TSTP Solution File: SEV141^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV141^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:12:07 EDT 2024
% Result : Theorem 1.48s 0.59s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 62
% Syntax : Number of formulae : 287 ( 16 unt; 46 typ; 0 def)
% Number of atoms : 2517 ( 229 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 8081 ( 349 ~; 437 |; 417 &;5074 @)
% ( 15 <=>; 652 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 677 ( 677 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 52 con; 0-2 aty)
% (1137 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1368 (1233 ^ 134 !; 0 ?;1368 :)
% ( 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 > a > $o ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a > a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a > a > $o ).
thf(func_def_29,type,
sK10: a > a > $o ).
thf(func_def_30,type,
sK11: a > a > $o ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: ( a > a > $o ) > a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a ).
thf(func_def_50,type,
sK31: a ).
thf(func_def_51,type,
sK32: a ).
thf(func_def_52,type,
sK33: a ).
thf(func_def_53,type,
sK34: a ).
thf(func_def_54,type,
sK35: a ).
thf(func_def_55,type,
sK36: a ).
thf(func_def_56,type,
sK37: a ).
thf(func_def_57,type,
sK38: a > a > $o ).
thf(func_def_58,type,
sK39: a > a > $o ).
thf(func_def_59,type,
sK40: a ).
thf(func_def_60,type,
sK41: a ).
thf(func_def_61,type,
sK42: a ).
thf(func_def_62,type,
sK43: a ).
thf(func_def_63,type,
sK44: a ).
thf(f1723,plain,
$false,
inference(avatar_sat_refutation,[],[f27,f34,f38,f101,f130,f345,f382,f452,f588,f633,f695,f817,f871,f875,f1312,f1356,f1722]) ).
thf(f1722,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f1721]) ).
thf(f1721,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f1720]) ).
thf(f1720,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1713,f1553]) ).
thf(f1553,plain,
( ( $false
= ( sK10 @ sK8 @ sK7 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1552]) ).
thf(f1552,plain,
( ( ( $true
=> ( sK10 @ sK8 @ sK7 ) )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(backward_demodulation,[],[f1544,f1551]) ).
thf(f1551,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1544]) ).
thf(f1544,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK10 @ sK8 @ sK7 ) )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1542]) ).
thf(f1542,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK10 )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(sigma_clausification,[],[f1420]) ).
thf(f1420,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1407]) ).
thf(f1407,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f1385]) ).
thf(f1385,plain,
( ( $true
= ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1376]) ).
thf(f1376,plain,
( ( $true
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f969,f1375]) ).
thf(f1375,plain,
( ( ( sK6 @ sK8 @ sK7 )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1374]) ).
thf(f1374,plain,
( ( ( $true
=> ( sK6 @ sK8 @ sK7 ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1373]) ).
thf(f1373,plain,
( ( $false
= ( ( $true
| ( sK3 @ sK8 @ sK7 ) )
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1372,f129]) ).
thf(f129,plain,
( ( ( sK2 @ sK8 @ sK7 )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f128,plain,
( spl0_8
<=> ( ( sK2 @ sK8 @ sK7 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f1372,plain,
( ( $false
= ( ( ( sK2 @ sK8 @ sK7 )
| ( sK3 @ sK8 @ sK7 ) )
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1371]) ).
thf(f1371,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK7 )
| ( sK3 @ Y0 @ sK7 ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK8 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f1366]) ).
thf(f1366,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK7 )
| ( sK3 @ Y0 @ sK7 ) )
=> ( sK6 @ Y0 @ sK7 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1362]) ).
thf(f1362,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK7 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f97]) ).
thf(f97,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f96]) ).
thf(f96,plain,
( spl0_5
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f969,plain,
( ! [X2: a,X1: a] :
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X2 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ X2 @ X1 ) ) ) )
=> ( sK6 @ X2 @ X1 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f968]) ).
thf(f968,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK6 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f958]) ).
thf(f958,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK6 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f957]) ).
thf(f957,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f905]) ).
thf(f905,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f896]) ).
thf(f896,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f892]) ).
thf(f892,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f891]) ).
thf(f891,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f30]) ).
thf(f30,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f29,plain,
( spl0_3
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f1713,plain,
( ( ( sK10 @ sK8 @ sK7 )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1709]) ).
thf(f1709,plain,
( ( ( $true
=> ( sK10 @ sK8 @ sK7 ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f1703,f129]) ).
thf(f1703,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X1 @ X2 )
=> ( sK10 @ X1 @ X2 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1702]) ).
thf(f1702,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK10 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(pi_clausification,[],[f1699]) ).
thf(f1699,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK10 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1698]) ).
thf(f1698,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK10 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(pi_clausification,[],[f1695]) ).
thf(f1695,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1694]) ).
thf(f1694,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
& $true ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(backward_demodulation,[],[f1551,f1692]) ).
thf(f1692,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y2 @ Y0 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1551]) ).
thf(f1356,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f1355]) ).
thf(f1355,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f1352]) ).
thf(f1352,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f923,f1345]) ).
thf(f1345,plain,
( ( $false
= ( ( ( sK6 @ sK40 @ sK41 )
& ( sK6 @ sK42 @ sK40 ) )
=> ( sK6 @ sK42 @ sK41 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1344]) ).
thf(f1344,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK40 @ sK41 )
& ( sK6 @ Y0 @ sK40 ) )
=> ( sK6 @ Y0 @ sK41 ) )
@ sK42 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f1341]) ).
thf(f1341,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK40 @ sK41 )
& ( sK6 @ Y0 @ sK40 ) )
=> ( sK6 @ Y0 @ sK41 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1340]) ).
thf(f1340,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK40 @ Y0 )
& ( sK6 @ Y1 @ sK40 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK41 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f1334]) ).
thf(f1334,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK40 @ Y0 )
& ( sK6 @ Y1 @ sK40 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1332]) ).
thf(f1332,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) )
@ sK40 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f100]) ).
thf(f100,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f99]) ).
thf(f99,plain,
( spl0_6
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f923,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK6 @ X3 @ X1 )
& ( sK6 @ X2 @ X3 ) )
=> ( sK6 @ X2 @ X1 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f922]) ).
thf(f922,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ X1 )
& ( sK6 @ X2 @ Y0 ) )
=> ( sK6 @ X2 @ X1 ) )
@ X3 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f917]) ).
thf(f917,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ X1 )
& ( sK6 @ X2 @ Y0 ) )
=> ( sK6 @ X2 @ X1 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f916]) ).
thf(f916,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ X1 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f915]) ).
thf(f915,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ X1 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ X1 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f914]) ).
thf(f914,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f907]) ).
thf(f907,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f906]) ).
thf(f906,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f896,f905]) ).
thf(f1312,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1311]) ).
thf(f1311,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f1310]) ).
thf(f1310,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1309]) ).
thf(f1309,plain,
( ( $true = ~ $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1304,f126]) ).
thf(f126,plain,
( ( ( sK3 @ sK8 @ sK7 )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f125]) ).
thf(f125,plain,
( spl0_7
<=> ( ( sK3 @ sK8 @ sK7 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f1304,plain,
( ( ( ~ ( sK3 @ sK8 @ sK7 ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1282]) ).
thf(f1282,plain,
( ( ( ( sK3 @ sK8 @ sK7 )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f1272,f1196]) ).
thf(f1196,plain,
( ( ( sK38 @ sK8 @ sK7 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1195]) ).
thf(f1195,plain,
( ( $false
= ( $true
=> ( sK38 @ sK8 @ sK7 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1182,f1194]) ).
thf(f1194,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK38 @ Y2 @ Y1 )
& ( sK38 @ Y0 @ Y2 ) )
=> ( sK38 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK38 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1182]) ).
thf(f1182,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK38 @ Y2 @ Y1 )
& ( sK38 @ Y0 @ Y2 ) )
=> ( sK38 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK38 @ Y0 @ Y1 ) ) ) ) )
=> ( sK38 @ sK8 @ sK7 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1179]) ).
thf(f1179,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK38 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f1007]) ).
thf(f1007,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f982]) ).
thf(f982,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(not_proxy_clausification,[],[f980]) ).
thf(f980,plain,
( ( $true
= ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f979]) ).
thf(f979,plain,
( ( $true
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f969,f114]) ).
thf(f114,plain,
( ( ( sK6 @ sK8 @ sK7 )
= $false )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f113]) ).
thf(f113,plain,
( ( ( $true
=> ( sK6 @ sK8 @ sK7 ) )
= $false )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f110,f112]) ).
thf(f112,plain,
( ( ( ( sK2 @ sK8 @ sK7 )
| ( sK3 @ sK8 @ sK7 ) )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f110]) ).
thf(f110,plain,
( ( $false
= ( ( ( sK2 @ sK8 @ sK7 )
| ( sK3 @ sK8 @ sK7 ) )
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f109]) ).
thf(f109,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK7 )
| ( sK3 @ Y0 @ sK7 ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK8 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f108]) ).
thf(f108,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK7 )
| ( sK3 @ Y0 @ sK7 ) )
=> ( sK6 @ Y0 @ sK7 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f104]) ).
thf(f104,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK7 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f97]) ).
thf(f1272,plain,
( ! [X2: a,X1: a] :
( ( ( sK3 @ X1 @ X2 )
=> ( sK38 @ X1 @ X2 ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1271]) ).
thf(f1271,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK38 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f1262]) ).
thf(f1262,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK38 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1261]) ).
thf(f1261,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK38 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f1252]) ).
thf(f1252,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK38 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1251]) ).
thf(f1251,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK38 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1194,f1250]) ).
thf(f1250,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK38 @ Y2 @ Y1 )
& ( sK38 @ Y0 @ Y2 ) )
=> ( sK38 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1194]) ).
thf(f875,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f874]) ).
thf(f874,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f873]) ).
thf(f873,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f23,f33]) ).
thf(f33,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f32,plain,
( spl0_4
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f23,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f22,plain,
( spl0_1
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f871,plain,
( ~ spl0_4
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f870]) ).
thf(f870,plain,
( $false
| ~ spl0_4
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f869]) ).
thf(f869,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_27 ),
inference(boolean_simplification,[],[f868]) ).
thf(f868,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_27 ),
inference(boolean_simplification,[],[f867]) ).
thf(f867,plain,
( ( ( ~ ( $true
| ( sK3 @ sK33 @ sK34 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_27 ),
inference(forward_demodulation,[],[f865,f844]) ).
thf(f844,plain,
( ( ( sK2 @ sK33 @ sK34 )
= $true )
| ~ spl0_27 ),
inference(binary_proxy_clausification,[],[f842]) ).
thf(f842,plain,
( ( $false
= ( ( sK2 @ sK33 @ sK34 )
=> ( sK11 @ sK33 @ sK34 ) ) )
| ~ spl0_27 ),
inference(beta_eta_normalization,[],[f841]) ).
thf(f841,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK33 @ Y0 )
=> ( sK11 @ sK33 @ Y0 ) )
@ sK34 )
= $false )
| ~ spl0_27 ),
inference(sigma_clausification,[],[f832]) ).
thf(f832,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK33 @ Y0 )
=> ( sK11 @ sK33 @ Y0 ) ) )
= $false )
| ~ spl0_27 ),
inference(beta_eta_normalization,[],[f828]) ).
thf(f828,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK33 ) )
| ~ spl0_27 ),
inference(sigma_clausification,[],[f816]) ).
thf(f816,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f815]) ).
thf(f815,plain,
( spl0_27
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
thf(f865,plain,
( ( ( ~ ( ( sK2 @ sK33 @ sK34 )
| ( sK3 @ sK33 @ sK34 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_27 ),
inference(boolean_simplification,[],[f860]) ).
thf(f860,plain,
( ( $true
= ( ( ( sK2 @ sK33 @ sK34 )
| ( sK3 @ sK33 @ sK34 ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_27 ),
inference(superposition,[],[f271,f843]) ).
thf(f843,plain,
( ( ( sK11 @ sK33 @ sK34 )
= $false )
| ~ spl0_27 ),
inference(binary_proxy_clausification,[],[f842]) ).
thf(f271,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
=> ( sK11 @ X2 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f270]) ).
thf(f270,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f269]) ).
thf(f269,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ X1 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f268]) ).
thf(f268,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f264]) ).
thf(f264,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f263]) ).
thf(f263,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f254,f262]) ).
thf(f262,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f254]) ).
thf(f254,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f252]) ).
thf(f252,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
=> ( sK11 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f251]) ).
thf(f251,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f33]) ).
thf(f817,plain,
( spl0_27
| spl0_12
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f811,f450,f340,f343,f815]) ).
thf(f343,plain,
( spl0_12
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f340,plain,
( spl0_11
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f450,plain,
( spl0_14
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f811,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_11
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f805]) ).
thf(f805,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_14 ),
inference(not_proxy_clausification,[],[f781]) ).
thf(f781,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ~ spl0_11
| ~ spl0_14 ),
inference(boolean_simplification,[],[f777]) ).
thf(f777,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f767,f401]) ).
thf(f401,plain,
( ( ( sK11 @ sK16 @ sK15 )
= $false )
| ~ spl0_11 ),
inference(boolean_simplification,[],[f400]) ).
thf(f400,plain,
( ( $false
= ( $true
=> ( sK11 @ sK16 @ sK15 ) ) )
| ~ spl0_11 ),
inference(backward_demodulation,[],[f397,f399]) ).
thf(f399,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) ) ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f397]) ).
thf(f397,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) ) )
=> ( sK11 @ sK16 @ sK15 ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f396]) ).
thf(f396,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK15 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK15 ) ) ) )
=> ( sK11 @ Y0 @ sK15 ) )
@ sK16 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f394]) ).
thf(f394,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK15 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK15 ) ) ) )
=> ( sK11 @ Y0 @ sK15 ) ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f389]) ).
thf(f389,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ sK15 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f341]) ).
thf(f341,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f340]) ).
thf(f767,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK16 @ sK15 ) )
= $true )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f766]) ).
thf(f766,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) )
@ X1 )
= $true )
| ~ spl0_14 ),
inference(pi_clausification,[],[f451]) ).
thf(f451,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f450]) ).
thf(f695,plain,
( ~ spl0_4
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f694]) ).
thf(f694,plain,
( $false
| ~ spl0_4
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f693]) ).
thf(f693,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_21 ),
inference(boolean_simplification,[],[f692]) ).
thf(f692,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_21 ),
inference(boolean_simplification,[],[f691]) ).
thf(f691,plain,
( ( ( ~ ( ( sK2 @ sK27 @ sK28 )
| $true ) )
= $true )
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f690,f666]) ).
thf(f666,plain,
( ( ( sK3 @ sK27 @ sK28 )
= $true )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f664]) ).
thf(f664,plain,
( ( $false
= ( ( sK3 @ sK27 @ sK28 )
=> ( sK11 @ sK27 @ sK28 ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f663]) ).
thf(f663,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK27 @ Y0 )
=> ( sK11 @ sK27 @ Y0 ) )
@ sK28 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f654]) ).
thf(f654,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK27 @ Y0 )
=> ( sK11 @ sK27 @ Y0 ) ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f650]) ).
thf(f650,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ sK27 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f584]) ).
thf(f584,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f583]) ).
thf(f583,plain,
( spl0_21
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f690,plain,
( ( $true
= ( ~ ( ( sK2 @ sK27 @ sK28 )
| ( sK3 @ sK27 @ sK28 ) ) ) )
| ~ spl0_4
| ~ spl0_21 ),
inference(boolean_simplification,[],[f684]) ).
thf(f684,plain,
( ( ( ( ( sK2 @ sK27 @ sK28 )
| ( sK3 @ sK27 @ sK28 ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_21 ),
inference(superposition,[],[f271,f665]) ).
thf(f665,plain,
( ( ( sK11 @ sK27 @ sK28 )
= $false )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f664]) ).
thf(f633,plain,
( ~ spl0_4
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f632]) ).
thf(f632,plain,
( $false
| ~ spl0_4
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f629]) ).
thf(f629,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_22 ),
inference(superposition,[],[f309,f614]) ).
thf(f614,plain,
( ( ( ( ( sK11 @ sK25 @ sK24 )
& ( sK11 @ sK23 @ sK25 ) )
=> ( sK11 @ sK23 @ sK24 ) )
= $false )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f613]) ).
thf(f613,plain,
( ( ( ^ [Y0: a] :
( ( ( sK11 @ Y0 @ sK24 )
& ( sK11 @ sK23 @ Y0 ) )
=> ( sK11 @ sK23 @ sK24 ) )
@ sK25 )
= $false )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f609]) ).
thf(f609,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 @ sK24 )
& ( sK11 @ sK23 @ Y0 ) )
=> ( sK11 @ sK23 @ sK24 ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f608]) ).
thf(f608,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ Y0 )
& ( sK11 @ sK23 @ Y1 ) )
=> ( sK11 @ sK23 @ Y0 ) ) )
@ sK24 )
= $false )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f603]) ).
thf(f603,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ Y0 )
& ( sK11 @ sK23 @ Y1 ) )
=> ( sK11 @ sK23 @ Y0 ) ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f599]) ).
thf(f599,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) )
@ sK23 )
= $false )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f587]) ).
thf(f587,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f586]) ).
thf(f586,plain,
( spl0_22
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f309,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK11 @ X1 @ X2 )
& ( sK11 @ X3 @ X1 ) )
=> ( sK11 @ X3 @ X2 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f308]) ).
thf(f308,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK11 @ X1 @ X2 )
& ( sK11 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ X2 ) )
@ X3 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f307]) ).
thf(f307,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ X1 @ X2 )
& ( sK11 @ Y0 @ X1 ) )
=> ( sK11 @ Y0 @ X2 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f306]) ).
thf(f306,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ X1 @ Y0 )
& ( sK11 @ Y1 @ X1 ) )
=> ( sK11 @ Y1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f299]) ).
thf(f299,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ X1 @ Y0 )
& ( sK11 @ Y1 @ X1 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f298]) ).
thf(f298,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y0 @ Y1 )
& ( sK11 @ Y2 @ Y0 ) )
=> ( sK11 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f262]) ).
thf(f588,plain,
( spl0_21
| spl0_22
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f579,f447,f340,f586,f583]) ).
thf(f447,plain,
( spl0_13
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f579,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_11
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f568]) ).
thf(f568,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_11
| ~ spl0_13 ),
inference(not_proxy_clausification,[],[f463]) ).
thf(f463,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_11
| ~ spl0_13 ),
inference(boolean_simplification,[],[f458]) ).
thf(f458,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y1 )
& ( sK11 @ Y0 @ Y2 ) )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f456,f401]) ).
thf(f456,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK16 @ sK15 ) )
= $true )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f455]) ).
thf(f455,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) )
@ X1 ) )
| ~ spl0_13 ),
inference(pi_clausification,[],[f448]) ).
thf(f448,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f447]) ).
thf(f452,plain,
( spl0_13
| spl0_14
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f445,f340,f450,f447]) ).
thf(f445,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) )
= $true )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK16 @ sK15 ) ) ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f399]) ).
thf(f382,plain,
( ~ spl0_4
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f381]) ).
thf(f381,plain,
( $false
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f377]) ).
thf(f377,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f374,f309]) ).
thf(f374,plain,
( ( $false
= ( ( ( sK11 @ sK14 @ sK12 )
& ( sK11 @ sK13 @ sK14 ) )
=> ( sK11 @ sK13 @ sK12 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f373]) ).
thf(f373,plain,
( ( ( ^ [Y0: a] :
( ( ( sK11 @ Y0 @ sK12 )
& ( sK11 @ sK13 @ Y0 ) )
=> ( sK11 @ sK13 @ sK12 ) )
@ sK14 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f372]) ).
thf(f372,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 @ sK12 )
& ( sK11 @ sK13 @ Y0 ) )
=> ( sK11 @ sK13 @ sK12 ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f371]) ).
thf(f371,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ sK12 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ sK12 ) ) )
@ sK13 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f361]) ).
thf(f361,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 @ sK12 )
& ( sK11 @ Y0 @ Y1 ) )
=> ( sK11 @ Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f357]) ).
thf(f357,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f344]) ).
thf(f344,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f343]) ).
thf(f345,plain,
( spl0_11
| spl0_12
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f336,f32,f25,f343,f340]) ).
thf(f25,plain,
( spl0_2
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f336,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f328]) ).
thf(f328,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f267,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f266]) ).
thf(f266,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK11 @ Y2 @ Y0 )
& ( sK11 @ Y1 @ Y2 ) )
=> ( sK11 @ Y1 @ Y0 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f260,f253]) ).
thf(f253,plain,
( ( ( sK11 @ sK4 @ sK5 )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f252]) ).
thf(f260,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f259]) ).
thf(f259,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f26]) ).
thf(f26,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f130,plain,
( spl0_7
| spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f123,f96,f128,f125]) ).
thf(f123,plain,
( ( ( sK3 @ sK8 @ sK7 )
= $true )
| ( ( sK2 @ sK8 @ sK7 )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f112]) ).
thf(f101,plain,
( spl0_5
| spl0_6
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f92,f29,f22,f99,f96]) ).
thf(f92,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f89]) ).
thf(f89,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f53]) ).
thf(f53,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f52]) ).
thf(f52,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f42,f46]) ).
thf(f46,plain,
( ( ( sK6 @ sK4 @ sK5 )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f45,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f30]) ).
thf(f42,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK4 @ sK5 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f41]) ).
thf(f41,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f23]) ).
thf(f38,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f37]) ).
thf(f37,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f36,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[],[f26,f30]) ).
thf(f34,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f20,f32,f29]) ).
thf(f20,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f18]) ).
thf(f18,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f13]) ).
thf(f13,plain,
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y8 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X5 )
& ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ! [X10: a > a > $o] :
( ( ! [X11: a,X12: a,X13: a] :
( ( ( X10 @ X12 @ X11 )
& ( X10 @ X11 @ X13 ) )
=> ( X10 @ X12 @ X13 ) )
& ! [X14: a,X15: a] :
( ( X1 @ X15 @ X14 )
=> ( X10 @ X15 @ X14 ) ) )
=> ( X10 @ X8 @ X9 ) )
| ! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ( X0 @ X18 @ X17 )
=> ( X16 @ X18 @ X17 ) )
& ! [X19: a,X20: a,X21: a] :
( ( ( X16 @ X21 @ X19 )
& ( X16 @ X19 @ X20 ) )
=> ( X16 @ X21 @ X20 ) ) )
=> ( X16 @ X8 @ X9 ) ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X22: a,X23: a] :
! [X24: a > a > $o] :
( ( ! [X25: a,X26: a] :
( ( ( X0 @ X25 @ X26 )
| ( X1 @ X25 @ X26 ) )
=> ( X24 @ X25 @ X26 ) )
& ! [X27: a,X28: a,X29: a] :
( ( ( X24 @ X27 @ X29 )
& ( X24 @ X29 @ X28 ) )
=> ( X24 @ X27 @ X28 ) ) )
=> ( X24 @ X22 @ X23 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X5: a,X6: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a,X7: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) )
& ! [X10: a,X9: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X5 @ X6 ) )
| ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X0 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ! [X10: a,X7: a,X9: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) ) )
=> ( X8 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X5: a,X6: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a,X7: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) )
& ! [X10: a,X9: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X5 @ X6 ) )
| ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X0 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ! [X10: a,X7: a,X9: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) ) )
=> ( X8 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM250_pme) ).
thf(f27,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f19,f25,f22]) ).
thf(f19,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV141^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:31:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38 % (24368)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (24370)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.38 % (24371)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (24372)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (24373)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.38 % (24374)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (24371)Instruction limit reached!
% 0.14/0.38 % (24371)------------------------------
% 0.14/0.38 % (24371)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (24371)Termination reason: Unknown
% 0.14/0.38 % (24371)Termination phase: Property scanning
% 0.14/0.38 % (24372)Instruction limit reached!
% 0.14/0.38 % (24372)------------------------------
% 0.14/0.38 % (24372)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38
% 0.14/0.38 % (24371)Memory used [KB]: 1023
% 0.14/0.38 % (24371)Time elapsed: 0.003 s
% 0.14/0.38 % (24371)Instructions burned: 2 (million)
% 0.14/0.38 % (24371)------------------------------
% 0.14/0.38 % (24371)------------------------------
% 0.14/0.38 % (24372)Termination reason: Unknown
% 0.14/0.38 % (24372)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (24372)Memory used [KB]: 1023
% 0.14/0.38 % (24372)Time elapsed: 0.003 s
% 0.14/0.38 % (24372)Instructions burned: 2 (million)
% 0.14/0.38 % (24372)------------------------------
% 0.14/0.38 % (24372)------------------------------
% 0.14/0.38 % (24375)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.38 % (24375)Instruction limit reached!
% 0.21/0.38 % (24375)------------------------------
% 0.21/0.38 % (24375)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (24375)Termination reason: Unknown
% 0.21/0.38 % (24375)Termination phase: Preprocessing 3
% 0.21/0.38
% 0.21/0.38 % (24375)Memory used [KB]: 1023
% 0.21/0.38 % (24375)Time elapsed: 0.004 s
% 0.21/0.38 % (24375)Instructions burned: 4 (million)
% 0.21/0.38 % (24375)------------------------------
% 0.21/0.38 % (24375)------------------------------
% 0.21/0.39 % (24374)Instruction limit reached!
% 0.21/0.39 % (24374)------------------------------
% 0.21/0.39 % (24374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (24374)Termination reason: Unknown
% 0.21/0.39 % (24374)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (24374)Memory used [KB]: 5500
% 0.21/0.39 % (24374)Time elapsed: 0.012 s
% 0.21/0.39 % (24374)Instructions burned: 19 (million)
% 0.21/0.39 % (24374)------------------------------
% 0.21/0.39 % (24374)------------------------------
% 0.21/0.39 % (24369)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.39 % (24370)Instruction limit reached!
% 0.21/0.39 % (24370)------------------------------
% 0.21/0.39 % (24370)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (24370)Termination reason: Unknown
% 0.21/0.39 % (24370)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (24370)Memory used [KB]: 5628
% 0.21/0.39 % (24370)Time elapsed: 0.016 s
% 0.21/0.39 % (24370)Instructions burned: 28 (million)
% 0.21/0.39 % (24370)------------------------------
% 0.21/0.39 % (24370)------------------------------
% 0.21/0.39 % (24369)Instruction limit reached!
% 0.21/0.39 % (24369)------------------------------
% 0.21/0.39 % (24369)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (24369)Termination reason: Unknown
% 0.21/0.39 % (24369)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (24369)Memory used [KB]: 5500
% 0.21/0.39 % (24369)Time elapsed: 0.005 s
% 0.21/0.39 % (24369)Instructions burned: 5 (million)
% 0.21/0.39 % (24369)------------------------------
% 0.21/0.39 % (24369)------------------------------
% 0.21/0.39 % (24376)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.40 % (24377)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.40 % (24379)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.41 % (24377)Instruction limit reached!
% 0.21/0.41 % (24377)------------------------------
% 0.21/0.41 % (24377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (24377)Termination reason: Unknown
% 0.21/0.41 % (24377)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (24377)Memory used [KB]: 5628
% 0.21/0.41 % (24377)Time elapsed: 0.010 s
% 0.21/0.41 % (24377)Instructions burned: 16 (million)
% 0.21/0.41 % (24377)------------------------------
% 0.21/0.41 % (24377)------------------------------
% 0.21/0.41 % (24378)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (24378)Instruction limit reached!
% 0.21/0.41 % (24378)------------------------------
% 0.21/0.41 % (24378)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (24378)Termination reason: Unknown
% 0.21/0.41 % (24378)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (24378)Memory used [KB]: 1023
% 0.21/0.41 % (24378)Time elapsed: 0.003 s
% 0.21/0.41 % (24378)Instructions burned: 3 (million)
% 0.21/0.41 % (24378)------------------------------
% 0.21/0.41 % (24378)------------------------------
% 0.21/0.41 % (24381)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41 % (24376)Instruction limit reached!
% 0.21/0.41 % (24376)------------------------------
% 0.21/0.41 % (24376)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (24376)Termination reason: Unknown
% 0.21/0.41 % (24376)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (24376)Memory used [KB]: 5628
% 0.21/0.41 % (24376)Time elapsed: 0.021 s
% 0.21/0.41 % (24376)Instructions burned: 38 (million)
% 0.21/0.41 % (24376)------------------------------
% 0.21/0.41 % (24376)------------------------------
% 0.21/0.42 % (24381)Instruction limit reached!
% 0.21/0.42 % (24381)------------------------------
% 0.21/0.42 % (24381)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (24381)Termination reason: Unknown
% 0.21/0.42 % (24381)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (24381)Memory used [KB]: 5756
% 0.21/0.42 % (24381)Time elapsed: 0.036 s
% 0.21/0.42 % (24381)Instructions burned: 17 (million)
% 0.21/0.42 % (24381)------------------------------
% 0.21/0.42 % (24381)------------------------------
% 0.21/0.42 % (24380)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.42 % (24383)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (24382)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (24383)Instruction limit reached!
% 0.21/0.42 % (24383)------------------------------
% 0.21/0.42 % (24383)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (24383)Termination reason: Unknown
% 0.21/0.42 % (24383)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (24383)Memory used [KB]: 1023
% 0.21/0.42 % (24383)Time elapsed: 0.003 s
% 0.21/0.42 % (24383)Instructions burned: 3 (million)
% 0.21/0.42 % (24383)------------------------------
% 0.21/0.42 % (24383)------------------------------
% 0.21/0.42 % (24382)Instruction limit reached!
% 0.21/0.42 % (24382)------------------------------
% 0.21/0.42 % (24382)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (24382)Termination reason: Unknown
% 0.21/0.42 % (24382)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (24382)Memory used [KB]: 1023
% 0.21/0.42 % (24382)Time elapsed: 0.003 s
% 0.21/0.42 % (24382)Instructions burned: 3 (million)
% 0.21/0.42 % (24382)------------------------------
% 0.21/0.42 % (24382)------------------------------
% 0.21/0.42 % (24380)Instruction limit reached!
% 0.21/0.42 % (24380)------------------------------
% 0.21/0.42 % (24380)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (24380)Termination reason: Unknown
% 0.21/0.42 % (24380)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (24380)Memory used [KB]: 1023
% 0.21/0.42 % (24380)Time elapsed: 0.035 s
% 0.21/0.42 % (24380)Instructions burned: 8 (million)
% 0.21/0.42 % (24380)------------------------------
% 0.21/0.42 % (24380)------------------------------
% 0.21/0.43 % (24384)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.43 % (24384)Instruction limit reached!
% 0.21/0.43 % (24384)------------------------------
% 0.21/0.43 % (24384)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (24384)Termination reason: Unknown
% 0.21/0.43 % (24384)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (24384)Memory used [KB]: 5500
% 0.21/0.43 % (24384)Time elapsed: 0.006 s
% 0.21/0.43 % (24384)Instructions burned: 8 (million)
% 0.21/0.43 % (24384)------------------------------
% 0.21/0.43 % (24384)------------------------------
% 0.21/0.43 % (24385)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43 % (24385)Instruction limit reached!
% 0.21/0.43 % (24385)------------------------------
% 0.21/0.43 % (24385)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (24385)Termination reason: Unknown
% 0.21/0.43 % (24385)Termination phase: Property scanning
% 0.21/0.43
% 0.21/0.43 % (24385)Memory used [KB]: 1023
% 0.21/0.43 % (24385)Time elapsed: 0.003 s
% 0.21/0.43 % (24385)Instructions burned: 3 (million)
% 0.21/0.43 % (24385)------------------------------
% 0.21/0.43 % (24385)------------------------------
% 0.21/0.44 % (24386)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.44 % (24387)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.44 % (24386)Instruction limit reached!
% 0.21/0.44 % (24386)------------------------------
% 0.21/0.44 % (24386)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (24386)Termination reason: Unknown
% 0.21/0.44 % (24386)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (24386)Memory used [KB]: 5500
% 0.21/0.44 % (24386)Time elapsed: 0.004 s
% 0.21/0.44 % (24386)Instructions burned: 5 (million)
% 0.21/0.44 % (24386)------------------------------
% 0.21/0.44 % (24386)------------------------------
% 0.21/0.44 % (24388)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.45 % (24389)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.45 % (24387)Instruction limit reached!
% 0.21/0.45 % (24387)------------------------------
% 0.21/0.45 % (24387)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (24387)Termination reason: Unknown
% 0.21/0.45 % (24387)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (24387)Memory used [KB]: 5500
% 0.21/0.45 % (24387)Time elapsed: 0.011 s
% 0.21/0.45 % (24387)Instructions burned: 19 (million)
% 0.21/0.45 % (24387)------------------------------
% 0.21/0.45 % (24387)------------------------------
% 0.21/0.45 % (24390)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.45 % (24389)Instruction limit reached!
% 0.21/0.45 % (24389)------------------------------
% 0.21/0.45 % (24389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (24389)Termination reason: Unknown
% 0.21/0.45 % (24389)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (24389)Memory used [KB]: 5500
% 0.21/0.45 % (24389)Time elapsed: 0.005 s
% 0.21/0.45 % (24389)Instructions burned: 6 (million)
% 0.21/0.45 % (24389)------------------------------
% 0.21/0.45 % (24389)------------------------------
% 0.21/0.45 % (24391)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.46 % (24392)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.46 % (24391)Instruction limit reached!
% 0.21/0.46 % (24391)------------------------------
% 0.21/0.46 % (24391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (24391)Termination reason: Unknown
% 0.21/0.46 % (24391)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (24391)Memory used [KB]: 5628
% 0.21/0.46 % (24391)Time elapsed: 0.013 s
% 0.21/0.46 % (24391)Instructions burned: 23 (million)
% 0.21/0.46 % (24391)------------------------------
% 0.21/0.46 % (24391)------------------------------
% 0.21/0.46 % (24392)Instruction limit reached!
% 0.21/0.46 % (24392)------------------------------
% 0.21/0.46 % (24392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (24392)Termination reason: Unknown
% 0.21/0.46 % (24392)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (24392)Memory used [KB]: 5500
% 0.21/0.46 % (24392)Time elapsed: 0.005 s
% 0.21/0.46 % (24392)Instructions burned: 5 (million)
% 0.21/0.46 % (24392)------------------------------
% 0.21/0.46 % (24392)------------------------------
% 0.21/0.46 % (24393)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.47 % (24393)Instruction limit reached!
% 0.21/0.47 % (24393)------------------------------
% 0.21/0.47 % (24393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (24393)Termination reason: Unknown
% 0.21/0.47 % (24393)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (24393)Memory used [KB]: 5500
% 0.21/0.47 % (24393)Time elapsed: 0.005 s
% 0.21/0.47 % (24393)Instructions burned: 6 (million)
% 0.21/0.47 % (24393)------------------------------
% 0.21/0.47 % (24393)------------------------------
% 0.21/0.47 % (24394)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.21/0.48 % (24368)Instruction limit reached!
% 0.21/0.48 % (24368)------------------------------
% 0.21/0.48 % (24368)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (24368)Termination reason: Unknown
% 0.21/0.48 % (24368)Termination phase: Saturation
% 0.21/0.48
% 0.21/0.48 % (24368)Memory used [KB]: 6524
% 0.21/0.48 % (24368)Time elapsed: 0.101 s
% 0.21/0.48 % (24368)Instructions burned: 184 (million)
% 0.21/0.48 % (24368)------------------------------
% 0.21/0.48 % (24368)------------------------------
% 0.21/0.48 % (24395)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2998ds/779Mi)
% 0.21/0.48 % (24396)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.21/0.49 % (24397)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.21/0.49 % (24396)Instruction limit reached!
% 0.21/0.49 % (24396)------------------------------
% 0.21/0.49 % (24396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (24396)Termination reason: Unknown
% 0.21/0.49 % (24396)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (24396)Memory used [KB]: 5500
% 0.21/0.49 % (24396)Time elapsed: 0.010 s
% 0.21/0.49 % (24396)Instructions burned: 20 (million)
% 0.21/0.49 % (24396)------------------------------
% 0.21/0.49 % (24396)------------------------------
% 0.21/0.50 % (24398)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.21/0.51 % (24398)Instruction limit reached!
% 0.21/0.51 % (24398)------------------------------
% 0.21/0.51 % (24398)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51 % (24398)Termination reason: Unknown
% 0.21/0.51 % (24398)Termination phase: Saturation
% 0.21/0.51
% 0.21/0.51 % (24398)Memory used [KB]: 5756
% 0.21/0.51 % (24398)Time elapsed: 0.007 s
% 0.21/0.51 % (24398)Instructions burned: 18 (million)
% 0.21/0.51 % (24398)------------------------------
% 0.21/0.51 % (24398)------------------------------
% 0.21/0.51 % (24373)Instruction limit reached!
% 0.21/0.51 % (24373)------------------------------
% 0.21/0.51 % (24373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51 % (24373)Termination reason: Unknown
% 0.21/0.51 % (24373)Termination phase: Saturation
% 0.21/0.51
% 0.21/0.51 % (24373)Memory used [KB]: 7164
% 0.21/0.51 % (24373)Time elapsed: 0.135 s
% 0.21/0.51 % (24373)Instructions burned: 277 (million)
% 0.21/0.51 % (24373)------------------------------
% 0.21/0.51 % (24373)------------------------------
% 0.21/0.51 % (24399)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.21/0.52 % (24399)Instruction limit reached!
% 0.21/0.52 % (24399)------------------------------
% 0.21/0.52 % (24399)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (24399)Termination reason: Unknown
% 0.21/0.52 % (24399)Termination phase: Preprocessing 3
% 0.21/0.52
% 0.21/0.52 % (24399)Memory used [KB]: 1023
% 0.21/0.52 % (24399)Time elapsed: 0.002 s
% 0.21/0.52 % (24399)Instructions burned: 3 (million)
% 0.21/0.52 % (24399)------------------------------
% 0.21/0.52 % (24399)------------------------------
% 0.21/0.52 % (24400)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 1.32/0.52 % (24401)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 1.32/0.52 % (24400)Refutation not found, incomplete strategy
% 1.32/0.52 % (24400)------------------------------
% 1.32/0.52 % (24400)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.32/0.52 % (24400)Termination reason: Refutation not found, incomplete strategy
% 1.32/0.52
% 1.32/0.52
% 1.32/0.52 % (24400)Memory used [KB]: 5500
% 1.32/0.52 % (24400)Time elapsed: 0.005 s
% 1.32/0.52 % (24400)Instructions burned: 13 (million)
% 1.32/0.52 % (24400)------------------------------
% 1.32/0.52 % (24400)------------------------------
% 1.32/0.53 % (24402)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 1.48/0.56 % (24401)Instruction limit reached!
% 1.48/0.56 % (24401)------------------------------
% 1.48/0.56 % (24401)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.56 % (24401)Termination reason: Unknown
% 1.48/0.56 % (24401)Termination phase: Saturation
% 1.48/0.56
% 1.48/0.56 % (24401)Memory used [KB]: 6140
% 1.48/0.56 % (24401)Time elapsed: 0.039 s
% 1.48/0.56 % (24401)Instructions burned: 129 (million)
% 1.48/0.56 % (24401)------------------------------
% 1.48/0.56 % (24401)------------------------------
% 1.48/0.56 % (24402)Instruction limit reached!
% 1.48/0.56 % (24402)------------------------------
% 1.48/0.56 % (24402)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.56 % (24402)Termination reason: Unknown
% 1.48/0.56 % (24402)Termination phase: Saturation
% 1.48/0.56
% 1.48/0.56 % (24402)Memory used [KB]: 5884
% 1.48/0.56 % (24402)Time elapsed: 0.032 s
% 1.48/0.56 % (24402)Instructions burned: 102 (million)
% 1.48/0.56 % (24402)------------------------------
% 1.48/0.56 % (24402)------------------------------
% 1.48/0.57 % (24403)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 1.48/0.57 % (24403)Instruction limit reached!
% 1.48/0.57 % (24403)------------------------------
% 1.48/0.57 % (24403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.57 % (24403)Termination reason: Unknown
% 1.48/0.57 % (24403)Termination phase: Property scanning
% 1.48/0.57
% 1.48/0.57 % (24403)Memory used [KB]: 1023
% 1.48/0.57 % (24403)Time elapsed: 0.002 s
% 1.48/0.57 % (24403)Instructions burned: 4 (million)
% 1.48/0.57 % (24403)------------------------------
% 1.48/0.57 % (24403)------------------------------
% 1.48/0.57 % (24404)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 1.48/0.57 % (24404)Refutation not found, incomplete strategy
% 1.48/0.57 % (24404)------------------------------
% 1.48/0.57 % (24404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.57 % (24404)Termination reason: Refutation not found, incomplete strategy
% 1.48/0.57
% 1.48/0.57
% 1.48/0.57 % (24404)Memory used [KB]: 5500
% 1.48/0.57 % (24404)Time elapsed: 0.003 s
% 1.48/0.57 % (24404)Instructions burned: 6 (million)
% 1.48/0.57 % (24404)------------------------------
% 1.48/0.57 % (24404)------------------------------
% 1.48/0.58 % (24394)Instruction limit reached!
% 1.48/0.58 % (24394)------------------------------
% 1.48/0.58 % (24394)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.58 % (24394)Termination reason: Unknown
% 1.48/0.58 % (24394)Termination phase: Saturation
% 1.48/0.58
% 1.48/0.58 % (24394)Memory used [KB]: 7547
% 1.48/0.58 % (24394)Time elapsed: 0.104 s
% 1.48/0.58 % (24394)Instructions burned: 378 (million)
% 1.48/0.58 % (24394)------------------------------
% 1.48/0.58 % (24394)------------------------------
% 1.48/0.58 % (24405)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2997ds/86Mi)
% 1.48/0.58 % (24379)First to succeed.
% 1.48/0.58 % (24407)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 1.48/0.58 % (24406)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2997ds/107Mi)
% 1.48/0.59 % (24379)Refutation found. Thanks to Tanya!
% 1.48/0.59 % SZS status Theorem for theBenchmark
% 1.48/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.48/0.59 % (24379)------------------------------
% 1.48/0.59 % (24379)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.59 % (24379)Termination reason: Refutation
% 1.48/0.59
% 1.48/0.59 % (24379)Memory used [KB]: 6908
% 1.48/0.59 % (24379)Time elapsed: 0.212 s
% 1.48/0.59 % (24379)Instructions burned: 394 (million)
% 1.48/0.59 % (24379)------------------------------
% 1.48/0.59 % (24379)------------------------------
% 1.48/0.59 % (24367)Success in time 0.224 s
% 1.48/0.59 % Vampire---4.8 exiting
%------------------------------------------------------------------------------