TSTP Solution File: SEV040^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV040^5 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n002.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 04:11:48 EDT 2024
% Result : Theorem 0.20s 0.56s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 79
% Syntax : Number of formulae : 362 ( 4 unt; 56 typ; 0 def)
% Number of atoms : 3898 ( 548 equ; 1 cnn)
% Maximal formula atoms : 6 ( 12 avg)
% Number of connectives : 9214 ( 485 ~; 466 |; 841 &;5507 @)
% ( 22 <=>; 628 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 464 ( 464 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 76 usr; 57 con; 0-2 aty)
% (1265 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1569 (1372 ^ 196 !; 0 ?;1569 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: a > a > $o ).
thf(func_def_19,type,
sK3: a > a > $o ).
thf(func_def_20,type,
sK4: a ).
thf(func_def_21,type,
sK5: a ).
thf(func_def_22,type,
sK6: a ).
thf(func_def_23,type,
sK7: a ).
thf(func_def_24,type,
sK8: a ).
thf(func_def_25,type,
sK9: a > a > $o ).
thf(func_def_26,type,
sK10: a > a > $o ).
thf(func_def_27,type,
sK11: a > a > $o ).
thf(func_def_28,type,
sK12: a ).
thf(func_def_29,type,
sK13: a ).
thf(func_def_30,type,
sK14: a ).
thf(func_def_31,type,
sK15: a > a > $o ).
thf(func_def_32,type,
sK16: a > a > $o ).
thf(func_def_33,type,
sK17: a ).
thf(func_def_34,type,
sK18: a ).
thf(func_def_35,type,
sK19: a ).
thf(func_def_36,type,
sK20: a ).
thf(func_def_37,type,
sK21: a > a > $o ).
thf(func_def_38,type,
sK22: a > a > $o ).
thf(func_def_39,type,
sK23: a > a > $o ).
thf(func_def_40,type,
sK24: a > a > $o ).
thf(func_def_41,type,
sK25: a > a > $o ).
thf(func_def_42,type,
sK26: a > a > $o ).
thf(func_def_43,type,
sK27: a ).
thf(func_def_44,type,
sK28: a ).
thf(func_def_45,type,
sK29: a ).
thf(func_def_46,type,
sK30: a ).
thf(func_def_47,type,
sK31: a ).
thf(func_def_48,type,
sK32: a > a > $o ).
thf(func_def_49,type,
sK33: a > a > $o ).
thf(func_def_50,type,
sK34: a > a > $o ).
thf(func_def_51,type,
sK35: a > a > $o ).
thf(func_def_52,type,
sK36: a ).
thf(func_def_53,type,
sK37: a ).
thf(func_def_54,type,
sK38: a > a > $o ).
thf(func_def_55,type,
sK39: a > a > $o ).
thf(func_def_56,type,
sK40: a ).
thf(func_def_57,type,
sK41: a ).
thf(func_def_58,type,
sK42: a ).
thf(func_def_59,type,
sK43: a ).
thf(func_def_60,type,
sK44: a ).
thf(func_def_61,type,
sK45: a ).
thf(func_def_62,type,
sK46: a ).
thf(func_def_63,type,
sK47: a > a > $o ).
thf(func_def_64,type,
sK48: a > a > $o ).
thf(func_def_65,type,
sK49: a ).
thf(func_def_66,type,
sK50: a ).
thf(func_def_67,type,
sK51: a > a > $o ).
thf(func_def_68,type,
sK52: a ).
thf(func_def_69,type,
sK53: a ).
thf(func_def_70,type,
sK54: a ).
thf(f1411,plain,
$false,
inference(avatar_sat_refutation,[],[f17,f37,f116,f173,f183,f203,f238,f271,f299,f631,f664,f671,f704,f711,f727,f730,f924,f978,f1031,f1283,f1337,f1394,f1410]) ).
thf(f1410,plain,
( ~ spl0_37
| ~ spl0_39 ),
inference(avatar_contradiction_clause,[],[f1409]) ).
thf(f1409,plain,
( $false
| ~ spl0_37
| ~ spl0_39 ),
inference(trivial_inequality_removal,[],[f1408]) ).
thf(f1408,plain,
( ( $false = $true )
| ~ spl0_37
| ~ spl0_39 ),
inference(forward_demodulation,[],[f700,f707]) ).
thf(f707,plain,
( ( ( ( sK32 = sK34 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f706]) ).
thf(f706,plain,
( spl0_39
<=> ( ( ( sK32 = sK34 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
thf(f700,plain,
( ( ( ( sK32 = sK34 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f699]) ).
thf(f699,plain,
( spl0_37
<=> ( ( ( sK32 = sK34 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
thf(f1394,plain,
( ~ spl0_5
| ~ spl0_33
| ~ spl0_66 ),
inference(avatar_contradiction_clause,[],[f1393]) ).
thf(f1393,plain,
( $false
| ~ spl0_5
| ~ spl0_33
| ~ spl0_66 ),
inference(trivial_inequality_removal,[],[f1389]) ).
thf(f1389,plain,
( ( $false = $true )
| ~ spl0_5
| ~ spl0_33
| ~ spl0_66 ),
inference(superposition,[],[f1246,f1371]) ).
thf(f1371,plain,
( ( ( ( ( sK32 @ sK52 @ sK54 )
& ( sK32 @ sK53 @ sK52 ) )
=> ( sK32 @ sK53 @ sK54 ) )
= $false )
| ~ spl0_66 ),
inference(beta_eta_normalization,[],[f1370]) ).
thf(f1370,plain,
( ( ( ^ [Y0: a] :
( ( ( sK32 @ sK52 @ Y0 )
& ( sK32 @ sK53 @ sK52 ) )
=> ( sK32 @ sK53 @ Y0 ) )
@ sK54 )
= $false )
| ~ spl0_66 ),
inference(sigma_clausification,[],[f1354]) ).
thf(f1354,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK32 @ sK52 @ Y0 )
& ( sK32 @ sK53 @ sK52 ) )
=> ( sK32 @ sK53 @ Y0 ) ) )
= $false )
| ~ spl0_66 ),
inference(beta_eta_normalization,[],[f1353]) ).
thf(f1353,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK32 @ sK52 @ Y1 )
& ( sK32 @ Y0 @ sK52 ) )
=> ( sK32 @ Y0 @ Y1 ) ) )
@ sK53 ) )
| ~ spl0_66 ),
inference(sigma_clausification,[],[f1350]) ).
thf(f1350,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK32 @ sK52 @ Y1 )
& ( sK32 @ Y0 @ sK52 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_66 ),
inference(beta_eta_normalization,[],[f1349]) ).
thf(f1349,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) )
@ sK52 ) )
| ~ spl0_66 ),
inference(sigma_clausification,[],[f1282]) ).
thf(f1282,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1281]) ).
thf(f1281,plain,
( spl0_66
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
thf(f1246,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK32 @ X3 @ X2 )
& ( sK32 @ X1 @ X3 ) )
=> ( sK32 @ X1 @ X2 ) )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(beta_eta_normalization,[],[f1245]) ).
thf(f1245,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK32 @ Y0 @ X2 )
& ( sK32 @ X1 @ Y0 ) )
=> ( sK32 @ X1 @ X2 ) )
@ X3 )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(pi_clausification,[],[f1243]) ).
thf(f1243,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK32 @ Y0 @ X2 )
& ( sK32 @ X1 @ Y0 ) )
=> ( sK32 @ X1 @ X2 ) ) )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(beta_eta_normalization,[],[f1242]) ).
thf(f1242,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK32 @ Y1 @ Y0 )
& ( sK32 @ X1 @ Y1 ) )
=> ( sK32 @ X1 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(pi_clausification,[],[f1235]) ).
thf(f1235,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK32 @ Y1 @ Y0 )
& ( sK32 @ X1 @ Y1 ) )
=> ( sK32 @ X1 @ Y0 ) ) ) )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(beta_eta_normalization,[],[f1234]) ).
thf(f1234,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(pi_clausification,[],[f1095]) ).
thf(f1095,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(binary_proxy_clausification,[],[f1073]) ).
thf(f1073,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(boolean_simplification,[],[f1071]) ).
thf(f1071,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& $true )
!= $false )
| ~ spl0_5
| ~ spl0_33 ),
inference(backward_demodulation,[],[f1061,f1068]) ).
thf(f1068,plain,
( ( $true
= ( sK32 = sK33 ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(binary_proxy_clausification,[],[f1061]) ).
thf(f1061,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& ( sK32 = sK33 ) ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(forward_demodulation,[],[f652,f660]) ).
thf(f660,plain,
( ( $false
= ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f659]) ).
thf(f659,plain,
( spl0_33
<=> ( $false
= ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
thf(f652,plain,
( ( ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& ( sK32 = sK33 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f651]) ).
thf(f651,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK32 @ Y2 @ Y1 )
=> ( sK32 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK32 @ Y3 @ Y2 )
& ( sK32 @ Y1 @ Y3 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) )
& ( sK32 = Y0 ) )
@ sK33 )
!= ( ^ [Y0: a > a > $o] :
( ( sK32 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK32 @ Y1 @ Y2 )
=> ( sK32 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK32 @ Y1 @ Y3 )
& ( sK32 @ Y2 @ Y1 ) )
=> ( sK32 @ Y2 @ Y3 ) ) ) ) ) )
@ sK33 ) )
| ~ spl0_5 ),
inference(negative_extensionality,[],[f640]) ).
thf(f640,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK32 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK32 @ Y1 @ Y2 )
=> ( sK32 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK32 @ Y1 @ Y3 )
& ( sK32 @ Y2 @ Y1 ) )
=> ( sK32 @ Y2 @ Y3 ) ) ) ) ) ) )
!= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK32 @ Y2 @ Y1 )
=> ( sK32 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK32 @ Y3 @ Y2 )
& ( sK32 @ Y1 @ Y3 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) )
& ( sK32 = Y0 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f639]) ).
thf(f639,plain,
( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
@ sK32 )
!= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) )
@ sK32 ) )
| ~ spl0_5 ),
inference(negative_extensionality,[],[f637]) ).
thf(f637,plain,
( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
!= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
| ~ spl0_5 ),
inference(equality_proxy_clausification,[],[f179]) ).
thf(f179,plain,
( ( $false
= ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f178]) ).
thf(f178,plain,
( spl0_5
<=> ( $false
= ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f1337,plain,
( ~ spl0_5
| ~ spl0_33
| ~ spl0_65 ),
inference(avatar_contradiction_clause,[],[f1336]) ).
thf(f1336,plain,
( $false
| ~ spl0_5
| ~ spl0_33
| ~ spl0_65 ),
inference(trivial_inequality_removal,[],[f1335]) ).
thf(f1335,plain,
( ( $false = $true )
| ~ spl0_5
| ~ spl0_33
| ~ spl0_65 ),
inference(backward_demodulation,[],[f1321,f1310]) ).
thf(f1310,plain,
( ( ( sK32 @ sK50 @ sK49 )
= $false )
| ~ spl0_65 ),
inference(binary_proxy_clausification,[],[f1309]) ).
thf(f1309,plain,
( ( ( ( sK32 @ sK49 @ sK50 )
=> ( sK32 @ sK50 @ sK49 ) )
= $false )
| ~ spl0_65 ),
inference(beta_eta_normalization,[],[f1308]) ).
thf(f1308,plain,
( ( ( ^ [Y0: a] :
( ( sK32 @ sK49 @ Y0 )
=> ( sK32 @ Y0 @ sK49 ) )
@ sK50 )
= $false )
| ~ spl0_65 ),
inference(sigma_clausification,[],[f1289]) ).
thf(f1289,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK32 @ sK49 @ Y0 )
=> ( sK32 @ Y0 @ sK49 ) ) ) )
| ~ spl0_65 ),
inference(beta_eta_normalization,[],[f1288]) ).
thf(f1288,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) )
@ sK49 ) )
| ~ spl0_65 ),
inference(sigma_clausification,[],[f1279]) ).
thf(f1279,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1278]) ).
thf(f1278,plain,
( spl0_65
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
thf(f1321,plain,
( ( ( sK32 @ sK50 @ sK49 )
= $true )
| ~ spl0_5
| ~ spl0_33
| ~ spl0_65 ),
inference(trivial_inequality_removal,[],[f1320]) ).
thf(f1320,plain,
( ( $false = $true )
| ( ( sK32 @ sK50 @ sK49 )
= $true )
| ~ spl0_5
| ~ spl0_33
| ~ spl0_65 ),
inference(boolean_simplification,[],[f1313]) ).
thf(f1313,plain,
( ( $false
= ( $false
=> ( sK32 @ sK50 @ sK49 ) ) )
| ( ( sK32 @ sK50 @ sK49 )
= $true )
| ~ spl0_5
| ~ spl0_33
| ~ spl0_65 ),
inference(superposition,[],[f1309,f1109]) ).
thf(f1109,plain,
( ! [X2: a,X1: a] :
( ( ( sK32 @ X2 @ X1 )
= $false )
| ( ( sK32 @ X1 @ X2 )
= $true ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(binary_proxy_clausification,[],[f1107]) ).
thf(f1107,plain,
( ! [X2: a,X1: a] :
( ( ( sK32 @ X2 @ X1 )
=> ( sK32 @ X1 @ X2 ) )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(beta_eta_normalization,[],[f1106]) ).
thf(f1106,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK32 @ Y0 @ X1 )
=> ( sK32 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(pi_clausification,[],[f1102]) ).
thf(f1102,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK32 @ Y0 @ X1 )
=> ( sK32 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(beta_eta_normalization,[],[f1101]) ).
thf(f1101,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(pi_clausification,[],[f1099]) ).
thf(f1099,plain,
( ( $false
!= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(boolean_simplification,[],[f1097]) ).
thf(f1097,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& $true )
!= $false )
| ~ spl0_5
| ~ spl0_33 ),
inference(backward_demodulation,[],[f1073,f1095]) ).
thf(f1283,plain,
( spl0_65
| spl0_66
| ~ spl0_38
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f1276,f706,f702,f1281,f1278]) ).
thf(f702,plain,
( spl0_38
<=> ( ( sK32 = sK34 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
thf(f1276,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_38
| ~ spl0_39 ),
inference(binary_proxy_clausification,[],[f1057]) ).
thf(f1057,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_38
| ~ spl0_39 ),
inference(boolean_simplification,[],[f1056]) ).
thf(f1056,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_38
| ~ spl0_39 ),
inference(forward_demodulation,[],[f707,f703]) ).
thf(f703,plain,
( ( ( sK32 = sK34 )
= $true )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f702]) ).
thf(f1031,plain,
( ~ spl0_5
| ~ spl0_34
| ~ spl0_48 ),
inference(avatar_contradiction_clause,[],[f1030]) ).
thf(f1030,plain,
( $false
| ~ spl0_5
| ~ spl0_34
| ~ spl0_48 ),
inference(trivial_inequality_removal,[],[f1022]) ).
thf(f1022,plain,
( ( $false = $true )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_48 ),
inference(superposition,[],[f1014,f843]) ).
thf(f843,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK32 @ X1 @ X3 )
& ( sK32 @ X2 @ X1 ) )
=> ( sK32 @ X2 @ X3 ) ) )
| ~ spl0_5
| ~ spl0_34 ),
inference(beta_eta_normalization,[],[f842]) ).
thf(f842,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK32 @ X1 @ Y0 )
& ( sK32 @ X2 @ X1 ) )
=> ( sK32 @ X2 @ Y0 ) )
@ X3 ) )
| ~ spl0_5
| ~ spl0_34 ),
inference(pi_clausification,[],[f839]) ).
thf(f839,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK32 @ X1 @ Y0 )
& ( sK32 @ X2 @ X1 ) )
=> ( sK32 @ X2 @ Y0 ) ) )
= $true )
| ~ spl0_5
| ~ spl0_34 ),
inference(beta_eta_normalization,[],[f838]) ).
thf(f838,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK32 @ X1 @ Y1 )
& ( sK32 @ Y0 @ X1 ) )
=> ( sK32 @ Y0 @ Y1 ) ) )
@ X2 )
= $true )
| ~ spl0_5
| ~ spl0_34 ),
inference(pi_clausification,[],[f835]) ).
thf(f835,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK32 @ X1 @ Y1 )
& ( sK32 @ Y0 @ X1 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_5
| ~ spl0_34 ),
inference(beta_eta_normalization,[],[f834]) ).
thf(f834,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true )
| ~ spl0_5
| ~ spl0_34 ),
inference(pi_clausification,[],[f736]) ).
thf(f736,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_34 ),
inference(binary_proxy_clausification,[],[f731]) ).
thf(f731,plain,
( ( $false
!= ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_34 ),
inference(forward_demodulation,[],[f652,f663]) ).
thf(f663,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& ( sK32 = sK33 ) ) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f662]) ).
thf(f662,plain,
( spl0_34
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& ( sK32 = sK33 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
thf(f1014,plain,
( ( ( ( ( sK32 @ sK46 @ sK45 )
& ( sK32 @ sK44 @ sK46 ) )
=> ( sK32 @ sK44 @ sK45 ) )
= $false )
| ~ spl0_48 ),
inference(beta_eta_normalization,[],[f1013]) ).
thf(f1013,plain,
( ( ( ^ [Y0: a] :
( ( ( sK32 @ Y0 @ sK45 )
& ( sK32 @ sK44 @ Y0 ) )
=> ( sK32 @ sK44 @ sK45 ) )
@ sK46 )
= $false )
| ~ spl0_48 ),
inference(sigma_clausification,[],[f1010]) ).
thf(f1010,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK32 @ Y0 @ sK45 )
& ( sK32 @ sK44 @ Y0 ) )
=> ( sK32 @ sK44 @ sK45 ) ) ) )
| ~ spl0_48 ),
inference(beta_eta_normalization,[],[f1009]) ).
thf(f1009,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK32 @ Y1 @ Y0 )
& ( sK32 @ sK44 @ Y1 ) )
=> ( sK32 @ sK44 @ Y0 ) ) )
@ sK45 ) )
| ~ spl0_48 ),
inference(sigma_clausification,[],[f995]) ).
thf(f995,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK32 @ Y1 @ Y0 )
& ( sK32 @ sK44 @ Y1 ) )
=> ( sK32 @ sK44 @ Y0 ) ) ) )
= $false )
| ~ spl0_48 ),
inference(beta_eta_normalization,[],[f994]) ).
thf(f994,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
@ sK44 ) )
| ~ spl0_48 ),
inference(sigma_clausification,[],[f923]) ).
thf(f923,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f922]) ).
thf(f922,plain,
( spl0_48
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
thf(f978,plain,
( ~ spl0_5
| ~ spl0_34
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f977]) ).
thf(f977,plain,
( $false
| ~ spl0_5
| ~ spl0_34
| ~ spl0_47 ),
inference(trivial_inequality_removal,[],[f976]) ).
thf(f976,plain,
( ( $false = $true )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_47 ),
inference(forward_demodulation,[],[f959,f971]) ).
thf(f971,plain,
( ( ( sK32 @ sK43 @ sK42 )
= $false )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_47 ),
inference(trivial_inequality_removal,[],[f970]) ).
thf(f970,plain,
( ( ( sK32 @ sK43 @ sK42 )
= $false )
| ( $false = $true )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_47 ),
inference(boolean_simplification,[],[f960]) ).
thf(f960,plain,
( ( ( sK32 @ sK43 @ sK42 )
= $false )
| ( $false
= ( ( sK32 @ sK43 @ sK42 )
=> $true ) )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_47 ),
inference(superposition,[],[f941,f820]) ).
thf(f820,plain,
( ! [X2: a,X1: a] :
( ( ( sK32 @ X2 @ X1 )
= $true )
| ( ( sK32 @ X1 @ X2 )
= $false ) )
| ~ spl0_5
| ~ spl0_34 ),
inference(binary_proxy_clausification,[],[f817]) ).
thf(f817,plain,
( ! [X2: a,X1: a] :
( ( ( sK32 @ X1 @ X2 )
=> ( sK32 @ X2 @ X1 ) )
= $true )
| ~ spl0_5
| ~ spl0_34 ),
inference(beta_eta_normalization,[],[f816]) ).
thf(f816,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK32 @ X1 @ Y0 )
=> ( sK32 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_5
| ~ spl0_34 ),
inference(pi_clausification,[],[f813]) ).
thf(f813,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK32 @ X1 @ Y0 )
=> ( sK32 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_5
| ~ spl0_34 ),
inference(beta_eta_normalization,[],[f812]) ).
thf(f812,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_5
| ~ spl0_34 ),
inference(pi_clausification,[],[f767]) ).
thf(f767,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_5
| ~ spl0_34 ),
inference(binary_proxy_clausification,[],[f743]) ).
thf(f743,plain,
( ( ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) ) )
!= $false )
| ~ spl0_5
| ~ spl0_34 ),
inference(boolean_simplification,[],[f740]) ).
thf(f740,plain,
( ( $false
!= ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_5
| ~ spl0_34 ),
inference(backward_demodulation,[],[f731,f736]) ).
thf(f941,plain,
( ( $false
= ( ( sK32 @ sK43 @ sK42 )
=> ( sK32 @ sK42 @ sK43 ) ) )
| ~ spl0_47 ),
inference(beta_eta_normalization,[],[f940]) ).
thf(f940,plain,
( ( ( ^ [Y0: a] :
( ( sK32 @ Y0 @ sK42 )
=> ( sK32 @ sK42 @ Y0 ) )
@ sK43 )
= $false )
| ~ spl0_47 ),
inference(sigma_clausification,[],[f928]) ).
thf(f928,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK32 @ Y0 @ sK42 )
=> ( sK32 @ sK42 @ Y0 ) ) )
= $false )
| ~ spl0_47 ),
inference(beta_eta_normalization,[],[f927]) ).
thf(f927,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) )
@ sK42 )
= $false )
| ~ spl0_47 ),
inference(sigma_clausification,[],[f920]) ).
thf(f920,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f919]) ).
thf(f919,plain,
( spl0_47
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
thf(f959,plain,
( ( ( sK32 @ sK43 @ sK42 )
= $true )
| ~ spl0_47 ),
inference(binary_proxy_clausification,[],[f941]) ).
thf(f924,plain,
( spl0_47
| spl0_48
| ~ spl0_5
| ~ spl0_34
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f917,f669,f662,f178,f922,f919]) ).
thf(f669,plain,
( spl0_36
<=> ( ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
thf(f917,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_36 ),
inference(binary_proxy_clausification,[],[f781]) ).
thf(f781,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_36 ),
inference(boolean_simplification,[],[f780]) ).
thf(f780,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& $true )
= $false )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_36 ),
inference(backward_demodulation,[],[f663,f778]) ).
thf(f778,plain,
( ( $true
= ( sK32 = sK33 ) )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_36 ),
inference(boolean_simplification,[],[f772]) ).
thf(f772,plain,
( ( ( ( sK32 = sK33 )
& $true )
= $true )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_36 ),
inference(backward_demodulation,[],[f744,f767]) ).
thf(f744,plain,
( ( ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_36 ),
inference(boolean_simplification,[],[f739]) ).
thf(f739,plain,
( ( $true
= ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_5
| ~ spl0_34
| ~ spl0_36 ),
inference(backward_demodulation,[],[f670,f736]) ).
thf(f670,plain,
( ( ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f669]) ).
thf(f730,plain,
( ~ spl0_34
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f729]) ).
thf(f729,plain,
( $false
| ~ spl0_34
| ~ spl0_35 ),
inference(trivial_inequality_removal,[],[f728]) ).
thf(f728,plain,
( ( $false = $true )
| ~ spl0_34
| ~ spl0_35 ),
inference(forward_demodulation,[],[f667,f663]) ).
thf(f667,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& ( sK32 = sK33 ) ) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f666]) ).
thf(f666,plain,
( spl0_35
<=> ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& ( sK32 = sK33 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
thf(f727,plain,
( ~ spl0_5
| ~ spl0_33
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f726]) ).
thf(f726,plain,
( $false
| ~ spl0_5
| ~ spl0_33
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f725]) ).
thf(f725,plain,
( ( $false != $false )
| ~ spl0_5
| ~ spl0_33
| ~ spl0_40 ),
inference(boolean_simplification,[],[f724]) ).
thf(f724,plain,
( ( $false
!= ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_33
| ~ spl0_40 ),
inference(boolean_simplification,[],[f723]) ).
thf(f723,plain,
( ( ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
!= $false )
| ~ spl0_5
| ~ spl0_33
| ~ spl0_40 ),
inference(forward_demodulation,[],[f687,f710]) ).
thf(f710,plain,
( ( $false
= ( sK32 = sK34 ) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f709]) ).
thf(f709,plain,
( spl0_40
<=> ( $false
= ( sK32 = sK34 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
thf(f687,plain,
( ( ( ( sK32 = sK34 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
!= ( sK32 = sK34 ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(beta_eta_normalization,[],[f686]) ).
thf(f686,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK32 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK32 @ Y1 @ Y2 )
=> ( sK32 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK32 @ Y1 @ Y3 )
& ( sK32 @ Y2 @ Y1 ) )
=> ( sK32 @ Y2 @ Y3 ) ) ) ) ) )
@ sK34 )
!= ( sK32 = sK34 ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(negative_extensionality,[],[f682]) ).
thf(f682,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK32 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK32 @ Y1 @ Y2 )
=> ( sK32 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK32 @ Y1 @ Y3 )
& ( sK32 @ Y2 @ Y1 ) )
=> ( sK32 @ Y2 @ Y3 ) ) ) ) ) ) )
!= ( (=) @ sK32 ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(beta_eta_normalization,[],[f681]) ).
thf(f681,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK32 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK32 @ Y1 @ Y2 )
=> ( sK32 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK32 @ Y1 @ Y3 )
& ( sK32 @ Y2 @ Y1 ) )
=> ( sK32 @ Y2 @ Y3 ) ) ) ) ) ) )
!= ( ^ [Y0: a > a > $o] : ( sK32 = Y0 ) ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(boolean_simplification,[],[f678]) ).
thf(f678,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( sK32 = Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK32 @ Y1 @ Y2 )
=> ( sK32 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK32 @ Y1 @ Y3 )
& ( sK32 @ Y2 @ Y1 ) )
=> ( sK32 @ Y2 @ Y3 ) ) ) ) ) ) )
!= ( ^ [Y0: a > a > $o] :
( $true
& ( sK32 = Y0 ) ) ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(backward_demodulation,[],[f640,f675]) ).
thf(f675,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(binary_proxy_clausification,[],[f672]) ).
thf(f672,plain,
( ( $false
!= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& ( sK32 = sK33 ) ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(backward_demodulation,[],[f652,f660]) ).
thf(f711,plain,
( spl0_39
| spl0_40
| ~ spl0_5
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f697,f659,f178,f709,f706]) ).
thf(f697,plain,
( ( ( ( sK32 = sK34 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( sK32 = sK34 ) )
| ~ spl0_5
| ~ spl0_33 ),
inference(binary_proxy_clausification,[],[f687]) ).
thf(f704,plain,
( spl0_37
| spl0_38
| ~ spl0_5
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f696,f659,f178,f702,f699]) ).
thf(f696,plain,
( ( ( sK32 = sK34 )
= $true )
| ( ( ( sK32 = sK34 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_5
| ~ spl0_33 ),
inference(binary_proxy_clausification,[],[f687]) ).
thf(f671,plain,
( spl0_35
| spl0_36
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f656,f178,f669,f666]) ).
thf(f656,plain,
( ( ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& ( sK32 = sK33 ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f652]) ).
thf(f664,plain,
( spl0_33
| spl0_34
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f657,f178,f662,f659]) ).
thf(f657,plain,
( ( $false
= ( ( sK32 = sK33 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y0 @ Y1 )
=> ( sK32 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y0 @ Y2 )
& ( sK32 @ Y1 @ Y0 ) )
=> ( sK32 @ Y1 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK32 @ Y1 @ Y0 )
=> ( sK32 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK32 @ Y2 @ Y1 )
& ( sK32 @ Y0 @ Y2 ) )
=> ( sK32 @ Y0 @ Y1 ) ) ) ) )
& ( sK32 = sK33 ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f652]) ).
thf(f631,plain,
( ~ spl0_6
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f630]) ).
thf(f630,plain,
( $false
| ~ spl0_6
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f629]) ).
thf(f629,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[],[f628]) ).
thf(f628,plain,
( ( ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y0 @ Y1 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[],[f627]) ).
thf(f627,plain,
( ( $true
= ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y0 @ Y1 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[],[f626]) ).
thf(f626,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y0 @ Y1 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f624,f267]) ).
thf(f267,plain,
( ( $false
= ( sK11 = sK9 ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f266,plain,
( spl0_13
<=> ( $false
= ( sK11 = sK9 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f624,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y0 @ Y1 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(backward_demodulation,[],[f619,f622]) ).
thf(f622,plain,
( ( sK9 = sK10 )
| ~ spl0_6
| ~ spl0_13 ),
inference(equality_proxy_clausification,[],[f621]) ).
thf(f621,plain,
( ( $true
= ( sK10 = sK9 ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[],[f620]) ).
thf(f620,plain,
( ( ( $true
& ( sK10 = sK9 ) )
= $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(backward_demodulation,[],[f596,f619]) ).
thf(f596,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 ) ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[],[f595]) ).
thf(f595,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& $true )
= $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(backward_demodulation,[],[f589,f593]) ).
thf(f593,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f589]) ).
thf(f589,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(not_proxy_clausification,[],[f588]) ).
thf(f588,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[],[f587]) ).
thf(f587,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> $false )
= $false )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[],[f586]) ).
thf(f586,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(boolean_simplification,[],[f585]) ).
thf(f585,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f584,f267]) ).
thf(f584,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f583]) ).
thf(f583,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y2 @ Y3 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y1 @ Y2 )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y1 @ Y3 )
& ( sK9 @ Y2 @ Y1 ) )
=> ( sK9 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y2 @ Y3 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y3 ) ) ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f582]) ).
thf(f582,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y2 @ Y3 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y1 @ Y2 )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y1 @ Y3 )
& ( sK9 @ Y2 @ Y1 ) )
=> ( sK9 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y2 @ Y3 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f581]) ).
thf(f581,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y2 @ Y4 )
& ( sK9 @ Y3 @ Y2 ) )
=> ( sK9 @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( Y1 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y3 @ Y4 )
& ( sK9 @ Y2 @ Y3 ) )
=> ( sK9 @ Y2 @ Y4 ) ) ) ) ) ) ) )
@ sK10 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f580]) ).
thf(f580,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y2 @ Y4 )
& ( sK9 @ Y3 @ Y2 ) )
=> ( sK9 @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( Y1 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y3 @ Y4 )
& ( sK9 @ Y2 @ Y3 ) )
=> ( sK9 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f579]) ).
thf(f579,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) )
@ sK9 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f182]) ).
thf(f182,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f181,plain,
( spl0_6
<=> ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f619,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f596]) ).
thf(f299,plain,
( ~ spl0_6
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f298]) ).
thf(f298,plain,
( $false
| ~ spl0_6
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f297,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[],[f296]) ).
thf(f296,plain,
( ( ~ $false = $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[],[f295]) ).
thf(f295,plain,
( ( ( ~ ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[],[f294]) ).
thf(f294,plain,
( ( ( ~ ( $false
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[],[f293]) ).
thf(f293,plain,
( ( ( ~ ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[],[f292]) ).
thf(f292,plain,
( ( ( ~ ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[],[f291]) ).
thf(f291,plain,
( ( $false
= ( ~ ( $false
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[],[f290]) ).
thf(f290,plain,
( ( ( ( $false
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> $false )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[],[f289]) ).
thf(f289,plain,
( ( ( ( $false
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_14 ),
inference(boolean_simplification,[],[f288]) ).
thf(f288,plain,
( ( $false
= ( ( $false
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( sK11 = sK9 )
& $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f287,f270]) ).
thf(f270,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f269,plain,
( spl0_14
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f287,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f286]) ).
thf(f286,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y2 @ Y3 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y1 @ Y2 )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y1 @ Y3 )
& ( sK9 @ Y2 @ Y1 ) )
=> ( sK9 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y2 @ Y3 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y3 ) ) ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f285]) ).
thf(f285,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y2 @ Y3 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y1 @ Y2 )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y1 @ Y3 )
& ( sK9 @ Y2 @ Y1 ) )
=> ( sK9 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y2 @ Y3 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f284]) ).
thf(f284,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y2 @ Y4 )
& ( sK9 @ Y3 @ Y2 ) )
=> ( sK9 @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( Y1 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y3 @ Y4 )
& ( sK9 @ Y2 @ Y3 ) )
=> ( sK9 @ Y2 @ Y4 ) ) ) ) ) ) ) )
@ sK10 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f283]) ).
thf(f283,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y2 @ Y4 )
& ( sK9 @ Y3 @ Y2 ) )
=> ( sK9 @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( Y1 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y3 @ Y4 )
& ( sK9 @ Y2 @ Y3 ) )
=> ( sK9 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f282]) ).
thf(f282,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) )
@ sK9 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f182]) ).
thf(f271,plain,
( spl0_13
| spl0_14
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f264,f198,f269,f266]) ).
thf(f198,plain,
( spl0_7
<=> ( ( ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f264,plain,
( ( $false
= ( sK11 = sK9 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f199]) ).
thf(f199,plain,
( ( ( ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f198]) ).
thf(f238,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f237]) ).
thf(f237,plain,
( $false
| ~ spl0_6
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f236,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_8 ),
inference(boolean_simplification,[],[f235]) ).
thf(f235,plain,
( ( ( $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y0 @ Y1 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_8 ),
inference(boolean_simplification,[],[f234]) ).
thf(f234,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK9 )
& $false
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y0 @ Y1 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f231,f202]) ).
thf(f202,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f201]) ).
thf(f201,plain,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f231,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y0 @ Y1 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f229,f230]) ).
thf(f230,plain,
( ( sK9 = sK10 )
| ~ spl0_6 ),
inference(equality_proxy_clausification,[],[f226]) ).
thf(f226,plain,
( ( $true
= ( sK10 = sK9 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f223]) ).
thf(f223,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 ) ) )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f222]) ).
thf(f222,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& $true )
= $true )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f193,f220]) ).
thf(f220,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f193]) ).
thf(f193,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f191]) ).
thf(f191,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f190]) ).
thf(f190,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y2 @ Y3 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y1 @ Y2 )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y1 @ Y3 )
& ( sK9 @ Y2 @ Y1 ) )
=> ( sK9 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y2 @ Y3 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y3 ) ) ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f189]) ).
thf(f189,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK10 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK10 @ Y2 @ Y3 )
& ( sK10 @ Y1 @ Y2 ) )
=> ( sK10 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK10 @ Y1 @ Y2 )
=> ( sK10 @ Y2 @ Y1 ) ) ) )
& ( sK10 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y1 @ Y3 )
& ( sK9 @ Y2 @ Y1 ) )
=> ( sK9 @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK9 @ Y2 @ Y1 )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK9 @ Y2 @ Y3 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f188]) ).
thf(f188,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y2 @ Y4 )
& ( sK9 @ Y3 @ Y2 ) )
=> ( sK9 @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( Y1 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y3 @ Y4 )
& ( sK9 @ Y2 @ Y3 ) )
=> ( sK9 @ Y2 @ Y4 ) ) ) ) ) ) ) )
@ sK10 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f187]) ).
thf(f187,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( Y0 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y2 @ Y4 )
& ( sK9 @ Y3 @ Y2 ) )
=> ( sK9 @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( Y1 = sK9 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK9 @ Y3 @ Y2 )
=> ( sK9 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK9 @ Y3 @ Y4 )
& ( sK9 @ Y2 @ Y3 ) )
=> ( sK9 @ Y2 @ Y4 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f186]) ).
thf(f186,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) )
@ sK9 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f182]) ).
thf(f229,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f228]) ).
thf(f228,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( sK11 = sK10 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK10 @ Y0 @ Y1 )
=> ( sK10 @ Y1 @ Y0 ) ) ) )
& $true )
= $true )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f223,f226]) ).
thf(f203,plain,
( spl0_7
| spl0_8
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f196,f181,f201,f198]) ).
thf(f196,plain,
( ( ( ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f195]) ).
thf(f195,plain,
( ( $false
= ( ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f194]) ).
thf(f194,plain,
( ( ( $true
=> ( ( sK11 = sK9 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK9 @ Y1 @ Y0 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f191,f193]) ).
thf(f183,plain,
( spl0_5
| spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f176,f12,f181,f178]) ).
thf(f12,plain,
( spl0_1
<=> ( ( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f176,plain,
( ( $false
= ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) ) )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f13]) ).
thf(f13,plain,
( ( ( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f12]) ).
thf(f173,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f172]) ).
thf(f172,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f171]) ).
thf(f171,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f170]) ).
thf(f170,plain,
( ( ~ $true = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f163,f130]) ).
thf(f130,plain,
( ( ( sK2 @ sK8 @ sK7 )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f128]) ).
thf(f128,plain,
( ( $false
= ( ( sK2 @ sK8 @ sK7 )
=> ( sK2 @ sK7 @ sK8 ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f127]) ).
thf(f127,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK7 )
=> ( sK2 @ sK7 @ Y0 ) )
@ sK8 ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(sigma_clausification,[],[f126]) ).
thf(f126,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK7 )
=> ( sK2 @ sK7 @ Y0 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f125]) ).
thf(f125,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) )
@ sK7 )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(sigma_clausification,[],[f122]) ).
thf(f122,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f121]) ).
thf(f121,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& $true ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f120]) ).
thf(f120,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( sK2 = sK2 ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f36,f60]) ).
thf(f60,plain,
( ( sK3 = sK2 )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[],[f56]) ).
thf(f56,plain,
( ( ( sK3 = sK2 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f55]) ).
thf(f55,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( sK3 = sK2 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f54]) ).
thf(f54,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( sK3 = sK2 )
& $true )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f25,f52]) ).
thf(f52,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK2 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y1 @ Y3 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( sK2 @ Y2 @ Y3 ) ) ) ) ) ) )
@ sK3 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f21]) ).
thf(f21,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK2 @ Y1 @ Y2 ) ) ) )
& ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y1 @ Y3 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( sK2 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f20]) ).
thf(f20,plain,
( ( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) )
@ sK2 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f16]) ).
thf(f16,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f15,plain,
( spl0_2
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f36,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( sK3 = sK2 ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f35,plain,
( spl0_4
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( sK3 = sK2 ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f163,plain,
( ( ( ~ ( sK2 @ sK8 @ sK7 ) )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f159]) ).
thf(f159,plain,
( ( $true
= ( ( sK2 @ sK8 @ sK7 )
=> $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f157,f129]) ).
thf(f129,plain,
( ( ( sK2 @ sK7 @ sK8 )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f128]) ).
thf(f157,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X1 @ X2 )
=> ( sK2 @ X2 @ X1 ) )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f156,f68]) ).
thf(f68,plain,
( ! [X2: a,X1: a] :
( ( sK2 @ X1 @ X2 )
= ( sK3 @ X1 @ X2 ) )
| ~ spl0_2 ),
inference(argument_congruence,[],[f65]) ).
thf(f65,plain,
( ! [X1: a] :
( ( sK3 @ X1 )
= ( sK2 @ X1 ) )
| ~ spl0_2 ),
inference(argument_congruence,[],[f60]) ).
thf(f156,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X1 @ X2 )
=> ( sK3 @ X2 @ X1 ) )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f155,f68]) ).
thf(f155,plain,
( ! [X2: a,X1: a] :
( ( ( sK3 @ X1 @ X2 )
=> ( sK3 @ X2 @ X1 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f154]) ).
thf(f154,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK3 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f102]) ).
thf(f102,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK3 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f101]) ).
thf(f101,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f52]) ).
thf(f116,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f115]) ).
thf(f115,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f114,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f107,f46]) ).
thf(f46,plain,
( ( ( sK2 @ sK5 @ sK6 )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f45,plain,
( ( ( ( ( sK2 @ sK4 @ sK6 )
& ( sK2 @ sK5 @ sK4 ) )
=> ( sK2 @ sK5 @ sK6 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
& ( sK2 @ sK5 @ sK4 ) )
=> ( sK2 @ sK5 @ Y0 ) )
@ sK6 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f43]) ).
thf(f43,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
& ( sK2 @ sK5 @ sK4 ) )
=> ( sK2 @ sK5 @ Y0 ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f42]) ).
thf(f42,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
& ( sK2 @ Y0 @ sK4 ) )
=> ( sK2 @ Y0 @ Y1 ) ) )
@ sK5 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f41]) ).
thf(f41,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
& ( sK2 @ Y0 @ sK4 ) )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f40]) ).
thf(f40,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) )
@ sK4 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f33]) ).
thf(f33,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f32,plain,
( spl0_3
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f107,plain,
( ( ( sK2 @ sK5 @ sK6 )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f106]) ).
thf(f106,plain,
( ( $true
= ( $true
=> ( sK2 @ sK5 @ sK6 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f92,f86]) ).
thf(f86,plain,
( ( ( sK2 @ sK4 @ sK6 )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f47]) ).
thf(f47,plain,
( ( ( ( sK2 @ sK4 @ sK6 )
& ( sK2 @ sK5 @ sK4 ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f92,plain,
( ! [X0: a] :
( ( ( sK2 @ sK4 @ X0 )
=> ( sK2 @ sK5 @ X0 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f89]) ).
thf(f89,plain,
( ! [X0: a] :
( ( ( $true
& ( sK2 @ sK4 @ X0 ) )
=> ( sK2 @ sK5 @ X0 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f73,f88]) ).
thf(f88,plain,
( ( $true
= ( sK2 @ sK5 @ sK4 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f87]) ).
thf(f87,plain,
( ( $true
= ( $true
& ( sK2 @ sK5 @ sK4 ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f47,f86]) ).
thf(f73,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK2 @ X3 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK2 @ X3 @ X2 ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f72,f68]) ).
thf(f72,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK2 @ X3 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK3 @ X3 @ X2 ) )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f71,f68]) ).
thf(f71,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK2 @ X3 @ X1 )
& ( sK3 @ X1 @ X2 ) )
=> ( sK3 @ X3 @ X2 ) )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f70,f68]) ).
thf(f70,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK3 @ X3 @ X1 )
& ( sK3 @ X1 @ X2 ) )
=> ( sK3 @ X3 @ X2 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f69]) ).
thf(f69,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK3 @ Y0 @ X1 )
& ( sK3 @ X1 @ X2 ) )
=> ( sK3 @ Y0 @ X2 ) )
@ X3 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f67]) ).
thf(f67,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ X1 )
& ( sK3 @ X1 @ X2 ) )
=> ( sK3 @ Y0 @ X2 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f66]) ).
thf(f66,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ X1 )
& ( sK3 @ X1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f64]) ).
thf(f64,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ X1 )
& ( sK3 @ X1 @ Y0 ) )
=> ( sK3 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f63]) ).
thf(f63,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f59]) ).
thf(f59,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f58]) ).
thf(f58,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK3 @ Y2 @ Y1 ) ) ) ) )
& $true )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f55,f56]) ).
thf(f37,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f30,f15,f35,f32]) ).
thf(f30,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( sK3 = sK2 ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f24]) ).
thf(f24,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
& ( sK3 = sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f10,f15,f12]) ).
thf(f10,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
= $false )
| ( ( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f7]) ).
thf(f7,plain,
( ( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( Y0 = Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y0 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
= ( ^ [Y0: a > a > $o,Y1: a > a > $o] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
& ( Y0 @ Y2 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( Y0 = Y1 ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( Y2 = Y1 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y1 @ Y4 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y0 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y0 @ Y3 @ Y4 ) )
=> ( Y0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) )
& ( Y1 = Y0 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > a > $o,X1: a > a > $o] :
( ( ! [X2: a,X3: a] :
( ( X0 @ X3 @ X2 )
=> ( X0 @ X2 @ X3 ) )
& ( X0 = X1 )
& ! [X4: a,X5: a,X6: a] :
( ( ( X0 @ X6 @ X5 )
& ( X0 @ X4 @ X6 ) )
=> ( X0 @ X4 @ X5 ) ) )
=> ( ! [X7: a,X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
& ( X1 @ X9 @ X7 ) )
=> ( X1 @ X8 @ X7 ) )
& ( X0 = X1 )
& ! [X10: a,X11: a] :
( ( X1 @ X10 @ X11 )
=> ( X1 @ X11 @ X10 ) ) ) )
& ! [X12: a > a > $o,X13: a > a > $o,X14: a > a > $o] :
( ( ! [X15: a,X16: a,X17: a] :
( ( ( X14 @ X16 @ X17 )
& ( X14 @ X17 @ X15 ) )
=> ( X14 @ X16 @ X15 ) )
& ( X13 = X14 )
& ! [X18: a,X19: a] :
( ( X13 @ X19 @ X18 )
=> ( X13 @ X18 @ X19 ) )
& ! [X20: a,X21: a,X22: a] :
( ( ( X13 @ X22 @ X21 )
& ( X13 @ X21 @ X20 ) )
=> ( X13 @ X22 @ X20 ) )
& ( X12 = X13 )
& ! [X23: a,X24: a] :
( ( X14 @ X23 @ X24 )
=> ( X14 @ X24 @ X23 ) ) )
=> ( ! [X25: a,X26: a,X27: a] :
( ( ( X14 @ X27 @ X26 )
& ( X14 @ X26 @ X25 ) )
=> ( X14 @ X27 @ X25 ) )
& ! [X28: a,X29: a] :
( ( X14 @ X28 @ X29 )
=> ( X14 @ X29 @ X28 ) )
& ( X12 = X14 ) ) )
& ( ( ^ [X30: a > a > $o,X31: a > a > $o] :
( ! [X32: a,X33: a,X34: a] :
( ( ( X30 @ X33 @ X34 )
& ( X30 @ X34 @ X32 ) )
=> ( X30 @ X33 @ X32 ) )
& ! [X35: a,X36: a] :
( ( X30 @ X36 @ X35 )
=> ( X30 @ X35 @ X36 ) )
& ( X30 = X31 ) ) )
= ( ^ [X37: a > a > $o,X38: a > a > $o] :
( ( X37 = X38 )
& ! [X39: a,X40: a,X41: a] :
( ( ( X37 @ X41 @ X39 )
& ( X37 @ X39 @ X40 ) )
=> ( X37 @ X41 @ X40 ) )
& ! [X42: a,X43: a] :
( ( X37 @ X42 @ X43 )
=> ( X37 @ X43 @ X42 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > a > $o,X1: a > a > $o] :
( ( ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ( X0 = X1 )
& ! [X2: a,X4: a,X3: a] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X4 ) ) )
=> ( ! [X4: a,X2: a,X3: a] :
( ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
& ( X0 = X1 )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) )
& ! [X4: a > a > $o,X1: a > a > $o,X0: a > a > $o] :
( ( ! [X5: a,X2: a,X3: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X5 ) )
=> ( X0 @ X2 @ X5 ) )
& ( X0 = X1 )
& ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ! [X5: a,X3: a,X2: a] :
( ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X5 ) )
=> ( X1 @ X2 @ X5 ) )
& ( X1 = X4 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) ) )
=> ( ! [X5: a,X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X5 ) )
=> ( X0 @ X2 @ X5 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ( X0 = X4 ) ) )
& ( ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ! [X4: a,X0: a,X1: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ! [X1: a,X0: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) )
& ( X6 = X7 ) ) )
= ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ( X6 = X7 )
& ! [X1: a,X4: a,X0: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ! [X0: a,X1: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ! [X0: a > a > $o,X1: a > a > $o] :
( ( ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ( X0 = X1 )
& ! [X2: a,X4: a,X3: a] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X4 ) ) )
=> ( ! [X4: a,X2: a,X3: a] :
( ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
& ( X0 = X1 )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) )
& ! [X4: a > a > $o,X1: a > a > $o,X0: a > a > $o] :
( ( ! [X5: a,X2: a,X3: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X5 ) )
=> ( X0 @ X2 @ X5 ) )
& ( X0 = X1 )
& ! [X3: a,X2: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ! [X5: a,X3: a,X2: a] :
( ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X5 ) )
=> ( X1 @ X2 @ X5 ) )
& ( X1 = X4 )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) ) )
=> ( ! [X5: a,X3: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X5 ) )
=> ( X0 @ X2 @ X5 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ( X0 = X4 ) ) )
& ( ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ! [X4: a,X0: a,X1: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ! [X1: a,X0: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) )
& ( X6 = X7 ) ) )
= ( ^ [X6: a > a > $o,X7: a > a > $o] :
( ( X6 = X7 )
& ! [X1: a,X4: a,X0: a] :
( ( ( X6 @ X0 @ X1 )
& ( X6 @ X1 @ X4 ) )
=> ( X6 @ X0 @ X4 ) )
& ! [X0: a,X1: a] :
( ( X6 @ X0 @ X1 )
=> ( X6 @ X1 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM515_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV040^5 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 18:27:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % (20436)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (20435)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (20437)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)
% 0.14/0.37 % (20439)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)
% 0.14/0.37 % (20440)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)
% 0.14/0.37 % (20441)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (20439)Instruction limit reached!
% 0.14/0.37 % (20439)------------------------------
% 0.14/0.37 % (20439)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (20439)Termination reason: Unknown
% 0.14/0.37 % (20439)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (20439)Memory used [KB]: 1023
% 0.14/0.37 % (20439)Time elapsed: 0.003 s
% 0.14/0.37 % (20439)Instructions burned: 2 (million)
% 0.14/0.37 % (20439)------------------------------
% 0.14/0.37 % (20439)------------------------------
% 0.14/0.37 % (20436)Instruction limit reached!
% 0.14/0.37 % (20436)------------------------------
% 0.14/0.37 % (20436)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (20436)Termination reason: Unknown
% 0.14/0.37 % (20436)Termination phase: Preprocessing 3
% 0.14/0.37
% 0.14/0.37 % (20436)Memory used [KB]: 1023
% 0.14/0.37 % (20436)Time elapsed: 0.004 s
% 0.14/0.37 % (20436)Instructions burned: 4 (million)
% 0.14/0.37 % (20436)------------------------------
% 0.14/0.37 % (20436)------------------------------
% 0.14/0.37 % (20438)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (20438)Instruction limit reached!
% 0.14/0.37 % (20438)------------------------------
% 0.14/0.37 % (20438)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (20438)Termination reason: Unknown
% 0.14/0.37 % (20438)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (20438)Memory used [KB]: 895
% 0.14/0.37 % (20438)Time elapsed: 0.003 s
% 0.14/0.37 % (20438)Instructions burned: 2 (million)
% 0.14/0.37 % (20438)------------------------------
% 0.14/0.37 % (20438)------------------------------
% 0.14/0.38 % (20441)Instruction limit reached!
% 0.14/0.38 % (20441)------------------------------
% 0.14/0.38 % (20441)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20441)Termination reason: Unknown
% 0.14/0.38 % (20441)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (20441)Memory used [KB]: 5628
% 0.14/0.38 % (20441)Time elapsed: 0.013 s
% 0.14/0.38 % (20441)Instructions burned: 19 (million)
% 0.14/0.38 % (20441)------------------------------
% 0.14/0.38 % (20441)------------------------------
% 0.14/0.38 % (20442)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.38 % (20442)Instruction limit reached!
% 0.14/0.38 % (20442)------------------------------
% 0.14/0.38 % (20442)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20442)Termination reason: Unknown
% 0.14/0.38 % (20442)Termination phase: Preprocessing 3
% 0.14/0.38
% 0.14/0.38 % (20442)Memory used [KB]: 1023
% 0.14/0.38 % (20442)Time elapsed: 0.004 s
% 0.14/0.38 % (20442)Instructions burned: 4 (million)
% 0.14/0.38 % (20442)------------------------------
% 0.14/0.38 % (20442)------------------------------
% 0.14/0.38 % (20443)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)
% 0.14/0.38 % (20437)Instruction limit reached!
% 0.14/0.38 % (20437)------------------------------
% 0.14/0.38 % (20437)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20437)Termination reason: Unknown
% 0.14/0.38 % (20437)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (20437)Memory used [KB]: 5756
% 0.14/0.38 % (20437)Time elapsed: 0.017 s
% 0.14/0.38 % (20437)Instructions burned: 28 (million)
% 0.14/0.38 % (20437)------------------------------
% 0.14/0.38 % (20437)------------------------------
% 0.14/0.39 % (20444)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)
% 0.14/0.39 % (20445)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)
% 0.14/0.39 % (20445)Instruction limit reached!
% 0.14/0.39 % (20445)------------------------------
% 0.14/0.39 % (20445)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (20445)Termination reason: Unknown
% 0.14/0.39 % (20445)Termination phase: Preprocessing 3
% 0.14/0.39
% 0.14/0.39 % (20445)Memory used [KB]: 1023
% 0.14/0.39 % (20445)Time elapsed: 0.004 s
% 0.14/0.39 % (20445)Instructions burned: 4 (million)
% 0.14/0.39 % (20445)------------------------------
% 0.14/0.39 % (20445)------------------------------
% 0.14/0.39 % (20444)Instruction limit reached!
% 0.14/0.39 % (20444)------------------------------
% 0.14/0.39 % (20444)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (20444)Termination reason: Unknown
% 0.14/0.39 % (20444)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (20444)Memory used [KB]: 5756
% 0.14/0.39 % (20444)Time elapsed: 0.011 s
% 0.14/0.39 % (20444)Instructions burned: 16 (million)
% 0.14/0.39 % (20444)------------------------------
% 0.14/0.39 % (20444)------------------------------
% 0.14/0.40 % (20446)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)
% 0.14/0.40 % (20447)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.40 % (20443)Instruction limit reached!
% 0.20/0.40 % (20443)------------------------------
% 0.20/0.40 % (20443)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (20443)Termination reason: Unknown
% 0.20/0.40 % (20443)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (20443)Memory used [KB]: 5628
% 0.20/0.40 % (20443)Time elapsed: 0.017 s
% 0.20/0.40 % (20443)Instructions burned: 39 (million)
% 0.20/0.40 % (20443)------------------------------
% 0.20/0.40 % (20443)------------------------------
% 0.20/0.40 % (20448)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.40 % (20447)Instruction limit reached!
% 0.20/0.40 % (20447)------------------------------
% 0.20/0.40 % (20447)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (20447)Termination reason: Unknown
% 0.20/0.40 % (20447)Termination phase: Property scanning
% 0.20/0.40
% 0.20/0.40 % (20447)Memory used [KB]: 1023
% 0.20/0.40 % (20447)Time elapsed: 0.006 s
% 0.20/0.40 % (20447)Instructions burned: 9 (million)
% 0.20/0.40 % (20447)------------------------------
% 0.20/0.40 % (20447)------------------------------
% 0.20/0.41 % (20449)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)
% 0.20/0.41 % (20449)Instruction limit reached!
% 0.20/0.41 % (20449)------------------------------
% 0.20/0.41 % (20449)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (20449)Termination reason: Unknown
% 0.20/0.41 % (20449)Termination phase: Preprocessing 3
% 0.20/0.41
% 0.20/0.41 % (20449)Memory used [KB]: 1023
% 0.20/0.41 % (20449)Time elapsed: 0.004 s
% 0.20/0.41 % (20449)Instructions burned: 4 (million)
% 0.20/0.41 % (20449)------------------------------
% 0.20/0.41 % (20449)------------------------------
% 0.20/0.41 % (20450)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)
% 0.20/0.41 % (20448)Instruction limit reached!
% 0.20/0.41 % (20448)------------------------------
% 0.20/0.41 % (20448)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (20448)Termination reason: Unknown
% 0.20/0.41 % (20448)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (20448)Memory used [KB]: 5756
% 0.20/0.41 % (20448)Time elapsed: 0.011 s
% 0.20/0.41 % (20448)Instructions burned: 16 (million)
% 0.20/0.41 % (20448)------------------------------
% 0.20/0.41 % (20448)------------------------------
% 0.20/0.41 % (20450)Instruction limit reached!
% 0.20/0.41 % (20450)------------------------------
% 0.20/0.41 % (20450)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (20450)Termination reason: Unknown
% 0.20/0.41 % (20450)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (20450)Memory used [KB]: 1023
% 0.20/0.41 % (20450)Time elapsed: 0.003 s
% 0.20/0.41 % (20450)Instructions burned: 3 (million)
% 0.20/0.41 % (20450)------------------------------
% 0.20/0.41 % (20450)------------------------------
% 0.20/0.41 % (20451)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)
% 0.20/0.41 % (20451)Instruction limit reached!
% 0.20/0.41 % (20451)------------------------------
% 0.20/0.41 % (20451)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (20451)Termination reason: Unknown
% 0.20/0.41 % (20451)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (20451)Memory used [KB]: 1023
% 0.20/0.41 % (20451)Time elapsed: 0.003 s
% 0.20/0.41 % (20451)Instructions burned: 7 (million)
% 0.20/0.41 % (20451)------------------------------
% 0.20/0.41 % (20451)------------------------------
% 0.20/0.42 % (20452)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)
% 0.20/0.42 % (20452)Instruction limit reached!
% 0.20/0.42 % (20452)------------------------------
% 0.20/0.42 % (20452)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (20452)Termination reason: Unknown
% 0.20/0.42 % (20452)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (20452)Memory used [KB]: 1023
% 0.20/0.42 % (20452)Time elapsed: 0.003 s
% 0.20/0.42 % (20452)Instructions burned: 3 (million)
% 0.20/0.42 % (20452)------------------------------
% 0.20/0.42 % (20452)------------------------------
% 0.20/0.42 % (20456)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.42 % (20456)Instruction limit reached!
% 0.20/0.42 % (20456)------------------------------
% 0.20/0.42 % (20456)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (20456)Termination reason: Unknown
% 0.20/0.42 % (20456)Termination phase: Equality resolution with deletion
% 0.20/0.42
% 0.20/0.42 % (20456)Memory used [KB]: 1023
% 0.20/0.42 % (20456)Time elapsed: 0.003 s
% 0.20/0.42 % (20456)Instructions burned: 7 (million)
% 0.20/0.42 % (20456)------------------------------
% 0.20/0.42 % (20456)------------------------------
% 0.20/0.42 % (20453)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.42 % (20453)Instruction limit reached!
% 0.20/0.42 % (20453)------------------------------
% 0.20/0.42 % (20453)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (20453)Termination reason: Unknown
% 0.20/0.42 % (20453)Termination phase: Preprocessing 3
% 0.20/0.42
% 0.20/0.42 % (20453)Memory used [KB]: 1023
% 0.20/0.42 % (20453)Time elapsed: 0.004 s
% 0.20/0.42 % (20453)Instructions burned: 4 (million)
% 0.20/0.42 % (20453)------------------------------
% 0.20/0.42 % (20453)------------------------------
% 0.20/0.42 % (20454)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)
% 0.20/0.42 % (20455)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.43 % (20458)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)
% 0.20/0.43 % (20457)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)
% 0.20/0.43 % (20454)Instruction limit reached!
% 0.20/0.43 % (20454)------------------------------
% 0.20/0.43 % (20454)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (20454)Termination reason: Unknown
% 0.20/0.43 % (20454)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (20454)Memory used [KB]: 5628
% 0.20/0.43 % (20454)Time elapsed: 0.012 s
% 0.20/0.43 % (20454)Instructions burned: 18 (million)
% 0.20/0.43 % (20454)------------------------------
% 0.20/0.43 % (20454)------------------------------
% 0.20/0.44 % (20458)Instruction limit reached!
% 0.20/0.44 % (20458)------------------------------
% 0.20/0.44 % (20458)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (20458)Termination reason: Unknown
% 0.20/0.44 % (20458)Termination phase: Saturation
% 0.20/0.44
% 0.20/0.44 % (20458)Memory used [KB]: 5756
% 0.20/0.44 % (20458)Time elapsed: 0.008 s
% 0.20/0.44 % (20458)Instructions burned: 21 (million)
% 0.20/0.44 % (20458)------------------------------
% 0.20/0.44 % (20458)------------------------------
% 0.20/0.44 % (20459)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.44 % (20459)Instruction limit reached!
% 0.20/0.44 % (20459)------------------------------
% 0.20/0.44 % (20459)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (20459)Termination reason: Unknown
% 0.20/0.44 % (20459)Termination phase: Property scanning
% 0.20/0.44
% 0.20/0.44 % (20459)Memory used [KB]: 1023
% 0.20/0.44 % (20459)Time elapsed: 0.004 s
% 0.20/0.44 % (20459)Instructions burned: 5 (million)
% 0.20/0.44 % (20459)------------------------------
% 0.20/0.44 % (20459)------------------------------
% 0.20/0.44 % (20461)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.20/0.45 % (20460)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)
% 0.20/0.45 % (20460)Instruction limit reached!
% 0.20/0.45 % (20460)------------------------------
% 0.20/0.45 % (20460)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (20460)Termination reason: Unknown
% 0.20/0.45 % (20460)Termination phase: Saturation
% 0.20/0.45
% 0.20/0.45 % (20460)Memory used [KB]: 5500
% 0.20/0.45 % (20460)Time elapsed: 0.005 s
% 0.20/0.45 % (20460)Instructions burned: 7 (million)
% 0.20/0.45 % (20460)------------------------------
% 0.20/0.45 % (20460)------------------------------
% 0.20/0.46 % (20462)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.20/0.47 % (20463)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.20/0.48 % (20463)Instruction limit reached!
% 0.20/0.48 % (20463)------------------------------
% 0.20/0.48 % (20463)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.48 % (20463)Termination reason: Unknown
% 0.20/0.48 % (20463)Termination phase: Saturation
% 0.20/0.48
% 0.20/0.48 % (20463)Memory used [KB]: 5500
% 0.20/0.48 % (20435)Instruction limit reached!
% 0.20/0.48 % (20435)------------------------------
% 0.20/0.48 % (20435)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.48 % (20435)Termination reason: Unknown
% 0.20/0.48 % (20435)Termination phase: Saturation
% 0.20/0.48
% 0.20/0.48 % (20435)Memory used [KB]: 6396
% 0.20/0.48 % (20435)Time elapsed: 0.110 s
% 0.20/0.48 % (20435)Instructions burned: 183 (million)
% 0.20/0.48 % (20435)------------------------------
% 0.20/0.48 % (20435)------------------------------
% 0.20/0.48 % (20463)Time elapsed: 0.012 s
% 0.20/0.48 % (20463)Instructions burned: 20 (million)
% 0.20/0.48 % (20463)------------------------------
% 0.20/0.48 % (20463)------------------------------
% 0.20/0.49 % (20465)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.20/0.50 % (20465)Instruction limit reached!
% 0.20/0.50 % (20465)------------------------------
% 0.20/0.50 % (20465)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.50 % (20465)Termination reason: Unknown
% 0.20/0.50 % (20465)Termination phase: Saturation
% 0.20/0.50
% 0.20/0.50 % (20465)Memory used [KB]: 5756
% 0.20/0.50 % (20465)Time elapsed: 0.008 s
% 0.20/0.50 % (20465)Instructions burned: 17 (million)
% 0.20/0.50 % (20465)------------------------------
% 0.20/0.50 % (20465)------------------------------
% 0.20/0.50 % (20464)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)
% 0.20/0.50 % (20466)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.20/0.50 % (20466)Instruction limit reached!
% 0.20/0.50 % (20466)------------------------------
% 0.20/0.50 % (20466)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.51 % (20466)Termination reason: Unknown
% 0.20/0.51 % (20466)Termination phase: shuffling
% 0.20/0.51
% 0.20/0.51 % (20466)Memory used [KB]: 1023
% 0.20/0.51 % (20466)Time elapsed: 0.002 s
% 0.20/0.51 % (20466)Instructions burned: 3 (million)
% 0.20/0.51 % (20466)------------------------------
% 0.20/0.51 % (20466)------------------------------
% 0.20/0.51 % (20467)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.20/0.52 % (20440)Instruction limit reached!
% 0.20/0.52 % (20440)------------------------------
% 0.20/0.52 % (20440)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.52 % (20440)Termination reason: Unknown
% 0.20/0.52 % (20440)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (20440)Memory used [KB]: 6396
% 0.20/0.52 % (20440)Time elapsed: 0.155 s
% 0.20/0.52 % (20440)Instructions burned: 277 (million)
% 0.20/0.52 % (20440)------------------------------
% 0.20/0.52 % (20440)------------------------------
% 0.20/0.52 % (20467)Instruction limit reached!
% 0.20/0.52 % (20467)------------------------------
% 0.20/0.52 % (20467)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.52 % (20467)Termination reason: Unknown
% 0.20/0.52 % (20467)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (20467)Memory used [KB]: 5756
% 0.20/0.52 % (20467)Time elapsed: 0.011 s
% 0.20/0.52 % (20467)Instructions burned: 30 (million)
% 0.20/0.52 % (20467)------------------------------
% 0.20/0.52 % (20467)------------------------------
% 0.20/0.53 % (20468)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.20/0.53 % (20469)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.20/0.55 % (20446)First to succeed.
% 0.20/0.56 % (20446)Refutation found. Thanks to Tanya!
% 0.20/0.56 % SZS status Theorem for theBenchmark
% 0.20/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.57 % (20446)------------------------------
% 0.20/0.57 % (20446)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.57 % (20446)Termination reason: Refutation
% 0.20/0.57
% 0.20/0.57 % (20446)Memory used [KB]: 6652
% 0.20/0.57 % (20446)Time elapsed: 0.179 s
% 0.20/0.57 % (20446)Instructions burned: 275 (million)
% 0.20/0.57 % (20446)------------------------------
% 0.20/0.57 % (20446)------------------------------
% 0.20/0.57 % (20434)Success in time 0.204 s
% 0.20/0.57 % Vampire---4.8 exiting
%------------------------------------------------------------------------------