22 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_26 ),
inference(forward_demodulation,[],[f984,f993]) ).
thf(f993,plain,
( ( ( sK3 @ sK8 @ sK22 )
= $true )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f992]) ).
thf(f992,plain,
( spl0_26
<=> ( ( sK3 @ sK8 @ sK22 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f984,plain,
( ( ( ~ ( ( sK3 @ sK8 @ sK22 )
| ( sK4 @ sK8 @ sK22 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19 ),
inference(boolean_simplification,[],[f975]) ).
thf(f975,plain,
( ( ( ( ( sK3 @ sK8 @ sK22 )
| ( sK4 @ sK8 @ sK22 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19 ),
inference(superposition,[],[f642,f966]) ).
thf(f966,plain,
( ( $false
= ( sK10 @ sK22 ) )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f951]) ).
thf(f951,plain,
( ( $false
= ( ( ( sK4 @ sK8 @ sK22 )
| ( sK3 @ sK8 @ sK22 ) )
=> ( sK10 @ sK22 ) ) )
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f949]) ).
thf(f949,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) )
@ sK22 ) )
| ~ spl0_19 ),
inference(sigma_clausification,[],[f837]) ).
thf(f837,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f836]) ).
thf(f836,plain,
( spl0_19
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f642,plain,
( ! [X0: a] :
( $true
= ( ( ( sK3 @ sK8 @ X0 )
| ( sK4 @ sK8 @ X0 ) )
=> ( sK10 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f639]) ).
thf(f639,plain,
( ! [X0: a] :
( ( ( $true
& ( ( sK3 @ sK8 @ X0 )
| ( sK4 @ sK8 @ X0 ) ) )
=> ( sK10 @ X0 ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f573,f238]) ).
thf(f238,plain,
( ( ( sK10 @ sK8 )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f237,plain,
( spl0_6
<=> ( ( sK10 @ sK8 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f1001,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f1000]) ).
thf(f1000,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f999]) ).
thf(f999,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_25 ),
inference(boolean_simplification,[],[f998]) ).
thf(f998,plain,
( ( ~ $true = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_25 ),
inference(boolean_simplification,[],[f995]) ).
thf(f995,plain,
( ( $true
= ( ~ ( ( sK3 @ sK8 @ sK22 )
| $true ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_19
| ~ spl0_25 ),
inference(backward_demodulation,[],[f984,f990]) ).
thf(f990,plain,
( ( ( sK4 @ sK8 @ sK22 )
= $true )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f989]) ).
thf(f989,plain,
( spl0_25
<=> ( ( sK4 @ sK8 @ sK22 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f994,plain,
( spl0_25
| spl0_26
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f985,f836,f992,f989]) ).
thf(f985,plain,
( ( ( sK3 @ sK8 @ sK22 )
= $true )
| ( ( sK4 @ sK8 @ sK22 )
= $true )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f967]) ).
thf(f967,plain,
( ( ( ( sK4 @ sK8 @ sK22 )
| ( sK3 @ sK8 @ sK22 ) )
= $true )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f951]) ).
thf(f937,plain,
( ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f936]) ).
thf(f936,plain,
( $false
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f935]) ).
thf(f935,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(backward_demodulation,[],[f894,f934]) ).
thf(f934,plain,
( ( $false
= ( sK10 @ sK21 ) )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f933]) ).
thf(f933,plain,
( ( $true = $false )
| ( $false
= ( sK10 @ sK21 ) )
| ~ spl0_3
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f923,f851]) ).
thf(f851,plain,
( ( $false
= ( sK10 @ sK19 ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f850]) ).
thf(f850,plain,
( ( ( ( ( sK10 @ sK20 )
& ( ( sK4 @ sK20 @ sK19 )
| ( sK3 @ sK20 @ sK19 ) ) )
=> ( sK10 @ sK19 ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f849]) ).
thf(f849,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) )
=> ( sK10 @ sK19 ) )
@ sK20 ) )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f846]) ).
thf(f846,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) )
=> ( sK10 @ sK19 ) ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f844]) ).
thf(f844,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) )
@ sK19 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f840]) ).
thf(f923,plain,
( ( $true
= ( sK10 @ sK19 ) )
| ( $false
= ( sK10 @ sK21 ) )
| ~ spl0_3
| ~ spl0_22 ),
inference(boolean_simplification,[],[f922]) ).
thf(f922,plain,
( ( $true
= ( sK10 @ sK19 ) )
| ( ( ( sK10 @ sK21 )
& $true )
= $false )
| ~ spl0_3
| ~ spl0_22 ),
inference(boolean_simplification,[],[f919]) ).
thf(f919,plain,
( ( ( ( sK10 @ sK21 )
& ( ( sK3 @ sK21 @ sK19 )
| $true ) )
= $false )
| ( $true
= ( sK10 @ sK19 ) )
| ~ spl0_3
| ~ spl0_22 ),
inference(superposition,[],[f584,f915]) ).
thf(f915,plain,
( ( ( sK4 @ sK21 @ sK19 )
= $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f914]) ).
thf(f914,plain,
( spl0_22
<=> ( ( sK4 @ sK21 @ sK19 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f894,plain,
( ( $true
= ( sK10 @ sK21 ) )
| ~ spl0_20 ),
inference(boolean_simplification,[],[f893]) ).
thf(f893,plain,
( ( ( ( sK10 @ sK21 )
& $true )
= $true )
| ~ spl0_20 ),
inference(backward_demodulation,[],[f877,f891]) ).
thf(f891,plain,
( ( ( ( sK4 @ sK21 @ sK19 )
| ( sK3 @ sK21 @ sK19 ) )
= $true )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f877]) ).
thf(f877,plain,
( ( $true
= ( ( sK10 @ sK21 )
& ( ( sK4 @ sK21 @ sK19 )
| ( sK3 @ sK21 @ sK19 ) ) ) )
| ~ spl0_20 ),
inference(not_proxy_clausification,[],[f873]) ).
thf(f873,plain,
( ( ( ~ ( ( sK10 @ sK21 )
& ( ( sK4 @ sK21 @ sK19 )
| ( sK3 @ sK21 @ sK19 ) ) ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f872]) ).
thf(f872,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) )
@ sK21 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f856]) ).
thf(f856,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) ) )
= $false )
| ~ spl0_20 ),
inference(boolean_simplification,[],[f854]) ).
thf(f854,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ sK19 )
| ( sK3 @ Y0 @ sK19 ) ) )
=> $false ) )
= $false )
| ~ spl0_20 ),
inference(backward_demodulation,[],[f846,f851]) ).
thf(f916,plain,
( spl0_21
| spl0_22
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f907,f839,f914,f911]) ).
thf(f907,plain,
( ( ( sK4 @ sK21 @ sK19 )
= $true )
| ( $true
= ( sK3 @ sK21 @ sK19 ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f891]) ).
thf(f841,plain,
( spl0_19
| spl0_20
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f832,f45,f839,f836]) ).
thf(f832,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f829]) ).
thf(f829,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f738]) ).
thf(f738,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f737]) ).
thf(f737,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_3 ),
inference(superposition,[],[f730,f561]) ).
thf(f561,plain,
( ( ( sK10 @ sK9 )
= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f560]) ).
thf(f560,plain,
( ( ( $true
=> ( sK10 @ sK9 ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f557,f559]) ).
thf(f730,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK8 @ Y0 )
| ( sK3 @ sK8 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK9 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f729]) ).
thf(f729,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f623]) ).
thf(f623,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f547]) ).
thf(f636,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f635]) ).
thf(f635,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f634]) ).
thf(f634,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f633,f550]) ).
thf(f550,plain,
( ( $false
= ( sK10 @ sK18 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f545]) ).
thf(f545,plain,
( ( ( ( ( ( sK3 @ sK17 @ sK18 )
| ( sK4 @ sK17 @ sK18 ) )
& ( sK10 @ sK17 ) )
=> ( sK10 @ sK18 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f544]) ).
thf(f544,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK3 @ sK17 @ Y0 )
| ( sK4 @ sK17 @ Y0 ) )
& ( sK10 @ sK17 ) )
=> ( sK10 @ Y0 ) )
@ sK18 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f541]) ).
thf(f541,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK3 @ sK17 @ Y0 )
| ( sK4 @ sK17 @ Y0 ) )
& ( sK10 @ sK17 ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f540]) ).
thf(f540,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) )
@ sK17 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f235]) ).
thf(f235,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f234,plain,
( spl0_5
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f633,plain,
( ( $true
= ( sK10 @ sK18 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(boolean_simplification,[],[f632]) ).
thf(f632,plain,
( ( $true
= ( $true
=> ( sK10 @ sK18 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f629,f566]) ).
thf(f566,plain,
( ( $true
= ( sK10 @ sK17 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f551]) ).
thf(f551,plain,
( ( ( ( ( sK3 @ sK17 @ sK18 )
| ( sK4 @ sK17 @ sK18 ) )
& ( sK10 @ sK17 ) )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f545]) ).
thf(f629,plain,
( ( ( ( sK10 @ sK17 )
=> ( sK10 @ sK18 ) )
= $true )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[],[f628]) ).
thf(f628,plain,
( ( $true
= ( ( ( sK10 @ sK17 )
& $true )
=> ( sK10 @ sK18 ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[],[f626]) ).
thf(f626,plain,
( ( $true
= ( ( ( sK10 @ sK17 )
& ( ( sK3 @ sK17 @ sK18 )
| $true ) )
=> ( sK10 @ sK18 ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f573,f580]) ).
thf(f580,plain,
( ( ( sK4 @ sK17 @ sK18 )
= $true )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f579]) ).
thf(f579,plain,
( spl0_18
<=> ( ( sK4 @ sK17 @ sK18 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f619,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f618]) ).
thf(f618,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f617]) ).
thf(f617,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f616,f550]) ).
thf(f616,plain,
( ( $true
= ( sK10 @ sK18 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(boolean_simplification,[],[f615]) ).
thf(f615,plain,
( ( $true
= ( $true
=> ( sK10 @ sK18 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f612,f566]) ).
thf(f612,plain,
( ( ( ( sK10 @ sK17 )
=> ( sK10 @ sK18 ) )
= $true )
| ~ spl0_3
| ~ spl0_17 ),
inference(boolean_simplification,[],[f611]) ).
thf(f611,plain,
( ( $true
= ( ( ( sK10 @ sK17 )
& $true )
=> ( sK10 @ sK18 ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(boolean_simplification,[],[f609]) ).
thf(f609,plain,
( ( ( ( ( sK10 @ sK17 )
& ( $true
| ( sK4 @ sK17 @ sK18 ) ) )
=> ( sK10 @ sK18 ) )
= $true )
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f573,f577]) ).
thf(f577,plain,
( ( ( sK3 @ sK17 @ sK18 )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f576]) ).
thf(f576,plain,
( spl0_17
<=> ( ( sK3 @ sK17 @ sK18 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f581,plain,
( spl0_17
| spl0_18
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f574,f234,f579,f576]) ).
thf(f574,plain,
( ( ( sK4 @ sK17 @ sK18 )
= $true )
| ( ( sK3 @ sK17 @ sK18 )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f569]) ).
thf(f569,plain,
( ( $true
= ( ( sK3 @ sK17 @ sK18 )
| ( sK4 @ sK17 @ sK18 ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f568]) ).
thf(f568,plain,
( ( ( ( ( sK3 @ sK17 @ sK18 )
| ( sK4 @ sK17 @ sK18 ) )
& $true )
= $true )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f551,f566]) ).
thf(f523,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f522]) ).
thf(f522,plain,
( $false
| ~ spl0_1
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f521]) ).
thf(f521,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_13 ),
inference(forward_demodulation,[],[f520,f463]) ).
thf(f463,plain,
( ( ( sK6 @ sK14 )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f462]) ).
thf(f462,plain,
( ( ( ( ( sK6 @ sK15 )
& ( ( sK3 @ sK15 @ sK14 )
| ( sK4 @ sK15 @ sK14 ) ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f461]) ).
thf(f461,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) )
=> ( sK6 @ sK14 ) )
@ sK15 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f458]) ).
thf(f458,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) )
=> ( sK6 @ sK14 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f456]) ).
thf(f456,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f453]) ).
thf(f453,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f450]) ).
thf(f450,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f449]) ).
thf(f449,plain,
( ( ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f448,f55]) ).
thf(f448,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f441]) ).
thf(f441,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f439,f37]) ).
thf(f439,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK4 @ sK5 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK2 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f438]) ).
thf(f438,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f30]) ).
thf(f520,plain,
( ( ( sK6 @ sK14 )
= $true )
| ~ spl0_1
| ~ spl0_13 ),
inference(boolean_simplification,[],[f519]) ).
thf(f519,plain,
( ( ( $true
=> ( sK6 @ sK14 ) )
= $true )
| ~ spl0_1
| ~ spl0_13 ),
inference(forward_demodulation,[],[f518,f495]) ).
thf(f495,plain,
( ( ( sK6 @ sK16 )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f485]) ).
thf(f485,plain,
( ( ( ( sK6 @ sK16 )
& ( ( sK3 @ sK16 @ sK14 )
| ( sK4 @ sK16 @ sK14 ) ) )
= $true )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f481]) ).
thf(f481,plain,
( ( ( ~ ( ( sK6 @ sK16 )
& ( ( sK3 @ sK16 @ sK14 )
| ( sK4 @ sK16 @ sK14 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f480]) ).
thf(f480,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) )
@ sK16 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f468]) ).
thf(f468,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f466]) ).
thf(f466,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK14 )
| ( sK4 @ Y0 @ sK14 ) ) )
=> $false ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f458,f463]) ).
thf(f518,plain,
( ( ( ( sK6 @ sK16 )
=> ( sK6 @ sK14 ) )
= $true )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f517]) ).
thf(f517,plain,
( ( ( ( $true
& ( sK6 @ sK16 ) )
=> ( sK6 @ sK14 ) )
= $true )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f516]) ).
thf(f516,plain,
( ( $true
= ( ( ( $true
| ( sK3 @ sK16 @ sK14 ) )
& ( sK6 @ sK16 ) )
=> ( sK6 @ sK14 ) ) )
| ~ spl0_13 ),
inference(superposition,[],[f109,f509]) ).
thf(f509,plain,
( ( ( sK4 @ sK16 @ sK14 )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f508]) ).
thf(f508,plain,
( spl0_13
<=> ( ( sK4 @ sK16 @ sK14 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f513,plain,
( spl0_13
| spl0_14
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f506,f29,f511,f508]) ).
thf(f506,plain,
( ( ( sK4 @ sK16 @ sK14 )
= $true )
| ( $true
= ( sK3 @ sK16 @ sK14 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f497]) ).
thf(f497,plain,
( ( ( ( sK3 @ sK16 @ sK14 )
| ( sK4 @ sK16 @ sK14 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f496]) ).
thf(f496,plain,
( ( ( $true
& ( ( sK3 @ sK16 @ sK14 )
| ( sK4 @ sK16 @ sK14 ) ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f485,f495]) ).
thf(f435,plain,
( spl0_11
| spl0_12
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f426,f270,f48,f433,f430]) ).
thf(f426,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f420]) ).
thf(f420,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f416]) ).
thf(f416,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f415]) ).
thf(f415,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f411,f255]) ).
thf(f255,plain,
( ( $false
= ( sK13 @ sK12 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f254]) ).
thf(f254,plain,
( ( ( $true
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f251,f253]) ).
thf(f253,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f251]) ).
thf(f251,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK3 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f250]) ).
thf(f250,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f249]) ).
thf(f249,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f248]) ).
thf(f248,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f245,f247]) ).
thf(f247,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f245]) ).
thf(f245,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK3 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f244]) ).
thf(f244,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK3 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f243]) ).
thf(f243,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK3 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f242]) ).
thf(f242,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f49]) ).
thf(f411,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK11 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK12 ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f410]) ).
thf(f410,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[],[f271]) ).
thf(f392,plain,
( spl0_9
| spl0_10
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f383,f267,f48,f390,f387]) ).
thf(f383,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f361]) ).
thf(f361,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f291,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f290]) ).
thf(f290,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f279,f255]) ).
thf(f279,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK11 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK12 ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f278]) ).
thf(f278,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f268]) ).
thf(f272,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f265,f48,f270,f267]) ).
thf(f265,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $true )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f247]) ).
thf(f239,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f232,f45,f237,f234]) ).
thf(f232,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
= $false )
| ( ( sK10 @ sK8 )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f148]) ).
thf(f148,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
=> ( sK10 @ sK8 ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f147]) ).
thf(f147,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK10 @ Y0 ) )
=> ( sK10 @ Y1 ) ) ) )
& $true )
=> ( sK10 @ sK8 ) ) )
| ~ spl0_3 ),
inference(superposition,[],[f100,f129]) ).
thf(f129,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f128]) ).
thf(f128,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f86,f126]) ).
thf(f126,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f86]) ).
thf(f86,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f78]) ).
thf(f78,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
=> ( sK10 @ sK9 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f77]) ).
thf(f77,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) )
@ sK10 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f68]) ).
thf(f68,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f64]) ).
thf(f64,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f63]) ).
thf(f63,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK8 @ Y2 )
| ( sK3 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK9 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f60]) ).
thf(f60,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK8 @ Y2 )
| ( sK3 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f59]) ).
thf(f59,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f54]) ).
thf(f54,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f53]) ).
thf(f53,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f46]) ).
thf(f100,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK8 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f99]) ).
thf(f99,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f94]) ).
thf(f94,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f93]) ).
thf(f93,plain,
( ( ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f69,f92]) ).
thf(f92,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f69]) ).
thf(f69,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK8 @ Y1 )
| ( sK3 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f64]) ).
thf(f50,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f43,f32,f48,f45]) ).
thf(f32,plain,
( spl0_2
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f43,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f33,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f34,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f27,f32,f29]) ).
thf(f27,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f22]) ).
thf(f22,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( $false
= ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) ) ) ) ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( $false
= ( $false
| ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK4 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) ) ) ) ),
inference(backward_demodulation,[],[f17,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV154^5 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.32 % Computer : n018.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri May 3 12:16:46 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.33 This is a TH0_THM_NEQ_NAR problem
% 0.10/0.33 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.mmAN5JKWoX/Vampire---4.8_23399
% 0.17/0.34 % (23524)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 Vampire---4 for (3000ds/27Mi)
% 0.17/0.34 % (23525)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.17/0.34 % (23526)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.17/0.34 % (23527)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (3000ds/275Mi)
% 0.17/0.34 % (23523)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 Vampire---4 for (3000ds/4Mi)
% 0.17/0.34 % (23522)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (3000ds/183Mi)
% 0.17/0.34 % (23528)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (3000ds/18Mi)
% 0.17/0.34 % (23529)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (3000ds/3Mi)
% 0.17/0.34 % (23526)Instruction limit reached!
% 0.17/0.34 % (23526)------------------------------
% 0.17/0.34 % (23526)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (23526)Termination reason: Unknown
% 0.17/0.34 % (23526)Termination phase: shuffling
% 0.17/0.34
% 0.17/0.34 % (23526)Memory used [KB]: 1023
% 0.17/0.34 % (23526)Time elapsed: 0.002 s
% 0.17/0.34 % (23526)Instructions burned: 2 (million)
% 0.17/0.34 % (23526)------------------------------
% 0.17/0.34 % (23526)------------------------------
% 0.17/0.34 % (23523)Instruction limit reached!
% 0.17/0.34 % (23523)------------------------------
% 0.17/0.34 % (23523)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (23523)Termination reason: Unknown
% 0.17/0.34 % (23523)Termination phase: Preprocessing 3
% 0.17/0.34
% 0.17/0.34 % (23523)Memory used [KB]: 1023
% 0.17/0.34 % (23523)Time elapsed: 0.003 s
% 0.17/0.34 % (23523)Instructions burned: 4 (million)
% 0.17/0.34 % (23523)------------------------------
% 0.17/0.34 % (23523)------------------------------
% 0.17/0.34 % (23525)Instruction limit reached!
% 0.17/0.34 % (23525)------------------------------
% 0.17/0.34 % (23525)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (23525)Termination reason: Unknown
% 0.17/0.34 % (23525)Termination phase: Preprocessing 3
% 0.17/0.34
% 0.17/0.34 % (23525)Memory used [KB]: 1023
% 0.17/0.34 % (23525)Time elapsed: 0.003 s
% 0.17/0.34 % (23525)Instructions burned: 4 (million)
% 0.17/0.34 % (23525)------------------------------
% 0.17/0.34 % (23525)------------------------------
% 0.17/0.34 % (23529)Instruction limit reached!
% 0.17/0.34 % (23529)------------------------------
% 0.17/0.34 % (23529)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (23529)Termination reason: Unknown
% 0.17/0.34 % (23529)Termination phase: Preprocessing 3
% 0.17/0.34
% 0.17/0.34 % (23529)Memory used [KB]: 1023
% 0.17/0.34 % (23529)Time elapsed: 0.003 s
% 0.17/0.34 % (23529)Instructions burned: 5 (million)
% 0.17/0.34 % (23529)------------------------------
% 0.17/0.34 % (23529)------------------------------
% 0.17/0.34 % (23528)Instruction limit reached!
% 0.17/0.34 % (23528)------------------------------
% 0.17/0.34 % (23528)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (23528)Termination reason: Unknown
% 0.17/0.34 % (23528)Termination phase: Saturation
% 0.17/0.34
% 0.17/0.34 % (23528)Memory used [KB]: 5628
% 0.17/0.34 % (23528)Time elapsed: 0.007 s
% 0.17/0.34 % (23528)Instructions burned: 18 (million)
% 0.17/0.34 % (23528)------------------------------
% 0.17/0.34 % (23528)------------------------------
% 0.17/0.34 % (23534)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 Vampire---4 for (2999ds/37Mi)
% 0.17/0.34 % (23524)Instruction limit reached!
% 0.17/0.34 % (23524)------------------------------
% 0.17/0.34 % (23524)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (23524)Termination reason: Unknown
% 0.17/0.35 % (23524)Termination phase: Saturation
% 0.17/0.35
% 0.17/0.35 % (23524)Memory used [KB]: 5756
% 0.17/0.35 % (23524)Time elapsed: 0.010 s
% 0.17/0.35 % (23524)Instructions burned: 28 (million)
% 0.17/0.35 % (23524)------------------------------
% 0.17/0.35 % (23524)------------------------------
% 0.17/0.35 % (23535)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 Vampire---4 for (2999ds/15Mi)
% 0.17/0.35 % (23536)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.17/0.35 % (23537)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 Vampire---4 for (2999ds/1041Mi)
% 0.17/0.35 % (23536)Instruction limit reached!
% 0.17/0.35 % (23536)------------------------------
% 0.17/0.35 % (23536)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (23536)Termination reason: Unknown
% 0.17/0.35 % (23536)Termination phase: Preprocessing 2
% 0.17/0.35
% 0.17/0.35 % (23536)Memory used [KB]: 1023
% 0.17/0.35 % (23536)Time elapsed: 0.002 s
% 0.17/0.35 % (23536)Instructions burned: 3 (million)
% 0.17/0.35 % (23536)------------------------------
% 0.17/0.35 % (23536)------------------------------
% 0.17/0.35 % (23540)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.17/0.35 % (23535)Instruction limit reached!
% 0.17/0.35 % (23535)------------------------------
% 0.17/0.35 % (23535)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (23535)Termination reason: Unknown
% 0.17/0.35 % (23535)Termination phase: Saturation
% 0.17/0.35
% 0.17/0.35 % (23535)Memory used [KB]: 5756
% 0.17/0.35 % (23535)Time elapsed: 0.006 s
% 0.17/0.35 % (23535)Instructions burned: 15 (million)
% 0.17/0.35 % (23535)------------------------------
% 0.17/0.35 % (23535)------------------------------
% 0.17/0.35 % (23540)Instruction limit reached!
% 0.17/0.35 % (23540)------------------------------
% 0.17/0.35 % (23540)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (23540)Termination reason: Unknown
% 0.17/0.35 % (23540)Termination phase: Saturation
% 0.17/0.35
% 0.17/0.35 % (23540)Memory used [KB]: 1151
% 0.17/0.35 % (23540)Time elapsed: 0.004 s
% 0.17/0.35 % (23540)Instructions burned: 10 (million)
% 0.17/0.35 % (23543)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.17/0.35 % (23540)------------------------------
% 0.17/0.35 % (23540)------------------------------
% 0.17/0.35 % (23545)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 Vampire---4 for (2999ds/3Mi)
% 0.17/0.35 % (23534)Instruction limit reached!
% 0.17/0.35 % (23534)------------------------------
% 0.17/0.35 % (23534)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (23534)Termination reason: Unknown
% 0.17/0.35 % (23534)Termination phase: Saturation
% 0.17/0.35
% 0.17/0.35 % (23534)Memory used [KB]: 5628
% 0.17/0.35 % (23534)Time elapsed: 0.011 s
% 0.17/0.35 % (23534)Instructions burned: 38 (million)
% 0.17/0.35 % (23534)------------------------------
% 0.17/0.35 % (23534)------------------------------
% 0.17/0.35 % (23545)Instruction limit reached!
% 0.17/0.35 % (23545)------------------------------
% 0.17/0.35 % (23545)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (23545)Termination reason: Unknown
% 0.17/0.35 % (23545)Termination phase: Property scanning
% 0.17/0.35
% 0.17/0.35 % (23545)Memory used [KB]: 1023
% 0.17/0.35 % (23545)Time elapsed: 0.002 s
% 0.17/0.35 % (23545)Instructions burned: 3 (million)
% 0.17/0.35 % (23545)------------------------------
% 0.17/0.35 % (23545)------------------------------
% 0.17/0.36 % (23543)Instruction limit reached!
% 0.17/0.36 % (23543)------------------------------
% 0.17/0.36 % (23543)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (23543)Termination reason: Unknown
% 0.17/0.36 % (23543)Termination phase: Saturation
% 0.17/0.36
% 0.17/0.36 % (23543)Memory used [KB]: 5628
% 0.17/0.36 % (23543)Time elapsed: 0.006 s
% 0.17/0.36 % (23543)Instructions burned: 18 (million)
% 0.17/0.36 % (23543)------------------------------
% 0.17/0.36 % (23543)------------------------------
% 0.17/0.36 % (23548)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 Vampire---4 for (2999ds/3Mi)
% 0.17/0.36 % (23548)Instruction limit reached!
% 0.17/0.36 % (23548)------------------------------
% 0.17/0.36 % (23548)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (23548)Termination reason: Unknown
% 0.17/0.36 % (23548)Termination phase: shuffling
% 0.17/0.36
% 0.17/0.36 % (23548)Memory used [KB]: 1023
% 0.17/0.36 % (23548)Time elapsed: 0.002 s
% 0.17/0.36 % (23548)Instructions burned: 3 (million)
% 0.17/0.36 % (23548)------------------------------
% 0.17/0.36 % (23548)------------------------------
% 0.17/0.36 % (23549)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.17/0.36 % (23551)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.17/0.36 % (23553)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.17/0.36 % (23551)Instruction limit reached!
% 0.17/0.36 % (23551)------------------------------
% 0.17/0.36 % (23551)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (23551)Termination reason: Unknown
% 0.17/0.36 % (23551)Termination phase: shuffling
% 0.17/0.36
% 0.17/0.36 % (23551)Memory used [KB]: 1023
% 0.17/0.36 % (23549)Instruction limit reached!
% 0.17/0.36 % (23549)------------------------------
% 0.17/0.36 % (23549)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (23549)Termination reason: Unknown
% 0.17/0.36 % (23549)Termination phase: Saturation
% 0.17/0.36
% 0.17/0.36 % (23549)Memory used [KB]: 5628
% 0.17/0.36 % (23549)Time elapsed: 0.004 s
% 0.17/0.36 % (23549)Instructions burned: 10 (million)
% 0.17/0.36 % (23549)------------------------------
% 0.17/0.36 % (23549)------------------------------
% 0.17/0.36 % (23551)Time elapsed: 0.002 s
% 0.17/0.36 % (23551)Instructions burned: 3 (million)
% 0.17/0.36 % (23551)------------------------------
% 0.17/0.36 % (23551)------------------------------
% 0.17/0.36 % (23553)Instruction limit reached!
% 0.17/0.36 % (23553)------------------------------
% 0.17/0.36 % (23553)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (23553)Termination reason: Unknown
% 0.17/0.36 % (23553)Termination phase: Preprocessing 3
% 0.17/0.36
% 0.17/0.36 % (23553)Memory used [KB]: 1151
% 0.17/0.36 % (23553)Time elapsed: 0.003 s
% 0.17/0.36 % (23553)Instructions burned: 6 (million)
% 0.17/0.36 % (23553)------------------------------
% 0.17/0.36 % (23553)------------------------------
% 0.17/0.37 % (23554)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.17/0.37 % (23556)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.17/0.37 % (23558)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.17/0.37 % (23559)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 Vampire---4 for (2999ds/902Mi)
% 0.17/0.37 % (23554)Instruction limit reached!
% 0.17/0.37 % (23554)------------------------------
% 0.17/0.37 % (23554)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (23554)Termination reason: Unknown
% 0.17/0.37 % (23554)Termination phase: Saturation
% 0.17/0.37
% 0.17/0.37 % (23554)Memory used [KB]: 5756
% 0.17/0.37 % (23554)Time elapsed: 0.007 s
% 0.17/0.37 % (23554)Instructions burned: 19 (million)
% 0.17/0.37 % (23554)------------------------------
% 0.17/0.37 % (23554)------------------------------
% 0.17/0.37 % (23561)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 Vampire---4 for (2999ds/21Mi)
% 0.17/0.37 % (23558)Instruction limit reached!
% 0.17/0.37 % (23558)------------------------------
% 0.17/0.37 % (23558)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (23558)Termination reason: Unknown
% 0.17/0.37 % (23558)Termination phase: Property scanning
% 0.17/0.37
% 0.17/0.37 % (23558)Memory used [KB]: 1151
% 0.17/0.37 % (23558)Time elapsed: 0.003 s
% 0.17/0.37 % (23558)Instructions burned: 6 (million)
% 0.17/0.37 % (23558)------------------------------
% 0.17/0.37 % (23558)------------------------------
% 0.17/0.38 % (23564)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.17/0.38 % (23561)Instruction limit reached!
% 0.17/0.38 % (23561)------------------------------
% 0.17/0.38 % (23561)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.38 % (23561)Termination reason: Unknown
% 0.17/0.38 % (23561)Termination phase: Saturation
% 0.17/0.38
% 0.17/0.38 % (23561)Memory used [KB]: 5756
% 0.17/0.38 % (23561)Time elapsed: 0.008 s
% 0.17/0.38 % (23561)Instructions burned: 23 (million)
% 0.17/0.38 % (23561)------------------------------
% 0.17/0.38 % (23561)------------------------------
% 0.17/0.38 % (23566)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 Vampire---4 for (2999ds/6Mi)
% 0.17/0.38 % (23564)Instruction limit reached!
% 0.17/0.38 % (23564)------------------------------
% 0.17/0.38 % (23564)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.38 % (23564)Termination reason: Unknown
% 0.17/0.38 % (23564)Termination phase: Saturation
% 0.17/0.38
% 0.17/0.38 % (23564)Memory used [KB]: 5500
% 0.17/0.38 % (23564)Time elapsed: 0.003 s
% 0.17/0.38 % (23564)Instructions burned: 7 (million)
% 0.17/0.38 % (23564)------------------------------
% 0.17/0.38 % (23564)------------------------------
% 0.17/0.38 % (23566)Instruction limit reached!
% 0.17/0.38 % (23566)------------------------------
% 0.17/0.38 % (23566)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.38 % (23566)Termination reason: Unknown
% 0.17/0.38 % (23566)Termination phase: Saturation
% 0.17/0.38
% 0.17/0.38 % (23566)Memory used [KB]: 1023
% 0.17/0.38 % (23566)Time elapsed: 0.003 s
% 0.17/0.38 % (23566)Instructions burned: 7 (million)
% 0.17/0.38 % (23566)------------------------------
% 0.17/0.38 % (23566)------------------------------
% 0.17/0.39 % (23572)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.17/0.39 % (23574)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 Vampire---4 for (2999ds/779Mi)
% 0.17/0.39 % (23576)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 Vampire---4 for (2999ds/19Mi)
% 0.17/0.39 % (23522)Instruction limit reached!
% 0.17/0.39 % (23522)------------------------------
% 0.17/0.39 % (23522)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.39 % (23522)Termination reason: Unknown
% 0.17/0.39 % (23522)Termination phase: Saturation
% 0.17/0.39
% 0.17/0.39 % (23522)Memory used [KB]: 6652
% 0.17/0.39 % (23522)Time elapsed: 0.057 s
% 0.17/0.39 % (23522)Instructions burned: 184 (million)
% 0.17/0.39 % (23522)------------------------------
% 0.17/0.39 % (23522)------------------------------
% 0.17/0.39 % (23576)Instruction limit reached!
% 0.17/0.39 % (23576)------------------------------
% 0.17/0.39 % (23576)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.39 % (23576)Termination reason: Unknown
% 0.17/0.39 % (23576)Termination phase: Saturation
% 0.17/0.39
% 0.17/0.39 % (23576)Memory used [KB]: 5500
% 0.17/0.39 % (23576)Time elapsed: 0.006 s
% 0.17/0.39 % (23576)Instructions burned: 20 (million)
% 0.17/0.39 % (23576)------------------------------
% 0.17/0.39 % (23576)------------------------------
% 0.17/0.40 % (23581)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2999ds/879Mi)
% 0.17/0.40 % (23583)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2999ds/17Mi)
% 0.17/0.41 % (23583)Instruction limit reached!
% 0.17/0.41 % (23583)------------------------------
% 0.17/0.41 % (23583)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (23583)Termination reason: Unknown
% 0.17/0.41 % (23583)Termination phase: Saturation
% 0.17/0.41
% 0.17/0.41 % (23583)Memory used [KB]: 5756
% 0.17/0.41 % (23583)Time elapsed: 0.007 s
% 0.17/0.41 % (23583)Instructions burned: 18 (million)
% 0.17/0.41 % (23583)------------------------------
% 0.17/0.41 % (23583)------------------------------
% 0.17/0.42 % (23588)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.17/0.42 % (23588)Instruction limit reached!
% 0.17/0.42 % (23588)------------------------------
% 0.17/0.42 % (23588)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.42 % (23588)Termination reason: Unknown
% 0.17/0.42 % (23588)Termination phase: shuffling
% 0.17/0.42
% 0.17/0.42 % (23588)Memory used [KB]: 1023
% 0.17/0.42 % (23588)Time elapsed: 0.002 s
% 0.17/0.42 % (23588)Instructions burned: 3 (million)
% 0.17/0.42 % (23588)------------------------------
% 0.17/0.42 % (23588)------------------------------
% 0.17/0.42 % (23527)Instruction limit reached!
% 0.17/0.42 % (23527)------------------------------
% 0.17/0.42 % (23527)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.42 % (23527)Termination reason: Unknown
% 0.17/0.42 % (23527)Termination phase: Saturation
% 0.17/0.42
% 0.17/0.42 % (23527)Memory used [KB]: 6396
% 0.17/0.42 % (23527)Time elapsed: 0.087 s
% 0.17/0.42 % (23527)Instructions burned: 277 (million)
% 0.17/0.42 % (23527)------------------------------
% 0.17/0.42 % (23527)------------------------------
% 0.17/0.42 % (23592)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2999ds/30Mi)
% 0.17/0.43 % (23597)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2999ds/127Mi)
% 0.17/0.43 % (23592)Instruction limit reached!
% 0.17/0.43 % (23592)------------------------------
% 0.17/0.43 % (23592)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.43 % (23592)Termination reason: Unknown
% 0.17/0.43 % (23592)Termination phase: Saturation
% 0.17/0.43
% 0.17/0.43 % (23592)Memory used [KB]: 5756
% 0.17/0.43 % (23592)Time elapsed: 0.011 s
% 0.17/0.43 % (23592)Instructions burned: 32 (million)
% 0.17/0.43 % (23592)------------------------------
% 0.17/0.43 % (23592)------------------------------
% 0.17/0.44 % (23603)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on Vampire---4 for (2999ds/100Mi)
% 0.17/0.47 % (23597)Instruction limit reached!
% 0.17/0.47 % (23597)------------------------------
% 0.17/0.47 % (23597)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.47 % (23597)Termination reason: Unknown
% 0.17/0.47 % (23597)Termination phase: Saturation
% 0.17/0.47
% 0.17/0.47 % (23597)Memory used [KB]: 6268
% 0.17/0.47 % (23597)Time elapsed: 0.039 s
% 0.17/0.47 % (23597)Instructions burned: 127 (million)
% 0.17/0.47 % (23597)------------------------------
% 0.17/0.47 % (23597)------------------------------
% 0.17/0.47 % (23537)First to succeed.
% 0.17/0.47 % (23603)Instruction limit reached!
% 0.17/0.47 % (23603)------------------------------
% 0.17/0.47 % (23603)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.47 % (23603)Termination reason: Unknown
% 0.17/0.47 % (23603)Termination phase: Saturation
% 0.17/0.47
% 0.17/0.47 % (23603)Memory used [KB]: 6140
% 0.17/0.47 % (23603)Time elapsed: 0.034 s
% 0.17/0.47 % (23603)Instructions burned: 100 (million)
% 0.17/0.47 % (23603)------------------------------
% 0.17/0.47 % (23603)------------------------------
% 0.17/0.48 % (23621)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.17/0.48 % (23621)Instruction limit reached!
% 0.17/0.48 % (23621)------------------------------
% 0.17/0.48 % (23621)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.48 % (23621)Termination reason: Unknown
% 0.17/0.48 % (23621)Termination phase: shuffling
% 0.17/0.48
% 0.17/0.48 % (23621)Memory used [KB]: 1023
% 0.17/0.48 % (23621)Time elapsed: 0.002 s
% 0.17/0.48 % (23621)Instructions burned: 3 (million)
% 0.17/0.48 % (23621)------------------------------
% 0.17/0.48 % (23621)------------------------------
% 0.17/0.48 % (23625)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on Vampire---4 for (2998ds/20Mi)
% 0.17/0.48 % (23537)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for Vampire---4
% 0.17/0.48 % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.49 % (23537)------------------------------
% 0.17/0.49 % (23537)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.49 % (23537)Termination reason: Refutation
% 0.17/0.49
% 0.17/0.49 % (23537)Memory used [KB]: 7164
% 0.17/0.49 % (23537)Time elapsed: 0.138 s
% 0.17/0.49 % (23537)Instructions burned: 369 (million)
% 0.17/0.49 % (23537)------------------------------
% 0.17/0.49 % (23537)------------------------------
% 0.17/0.49 % (23520)Success in time 0.141 s
% 0.17/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------