%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV157^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:12:11 EDT 2024
% Result : Theorem 1.88s 0.61s
% Output : Refutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 51
% Syntax : Number of formulae : 369 ( 27 unt; 34 typ; 0 def)
% Number of atoms : 3995 ( 313 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 13873 ( 487 ~; 767 |; 745 &;8808 @)
% ( 16 <=>;1119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 1138 (1138 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 45 con; 0-2 aty)
% (1931 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2241 (1991 ^ 249 !; 0 ?;2241 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a > a > $o ).
thf(func_def_22,type,
sK3: a ).
thf(func_def_23,type,
sK4: a > a > $o ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a > a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a > a > $o ).
thf(func_def_29,type,
sK10: a ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a > a > $o ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a ).
thf(func_def_50,type,
sK31: a ).
thf(func_def_51,type,
sK32: a ).
thf(f1294,plain,
$false,
inference(avatar_sat_refutation,[],[f60,f74,f137,f289,f355,f508,f538,f588,f646,f710,f716,f722,f1097,f1159,f1165,f1173,f1293]) ).
thf(f1293,plain,
( ~ spl0_4
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1292]) ).
thf(f1292,plain,
( $false
| ~ spl0_4
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f1291]) ).
thf(f1291,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1284,f1216]) ).
thf(f1216,plain,
( ( $false
= ( sK13 @ sK30 @ sK31 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f1212]) ).
thf(f1212,plain,
( ( $false
= ( ( ( sK13 @ sK29 @ sK31 )
& ( sK13 @ sK30 @ sK29 ) )
=> ( sK13 @ sK30 @ sK31 ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f1211]) ).
thf(f1211,plain,
( ( ( ^ [Y0: a] :
( ( ( sK13 @ sK29 @ Y0 )
& ( sK13 @ sK30 @ sK29 ) )
=> ( sK13 @ sK30 @ Y0 ) )
@ sK31 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f1202]) ).
thf(f1202,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ sK29 @ Y0 )
& ( sK13 @ sK30 @ sK29 ) )
=> ( sK13 @ sK30 @ Y0 ) ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f1201]) ).
thf(f1201,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ sK29 @ Y1 )
& ( sK13 @ Y0 @ sK29 ) )
=> ( sK13 @ Y0 @ Y1 ) ) )
@ sK30 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f1188]) ).
thf(f1188,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ sK29 @ Y1 )
& ( sK13 @ Y0 @ sK29 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f1185]) ).
thf(f1185,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y2 ) ) ) )
@ sK29 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f1093]) ).
thf(f1093,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1092]) ).
thf(f1092,plain,
( spl0_14
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f1284,plain,
( ( $true
= ( sK13 @ sK30 @ sK31 ) )
| ~ spl0_4
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1283]) ).
thf(f1283,plain,
( ( ( $true
=> ( sK13 @ sK30 @ sK31 ) )
= $true )
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f1243,f1233]) ).
thf(f1233,plain,
( ( $true
= ( sK13 @ sK29 @ sK31 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f1217]) ).
thf(f1217,plain,
( ( $true
= ( ( sK13 @ sK29 @ sK31 )
& ( sK13 @ sK30 @ sK29 ) ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f1212]) ).
thf(f1243,plain,
( ! [X0: a] :
( ( ( sK13 @ sK29 @ X0 )
=> ( sK13 @ sK30 @ X0 ) )
= $true )
| ~ spl0_4
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1236]) ).
thf(f1236,plain,
( ! [X0: a] :
( ( ( $true
& ( sK13 @ sK29 @ X0 ) )
=> ( sK13 @ sK30 @ X0 ) )
= $true )
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f819,f1235]) ).
thf(f1235,plain,
( ( $true
= ( sK13 @ sK30 @ sK29 ) )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1234]) ).
thf(f1234,plain,
( ( ( $true
& ( sK13 @ sK30 @ sK29 ) )
= $true )
| ~ spl0_14 ),
inference(backward_demodulation,[],[f1217,f1233]) ).
thf(f819,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK13 @ X3 @ X2 )
& ( sK13 @ X2 @ X1 ) )
=> ( sK13 @ X3 @ X1 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f818]) ).
thf(f818,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK13 @ Y0 @ X2 )
& ( sK13 @ X2 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) )
@ X3 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f807]) ).
thf(f807,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ Y0 @ X2 )
& ( sK13 @ X2 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f806]) ).
thf(f806,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ Y0 )
& ( sK13 @ Y0 @ X1 ) )
=> ( sK13 @ Y1 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f797]) ).
thf(f797,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ Y0 )
& ( sK13 @ Y0 @ X1 ) )
=> ( sK13 @ Y1 @ X1 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f796]) ).
thf(f796,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f753]) ).
thf(f753,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f752]) ).
thf(f752,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
& $true ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f745,f750]) ).
thf(f750,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f745]) ).
thf(f745,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f743]) ).
thf(f743,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
=> ( sK13 @ sK10 @ sK11 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f742]) ).
thf(f742,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ sK13 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f739]) ).
thf(f739,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f738]) ).
thf(f738,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f735,f737]) ).
thf(f737,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK12 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 @ sK11 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f735]) ).
thf(f735,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK12 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 @ sK11 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f734]) ).
thf(f734,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ sK11 ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f733]) ).
thf(f733,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ sK11 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f732]) ).
thf(f732,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y0 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f731]) ).
thf(f731,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y0 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f730]) ).
thf(f730,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f73]) ).
thf(f73,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f72,plain,
( spl0_4
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f1173,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f1172]) ).
thf(f1172,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f1171]) ).
thf(f1171,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16 ),
inference(boolean_simplification,[],[f1170]) ).
thf(f1170,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16 ),
inference(boolean_simplification,[],[f1169]) ).
thf(f1169,plain,
( ( ( ~ ( $true
| ( sK4 @ sK27 @ sK28 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1147,f1155]) ).
thf(f1155,plain,
( ( ( sK2 @ sK27 @ sK28 )
= $true )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f1154]) ).
thf(f1154,plain,
( spl0_16
<=> ( ( sK2 @ sK27 @ sK28 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f1147,plain,
( ( $true
= ( ~ ( ( sK2 @ sK27 @ sK28 )
| ( sK4 @ sK27 @ sK28 ) ) ) )
| ~ spl0_4
| ~ spl0_15 ),
inference(boolean_simplification,[],[f1145]) ).
thf(f1145,plain,
( ( ( ( ( sK2 @ sK27 @ sK28 )
| ( sK4 @ sK27 @ sK28 ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f764,f1141]) ).
thf(f1141,plain,
( ( $false
= ( sK13 @ sK27 @ sK28 ) )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f1140]) ).
thf(f1140,plain,
( ( $false
= ( $true
=> ( sK13 @ sK27 @ sK28 ) ) )
| ~ spl0_15 ),
inference(backward_demodulation,[],[f1137,f1139]) ).
thf(f1139,plain,
( ( ( ( sK4 @ sK27 @ sK28 )
| ( sK2 @ sK27 @ sK28 ) )
= $true )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f1137]) ).
thf(f1137,plain,
( ( $false
= ( ( ( sK4 @ sK27 @ sK28 )
| ( sK2 @ sK27 @ sK28 ) )
=> ( sK13 @ sK27 @ sK28 ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f1136]) ).
thf(f1136,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK27 @ Y0 )
| ( sK2 @ sK27 @ Y0 ) )
=> ( sK13 @ sK27 @ Y0 ) )
@ sK28 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f1131]) ).
thf(f1131,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK27 @ Y0 )
| ( sK2 @ sK27 @ Y0 ) )
=> ( sK13 @ sK27 @ Y0 ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f1128]) ).
thf(f1128,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) )
@ sK27 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f1096]) ).
thf(f1096,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f1095]) ).
thf(f1095,plain,
( spl0_15
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f764,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK2 @ X1 @ X2 )
| ( sK4 @ X1 @ X2 ) )
=> ( sK13 @ X1 @ X2 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f763]) ).
thf(f763,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK13 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f758]) ).
thf(f758,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK13 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f757]) ).
thf(f757,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f750]) ).
thf(f1165,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1164]) ).
thf(f1164,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f1163]) ).
thf(f1163,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(boolean_simplification,[],[f1162]) ).
thf(f1162,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(boolean_simplification,[],[f1160]) ).
thf(f1160,plain,
( ( ( ~ ( ( sK2 @ sK27 @ sK28 )
| $true ) )
= $true )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_17 ),
inference(backward_demodulation,[],[f1147,f1158]) ).
thf(f1158,plain,
( ( $true
= ( sK4 @ sK27 @ sK28 ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f1157]) ).
thf(f1157,plain,
( spl0_17
<=> ( $true
= ( sK4 @ sK27 @ sK28 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f1159,plain,
( spl0_16
| spl0_17
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f1152,f1095,f1157,f1154]) ).
thf(f1152,plain,
( ( $true
= ( sK4 @ sK27 @ sK28 ) )
| ( ( sK2 @ sK27 @ sK28 )
= $true )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f1139]) ).
thf(f1097,plain,
( spl0_14
| spl0_15
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1086,f287,f72,f1095,f1092]) ).
thf(f287,plain,
( spl0_8
<=> ( ( sK13 @ sK14 @ sK11 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f1086,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y2 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1083]) ).
thf(f1083,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f881]) ).
thf(f881,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f876]) ).
thf(f876,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y0 @ Y2 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f855,f864]) ).
thf(f864,plain,
( ( $false
= ( sK13 @ sK10 @ sK14 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f862]) ).
thf(f862,plain,
( ( $true
= ( ~ ( sK13 @ sK10 @ sK14 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f859]) ).
thf(f859,plain,
( ( ( ( sK13 @ sK10 @ sK14 )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f843,f747]) ).
thf(f747,plain,
( ( $false
= ( sK13 @ sK10 @ sK11 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f746]) ).
thf(f746,plain,
( ( $false
= ( $true
=> ( sK13 @ sK10 @ sK11 ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f743,f745]) ).
thf(f843,plain,
( ! [X0: a] :
( ( ( sK13 @ X0 @ sK14 )
=> ( sK13 @ X0 @ sK11 ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f834]) ).
thf(f834,plain,
( ! [X0: a] :
( $true
= ( ( ( sK13 @ X0 @ sK14 )
& $true )
=> ( sK13 @ X0 @ sK11 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f819,f288]) ).
thf(f288,plain,
( ( ( sK13 @ sK14 @ sK11 )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f287]) ).
thf(f855,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK10 @ sK14 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f854]) ).
thf(f854,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK14 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f760]) ).
thf(f760,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK14 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f754]) ).
thf(f754,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK14 @ sK11 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f749]) ).
thf(f749,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK14 @ sK11 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f748]) ).
thf(f748,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) )
@ sK14 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f741]) ).
thf(f741,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f740]) ).
thf(f740,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) )
=> $false ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f733,f739]) ).
thf(f722,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f721]) ).
thf(f721,plain,
( $false
| ~ spl0_1
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f720]) ).
thf(f720,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_13 ),
inference(boolean_simplification,[],[f719]) ).
thf(f719,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_13 ),
inference(boolean_simplification,[],[f718]) ).
thf(f718,plain,
( ( ( ~ ( $true
| ( sK4 @ sK25 @ sK26 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_13 ),
inference(forward_demodulation,[],[f694,f709]) ).
thf(f709,plain,
( ( $true
= ( sK2 @ sK25 @ sK26 ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f708]) ).
thf(f708,plain,
( spl0_13
<=> ( $true
= ( sK2 @ sK25 @ sK26 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f694,plain,
( ( ( ~ ( ( sK2 @ sK25 @ sK26 )
| ( sK4 @ sK25 @ sK26 ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f693]) ).
thf(f693,plain,
( ( $true
= ( ( ( sK2 @ sK25 @ sK26 )
| ( sK4 @ sK25 @ sK26 ) )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[],[f37,f689]) ).
thf(f689,plain,
( ( ( sK6 @ sK25 @ sK26 )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f688]) ).
thf(f688,plain,
( ( $false
= ( $true
=> ( sK6 @ sK25 @ sK26 ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f685,f687]) ).
thf(f687,plain,
( ( $true
= ( ( sK4 @ sK25 @ sK26 )
| ( sK2 @ sK25 @ sK26 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f685]) ).
thf(f685,plain,
( ( $false
= ( ( ( sK4 @ sK25 @ sK26 )
| ( sK2 @ sK25 @ sK26 ) )
=> ( sK6 @ sK25 @ sK26 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f684]) ).
thf(f684,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK25 @ Y0 )
| ( sK2 @ sK25 @ Y0 ) )
=> ( sK6 @ sK25 @ Y0 ) )
@ sK26 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f683]) ).
thf(f683,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK25 @ Y0 )
| ( sK2 @ sK25 @ Y0 ) )
=> ( sK6 @ sK25 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f679]) ).
thf(f679,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK25 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f676]) ).
thf(f676,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f671]) ).
thf(f671,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f670]) ).
thf(f670,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
=> $false )
= $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f669,f24]) ).
thf(f24,plain,
( $false
= ( sK6 @ sK3 @ sK5 ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ sK3 @ sK5 ) ) ),
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 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) )
@ sK6 ) ),
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 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
| $false ) ),
inference(backward_demodulation,[],[f17,f18]) ).
thf(f18,plain,
( $false
= ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( $false
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a,X3: a > a > $o] :
( ~ ( ( ! [X4: a,X5: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a,X9: a] :
( ( ( X6 @ X9 @ X8 )
& ( X6 @ X8 @ X7 ) )
=> ( X6 @ X9 @ X7 ) )
& ! [X10: a,X11: a] :
( ( X1 @ X11 @ X10 )
=> ( X6 @ X11 @ X10 ) ) )
=> ( X6 @ X4 @ X5 ) )
| ! [X12: a > a > $o] :
( ( ! [X13: a,X14: a] :
( ( X3 @ X14 @ X13 )
=> ( X12 @ X14 @ X13 ) )
& ! [X15: a,X16: a,X17: a] :
( ( ( X12 @ X16 @ X17 )
& ( X12 @ X15 @ X16 ) )
=> ( X12 @ X15 @ X17 ) ) )
=> ( X12 @ X4 @ X5 ) ) )
=> ! [X18: a > a > $o] :
( ( ! [X19: a,X20: a,X21: a] :
( ( ( X18 @ X20 @ X21 )
& ( X18 @ X19 @ X20 ) )
=> ( X18 @ X19 @ X21 ) )
& ! [X22: a,X23: a] :
( ( ( X1 @ X23 @ X22 )
| ( X3 @ X23 @ X22 ) )
=> ( X18 @ X23 @ X22 ) ) )
=> ( X18 @ X4 @ X5 ) ) )
& ! [X24: a,X25: a,X26: a] :
( ( ! [X27: a > a > $o] :
( ( ! [X28: a,X29: a] :
( ( ( X1 @ X29 @ X28 )
| ( X3 @ X29 @ X28 ) )
=> ( X27 @ X29 @ X28 ) )
& ! [X30: a,X31: a,X32: a] :
( ( ( X27 @ X32 @ X31 )
& ( X27 @ X31 @ X30 ) )
=> ( X27 @ X32 @ X30 ) ) )
=> ( X27 @ X24 @ X25 ) )
& ! [X33: a > a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( X3 @ X35 @ X34 )
| ( X1 @ X35 @ X34 ) )
=> ( X33 @ X35 @ X34 ) )
& ! [X36: a,X37: a,X38: a] :
( ( ( X33 @ X37 @ X38 )
& ( X33 @ X38 @ X36 ) )
=> ( X33 @ X37 @ X36 ) ) )
=> ( X33 @ X26 @ X24 ) ) )
=> ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a] :
( ( ( X1 @ X41 @ X40 )
| ( X3 @ X41 @ X40 ) )
=> ( X39 @ X41 @ X40 ) )
& ! [X42: a,X43: a,X44: a] :
( ( ( X39 @ X43 @ X44 )
& ( X39 @ X42 @ X43 ) )
=> ( X39 @ X42 @ X44 ) ) )
=> ( X39 @ X26 @ X25 ) ) ) )
=> ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a] :
( ( ( X3 @ X47 @ X46 )
| ( X1 @ X47 @ X46 ) )
=> ( X45 @ X47 @ X46 ) )
& ! [X48: a,X49: a,X50: a] :
( ( ( X45 @ X50 @ X49 )
& ( X45 @ X48 @ X50 ) )
=> ( X45 @ X48 @ X49 ) ) )
=> ( X45 @ X2 @ X0 ) ) )
| ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a] :
( ( ( X1 @ X52 @ X53 )
| ( X3 @ X52 @ X53 ) )
=> ( X51 @ X52 @ X53 ) )
& ! [X54: a,X55: a,X56: a] :
( ( ( X51 @ X56 @ X55 )
& ( X51 @ X54 @ X56 ) )
=> ( X51 @ X54 @ X55 ) ) )
=> ( X51 @ X2 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X1: a > a > $o,X2: a,X0: a > a > $o] :
( ~ ( ( ! [X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X7: a,X9: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ! [X6: a,X7: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X10: a,X9: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) )
& ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X10: a,X8: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X7 ) ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
| ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X3: a,X1: a > a > $o,X2: a,X0: a > a > $o] :
( ~ ( ( ! [X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X7: a,X9: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ! [X6: a,X7: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X10: a,X9: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) )
& ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X10: a,X8: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X7 ) ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
| ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X1 @ X5 @ X6 )
| ( X0 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM250G_pme) ).
thf(f669,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ sK3 @ sK5 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f664]) ).
thf(f664,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK3 @ sK5 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f650,f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f650,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK3 @ sK5 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f649]) ).
thf(f649,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f56]) ).
thf(f56,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f55,plain,
( spl0_1
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f37,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) )
=> ( sK6 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f36]) ).
thf(f36,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f35]) ).
thf(f35,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f34]) ).
thf(f34,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f33]) ).
thf(f33,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f32]) ).
thf(f32,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
inference(backward_demodulation,[],[f25,f31]) ).
thf(f716,plain,
( ~ spl0_1
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f715]) ).
thf(f715,plain,
( $false
| ~ spl0_1
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f714]) ).
thf(f714,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[],[f713]) ).
thf(f713,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[],[f711]) ).
thf(f711,plain,
( ( $true
= ( ~ ( ( sK2 @ sK25 @ sK26 )
| $true ) ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(backward_demodulation,[],[f694,f706]) ).
thf(f706,plain,
( ( $true
= ( sK4 @ sK25 @ sK26 ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f705]) ).
thf(f705,plain,
( spl0_12
<=> ( $true
= ( sK4 @ sK25 @ sK26 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f710,plain,
( spl0_12
| spl0_13
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f703,f55,f708,f705]) ).
thf(f703,plain,
( ( $true
= ( sK2 @ sK25 @ sK26 ) )
| ( $true
= ( sK4 @ sK25 @ sK26 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f687]) ).
thf(f646,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f645]) ).
thf(f645,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f644]) ).
thf(f644,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f643]) ).
thf(f643,plain,
( ( $true = ~ $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f642]) ).
thf(f642,plain,
( ( $true
= ( ~ ( $true
| ( sK4 @ sK23 @ sK24 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f641,f637]) ).
thf(f637,plain,
( ( $true
= ( sK2 @ sK23 @ sK24 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f624]) ).
thf(f624,plain,
( ( $false
= ( ( sK2 @ sK23 @ sK24 )
=> ( sK9 @ sK23 @ sK24 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f623]) ).
thf(f623,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ sK23 @ Y0 )
=> ( sK9 @ sK23 @ Y0 ) )
@ sK24 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f620]) ).
thf(f620,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK23 @ Y0 )
=> ( sK9 @ sK23 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f616]) ).
thf(f616,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ sK23 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f611]) ).
thf(f611,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(not_proxy_clausification,[],[f610]) ).
thf(f610,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f607]) ).
thf(f607,plain,
( ( ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f604,f605]) ).
thf(f605,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f600]) ).
thf(f600,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f597]) ).
thf(f597,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK9 @ sK8 @ sK7 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f596]) ).
thf(f596,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK9 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f593]) ).
thf(f593,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f592]) ).
thf(f592,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f591]) ).
thf(f591,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f397,f133]) ).
thf(f133,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f132,plain,
( spl0_5
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f397,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f396]) ).
thf(f396,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f394]) ).
thf(f394,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f393]) ).
thf(f393,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK7 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f70]) ).
thf(f70,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f69,plain,
( spl0_3
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f604,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f603]) ).
thf(f603,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f595,f602]) ).
thf(f602,plain,
( ( $false
= ( sK9 @ sK8 @ sK7 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f601]) ).
thf(f601,plain,
( ( $false
= ( $true
=> ( sK9 @ sK8 @ sK7 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f597,f600]) ).
thf(f595,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK8 @ sK7 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f594]) ).
thf(f594,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[],[f133]) ).
thf(f641,plain,
( ( $true
= ( ~ ( ( sK2 @ sK23 @ sK24 )
| ( sK4 @ sK23 @ sK24 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f640]) ).
thf(f640,plain,
( ( ( ( ( sK2 @ sK23 @ sK24 )
| ( sK4 @ sK23 @ sK24 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f622,f639]) ).
thf(f639,plain,
( ( $false
= ( sK9 @ sK23 @ sK24 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f638]) ).
thf(f638,plain,
( ( $false
= ( $true
=> ( sK9 @ sK23 @ sK24 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f624,f637]) ).
thf(f622,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X1 @ X2 )
| ( sK4 @ X1 @ X2 ) )
=> ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f621]) ).
thf(f621,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f615]) ).
thf(f615,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f614]) ).
thf(f614,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f609]) ).
thf(f609,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f608]) ).
thf(f608,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& $true ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f600,f605]) ).
thf(f588,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f587]) ).
thf(f587,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f586]) ).
thf(f586,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(boolean_simplification,[],[f585]) ).
thf(f585,plain,
( ( $true = ~ $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_demodulation,[],[f580,f564]) ).
thf(f564,plain,
( ( $true
= ( sK9 @ sK20 @ sK21 ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f551]) ).
thf(f551,plain,
( ( $true
= ( ( sK9 @ sK21 @ sK22 )
& ( sK9 @ sK20 @ sK21 ) ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f549]) ).
thf(f549,plain,
( ( $false
= ( ( ( sK9 @ sK21 @ sK22 )
& ( sK9 @ sK20 @ sK21 ) )
=> ( sK9 @ sK20 @ sK22 ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f548]) ).
thf(f548,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK9 @ sK21 @ Y0 )
& ( sK9 @ sK20 @ sK21 ) )
=> ( sK9 @ sK20 @ Y0 ) )
@ sK22 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f547]) ).
thf(f547,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ sK21 @ Y0 )
& ( sK9 @ sK20 @ sK21 ) )
=> ( sK9 @ sK20 @ Y0 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f546]) ).
thf(f546,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ sK20 @ Y0 ) )
=> ( sK9 @ sK20 @ Y1 ) ) )
@ sK21 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f543]) ).
thf(f543,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ sK20 @ Y0 ) )
=> ( sK9 @ sK20 @ Y1 ) ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f541]) ).
thf(f541,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) )
@ sK20 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f504]) ).
thf(f504,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f503]) ).
thf(f503,plain,
( spl0_10
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f580,plain,
( ( $true
= ( ~ ( sK9 @ sK20 @ sK21 ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(boolean_simplification,[],[f578]) ).
thf(f578,plain,
( ( ( ~ ( ( sK9 @ sK20 @ sK21 )
& $true ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f562,f567]) ).
thf(f567,plain,
( ( $true
= ( sK9 @ sK21 @ sK22 ) )
| ~ spl0_10 ),
inference(boolean_simplification,[],[f566]) ).
thf(f566,plain,
( ( ( ( sK9 @ sK21 @ sK22 )
& $true )
= $true )
| ~ spl0_10 ),
inference(backward_demodulation,[],[f551,f564]) ).
thf(f562,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK9 @ sK20 @ X0 )
& ( sK9 @ X0 @ sK22 ) ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(boolean_simplification,[],[f556]) ).
thf(f556,plain,
( ! [X0: a] :
( $true
= ( ( ( sK9 @ sK20 @ X0 )
& ( sK9 @ X0 @ sK22 ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f435,f553]) ).
thf(f553,plain,
( ( $false
= ( sK9 @ sK20 @ sK22 ) )
| ~ spl0_10 ),
inference(boolean_simplification,[],[f552]) ).
thf(f552,plain,
( ( $false
= ( $true
=> ( sK9 @ sK20 @ sK22 ) ) )
| ~ spl0_10 ),
inference(backward_demodulation,[],[f549,f551]) ).
thf(f435,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK9 @ X3 @ X2 )
& ( sK9 @ X2 @ X1 ) )
=> ( sK9 @ X3 @ X1 ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f434]) ).
thf(f434,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK9 @ Y0 @ X2 )
& ( sK9 @ X2 @ X1 ) )
=> ( sK9 @ Y0 @ X1 ) )
@ X3 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f422]) ).
thf(f422,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ Y0 @ X2 )
& ( sK9 @ X2 @ X1 ) )
=> ( sK9 @ Y0 @ X1 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f421]) ).
thf(f421,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ X1 ) )
=> ( sK9 @ Y1 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f418]) ).
thf(f418,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ X1 ) )
=> ( sK9 @ Y1 @ X1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f417]) ).
thf(f417,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f414]) ).
thf(f414,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f413]) ).
thf(f413,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[],[f404,f412]) ).
thf(f412,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f404]) ).
thf(f404,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f402]) ).
thf(f402,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK9 @ sK8 @ sK7 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f401]) ).
thf(f401,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ sK9 )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[],[f400]) ).
thf(f400,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f399]) ).
thf(f399,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f398]) ).
thf(f398,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f397,f136]) ).
thf(f136,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f135,plain,
( spl0_6
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f538,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f537]) ).
thf(f537,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f536]) ).
thf(f536,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(boolean_simplification,[],[f535]) ).
thf(f535,plain,
( ( $true = ~ $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(boolean_simplification,[],[f534]) ).
thf(f534,plain,
( ( ( ~ ( ( sK2 @ sK18 @ sK19 )
| $true ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_demodulation,[],[f533,f519]) ).
thf(f519,plain,
( ( ( sK4 @ sK18 @ sK19 )
= $true )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f517]) ).
thf(f517,plain,
( ( ( ( sK4 @ sK18 @ sK19 )
=> ( sK9 @ sK18 @ sK19 ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f516]) ).
thf(f516,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK4 @ sK18 @ Y0 )
=> ( sK9 @ sK18 @ Y0 ) )
@ sK19 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f515]) ).
thf(f515,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK18 @ Y0 )
=> ( sK9 @ sK18 @ Y0 ) ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f511]) ).
thf(f511,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ sK18 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f507]) ).
thf(f507,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f506]) ).
thf(f506,plain,
( spl0_11
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f533,plain,
( ( $true
= ( ~ ( ( sK2 @ sK18 @ sK19 )
| ( sK4 @ sK18 @ sK19 ) ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(boolean_simplification,[],[f527]) ).
thf(f527,plain,
( ( $true
= ( ( ( sK2 @ sK18 @ sK19 )
| ( sK4 @ sK18 @ sK19 ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f420,f518]) ).
thf(f518,plain,
( ( $false
= ( sK9 @ sK18 @ sK19 ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f517]) ).
thf(f420,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X1 @ X2 )
| ( sK4 @ X1 @ X2 ) )
=> ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f419]) ).
thf(f419,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f416]) ).
thf(f416,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK4 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f415]) ).
thf(f415,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f412]) ).
thf(f508,plain,
( spl0_10
| spl0_11
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f499,f135,f69,f506,f503]) ).
thf(f499,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f493]) ).
thf(f493,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(not_proxy_clausification,[],[f410]) ).
thf(f410,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f409]) ).
thf(f409,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y1 @ Y2 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y2 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f392,f403]) ).
thf(f403,plain,
( ( $false
= ( sK9 @ sK8 @ sK7 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f402]) ).
thf(f392,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK8 @ sK7 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f391]) ).
thf(f391,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 ) )
| ~ spl0_6 ),
inference(pi_clausification,[],[f136]) ).
thf(f355,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f354]) ).
thf(f354,plain,
( $false
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f353,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f352]) ).
thf(f352,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f347,f323]) ).
thf(f323,plain,
( ( $true
= ( sK13 @ sK16 @ sK17 ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f307]) ).
thf(f307,plain,
( ( $true
= ( ( sK13 @ sK16 @ sK17 )
& ( sK13 @ sK15 @ sK16 ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f305]) ).
thf(f305,plain,
( ( $false
= ( ( ( sK13 @ sK16 @ sK17 )
& ( sK13 @ sK15 @ sK16 ) )
=> ( sK13 @ sK15 @ sK17 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f304]) ).
thf(f304,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK13 @ sK16 @ Y0 )
& ( sK13 @ sK15 @ sK16 ) )
=> ( sK13 @ sK15 @ Y0 ) )
@ sK17 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f303]) ).
thf(f303,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ sK16 @ Y0 )
& ( sK13 @ sK15 @ sK16 ) )
=> ( sK13 @ sK15 @ Y0 ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f302]) ).
thf(f302,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ sK15 @ Y0 ) )
=> ( sK13 @ sK15 @ Y1 ) ) )
@ sK16 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f297]) ).
thf(f297,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ sK15 @ Y0 ) )
=> ( sK13 @ sK15 @ Y1 ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f294]) ).
thf(f294,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y2 ) ) ) )
@ sK15 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f285]) ).
thf(f285,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f284,plain,
( spl0_7
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y2 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f347,plain,
( ( ( ~ ( sK13 @ sK16 @ sK17 ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f344]) ).
thf(f344,plain,
( ( ( ( sK13 @ sK16 @ sK17 )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f330,f306]) ).
thf(f306,plain,
( ( ( sK13 @ sK15 @ sK17 )
= $false )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f305]) ).
thf(f330,plain,
( ! [X0: a] :
( ( ( sK13 @ sK16 @ X0 )
=> ( sK13 @ sK15 @ X0 ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f326]) ).
thf(f326,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK13 @ sK16 @ X0 ) )
=> ( sK13 @ sK15 @ X0 ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f237,f325]) ).
thf(f325,plain,
( ( $true
= ( sK13 @ sK15 @ sK16 ) )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f324]) ).
thf(f324,plain,
( ( $true
= ( $true
& ( sK13 @ sK15 @ sK16 ) ) )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f307,f323]) ).
thf(f237,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK13 @ X3 @ X2 )
& ( sK13 @ X2 @ X1 ) )
=> ( sK13 @ X3 @ X1 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f236]) ).
thf(f236,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK13 @ Y0 @ X2 )
& ( sK13 @ X2 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) )
@ X3 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f235]) ).
thf(f235,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ Y0 @ X2 )
& ( sK13 @ X2 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f234]) ).
thf(f234,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ Y0 )
& ( sK13 @ Y0 @ X1 ) )
=> ( sK13 @ Y1 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f233]) ).
thf(f233,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ Y0 )
& ( sK13 @ Y0 @ X1 ) )
=> ( sK13 @ Y1 @ X1 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f232]) ).
thf(f232,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f174]) ).
thf(f174,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f173]) ).
thf(f173,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
& $true ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f159,f171]) ).
thf(f171,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f159]) ).
thf(f159,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f155]) ).
thf(f155,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
=> ( sK13 @ sK10 @ sK11 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f154]) ).
thf(f154,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ sK13 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f146]) ).
thf(f146,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f145]) ).
thf(f145,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK12 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 @ sK11 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f144]) ).
thf(f144,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ sK11 ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f143]) ).
thf(f143,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ sK11 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f142]) ).
thf(f142,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y0 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f141]) ).
thf(f141,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 @ Y0 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f140]) ).
thf(f140,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f73]) ).
thf(f289,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f282,f72,f287,f284]) ).
thf(f282,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ( ( sK13 @ sK14 @ sK11 )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f197]) ).
thf(f197,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y2 ) ) ) ) )
=> ( sK13 @ sK14 @ sK11 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f196]) ).
thf(f196,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y0 @ Y2 ) ) ) ) )
& $true )
=> ( sK13 @ sK14 @ sK11 ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[],[f183,f171]) ).
thf(f183,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK14 @ sK11 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f182]) ).
thf(f182,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK14 @ sK11 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f167]) ).
thf(f167,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK14 @ sK11 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f164]) ).
thf(f164,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK14 @ sK11 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f157,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK14 @ sK11 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f156]) ).
thf(f156,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) )
@ sK14 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f150]) ).
thf(f150,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f149]) ).
thf(f149,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK11 ) ) ) )
=> $false ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f143,f146]) ).
thf(f137,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f130,f69,f135,f132]) ).
thf(f130,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f90]) ).
thf(f90,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f86]) ).
thf(f86,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f85]) ).
thf(f85,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f82]) ).
thf(f82,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f81]) ).
thf(f81,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK7 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f70]) ).
thf(f74,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f67,f58,f72,f69]) ).
thf(f58,plain,
( spl0_2
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f67,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f59]) ).
thf(f59,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f60,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f53,f58,f55]) ).
thf(f53,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
= $true )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) ) ),
inference(not_proxy_clausification,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV157^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:57:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_NEQ_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38 % (15169)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 % (15163)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)
% 0.14/0.38 % (15167)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.38 % (15164)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.38 % (15168)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (15165)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (15166)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (15162)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (15165)Instruction limit reached!
% 0.14/0.38 % (15165)------------------------------
% 0.14/0.38 % (15165)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (15165)Termination reason: Unknown
% 0.14/0.38 % (15166)Instruction limit reached!
% 0.14/0.38 % (15166)------------------------------
% 0.14/0.38 % (15166)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (15166)Termination reason: Unknown
% 0.14/0.38 % (15166)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (15166)Memory used [KB]: 1023
% 0.14/0.38 % (15166)Time elapsed: 0.003 s
% 0.14/0.38 % (15166)Instructions burned: 2 (million)
% 0.14/0.38 % (15166)------------------------------
% 0.14/0.38 % (15166)------------------------------
% 0.14/0.38 % (15165)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (15165)Memory used [KB]: 1023
% 0.14/0.38 % (15165)Time elapsed: 0.003 s
% 0.14/0.38 % (15165)Instructions burned: 2 (million)
% 0.14/0.38 % (15165)------------------------------
% 0.14/0.38 % (15165)------------------------------
% 0.14/0.39 % (15169)Instruction limit reached!
% 0.14/0.39 % (15169)------------------------------
% 0.14/0.39 % (15169)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15169)Termination reason: Unknown
% 0.14/0.39 % (15169)Termination phase: Preprocessing 3
% 0.14/0.39
% 0.14/0.39 % (15169)Memory used [KB]: 1023
% 0.14/0.39 % (15169)Time elapsed: 0.004 s
% 0.14/0.39 % (15169)Instructions burned: 4 (million)
% 0.14/0.39 % (15169)------------------------------
% 0.14/0.39 % (15169)------------------------------
% 0.14/0.39 % (15163)Instruction limit reached!
% 0.14/0.39 % (15163)------------------------------
% 0.14/0.39 % (15163)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15163)Termination reason: Unknown
% 0.14/0.39 % (15163)Termination phase: Preprocessing 3
% 0.14/0.39
% 0.14/0.39 % (15163)Memory used [KB]: 1023
% 0.14/0.39 % (15163)Time elapsed: 0.005 s
% 0.14/0.39 % (15163)Instructions burned: 5 (million)
% 0.14/0.39 % (15163)------------------------------
% 0.14/0.39 % (15163)------------------------------
% 0.14/0.39 % (15168)Instruction limit reached!
% 0.14/0.39 % (15168)------------------------------
% 0.14/0.39 % (15168)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15168)Termination reason: Unknown
% 0.14/0.39 % (15168)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (15168)Memory used [KB]: 5628
% 0.14/0.39 % (15168)Time elapsed: 0.013 s
% 0.14/0.39 % (15168)Instructions burned: 19 (million)
% 0.14/0.39 % (15168)------------------------------
% 0.14/0.39 % (15168)------------------------------
% 0.21/0.40 % (15164)Instruction limit reached!
% 0.21/0.40 % (15164)------------------------------
% 0.21/0.40 % (15164)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (15164)Termination reason: Unknown
% 0.21/0.40 % (15164)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (15164)Memory used [KB]: 5756
% 0.21/0.40 % (15164)Time elapsed: 0.018 s
% 0.21/0.40 % (15164)Instructions burned: 27 (million)
% 0.21/0.40 % (15164)------------------------------
% 0.21/0.40 % (15164)------------------------------
% 0.21/0.40 % (15170)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.40 % (15172)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.40 % (15173)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.40 % (15172)Instruction limit reached!
% 0.21/0.40 % (15172)------------------------------
% 0.21/0.40 % (15172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (15172)Termination reason: Unknown
% 0.21/0.40 % (15172)Termination phase: Naming
% 0.21/0.40
% 0.21/0.40 % (15172)Memory used [KB]: 1023
% 0.21/0.40 % (15172)Time elapsed: 0.004 s
% 0.21/0.40 % (15172)Instructions burned: 4 (million)
% 0.21/0.40 % (15172)------------------------------
% 0.21/0.40 % (15172)------------------------------
% 0.21/0.41 % (15174)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.41 % (15171)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.41 % (15174)Instruction limit reached!
% 0.21/0.41 % (15174)------------------------------
% 0.21/0.41 % (15174)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (15174)Termination reason: Unknown
% 0.21/0.41 % (15174)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (15174)Memory used [KB]: 1151
% 0.21/0.41 % (15174)Time elapsed: 0.006 s
% 0.21/0.41 % (15174)Instructions burned: 7 (million)
% 0.21/0.41 % (15174)------------------------------
% 0.21/0.41 % (15174)------------------------------
% 0.21/0.42 % (15176)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (15176)Instruction limit reached!
% 0.21/0.42 % (15176)------------------------------
% 0.21/0.42 % (15176)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (15176)Termination reason: Unknown
% 0.21/0.42 % (15176)Termination phase: SInE selection
% 0.21/0.42
% 0.21/0.42 % (15176)Memory used [KB]: 1023
% 0.21/0.42 % (15176)Time elapsed: 0.003 s
% 0.21/0.42 % (15176)Instructions burned: 3 (million)
% 0.21/0.42 % (15176)------------------------------
% 0.21/0.42 % (15176)------------------------------
% 0.21/0.42 % (15170)Instruction limit reached!
% 0.21/0.42 % (15170)------------------------------
% 0.21/0.42 % (15170)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (15170)Termination reason: Unknown
% 0.21/0.42 % (15170)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (15170)Memory used [KB]: 5628
% 0.21/0.42 % (15170)Time elapsed: 0.021 s
% 0.21/0.42 % (15170)Instructions burned: 37 (million)
% 0.21/0.42 % (15170)------------------------------
% 0.21/0.42 % (15170)------------------------------
% 0.21/0.42 % (15171)Instruction limit reached!
% 0.21/0.42 % (15171)------------------------------
% 0.21/0.42 % (15171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (15171)Termination reason: Unknown
% 0.21/0.42 % (15171)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (15171)Memory used [KB]: 5756
% 0.21/0.42 % (15171)Time elapsed: 0.011 s
% 0.21/0.42 % (15171)Instructions burned: 15 (million)
% 0.21/0.42 % (15171)------------------------------
% 0.21/0.42 % (15171)------------------------------
% 0.21/0.42 % (15175)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.43 % (15175)Instruction limit reached!
% 0.21/0.43 % (15175)------------------------------
% 0.21/0.43 % (15175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (15175)Termination reason: Unknown
% 0.21/0.43 % (15175)Termination phase: Property scanning
% 0.21/0.43
% 0.21/0.43 % (15175)Memory used [KB]: 1151
% 0.21/0.43 % (15175)Time elapsed: 0.011 s
% 0.21/0.43 % (15175)Instructions burned: 17 (million)
% 0.21/0.43 % (15175)------------------------------
% 0.21/0.43 % (15175)------------------------------
% 0.21/0.43 % (15177)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43 % (15177)Instruction limit reached!
% 0.21/0.43 % (15177)------------------------------
% 0.21/0.43 % (15177)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (15177)Termination reason: Unknown
% 0.21/0.43 % (15177)Termination phase: Naming
% 0.21/0.43
% 0.21/0.43 % (15177)Memory used [KB]: 1023
% 0.21/0.43 % (15177)Time elapsed: 0.004 s
% 0.21/0.43 % (15177)Instructions burned: 4 (million)
% 0.21/0.43 % (15177)------------------------------
% 0.21/0.43 % (15177)------------------------------
% 0.21/0.43 % (15179)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43 % (15178)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.44 % (15179)Instruction limit reached!
% 0.21/0.44 % (15179)------------------------------
% 0.21/0.44 % (15179)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (15179)Termination reason: Unknown
% 0.21/0.44 % (15179)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (15179)Memory used [KB]: 1023
% 0.21/0.44 % (15179)Time elapsed: 0.003 s
% 0.21/0.44 % (15179)Instructions burned: 3 (million)
% 0.21/0.44 % (15179)------------------------------
% 0.21/0.44 % (15179)------------------------------
% 0.21/0.44 % (15180)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.44 % (15180)Instruction limit reached!
% 0.21/0.44 % (15180)------------------------------
% 0.21/0.44 % (15180)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (15180)Termination reason: Unknown
% 0.21/0.44 % (15180)Termination phase: Naming
% 0.21/0.44
% 0.21/0.44 % (15180)Memory used [KB]: 1023
% 0.21/0.44 % (15180)Time elapsed: 0.003 s
% 0.21/0.44 % (15180)Instructions burned: 4 (million)
% 0.21/0.44 % (15180)------------------------------
% 0.21/0.44 % (15180)------------------------------
% 0.21/0.44 % (15178)Instruction limit reached!
% 0.21/0.44 % (15178)------------------------------
% 0.21/0.44 % (15178)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (15178)Termination reason: Unknown
% 0.21/0.44 % (15178)Termination phase: Property scanning
% 0.21/0.44
% 0.21/0.44 % (15178)Memory used [KB]: 1151
% 0.21/0.44 % (15178)Time elapsed: 0.006 s
% 0.21/0.44 % (15178)Instructions burned: 7 (million)
% 0.21/0.44 % (15178)------------------------------
% 0.21/0.44 % (15178)------------------------------
% 0.21/0.45 % (15182)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.45 % (15181)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.45 % (15183)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.45 % (15184)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.45 % (15183)Instruction limit reached!
% 0.21/0.45 % (15183)------------------------------
% 0.21/0.45 % (15183)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (15183)Termination reason: Unknown
% 0.21/0.45 % (15183)Termination phase: Property scanning
% 0.21/0.45
% 0.21/0.45 % (15183)Memory used [KB]: 1151
% 0.21/0.45 % (15183)Time elapsed: 0.005 s
% 0.21/0.45 % (15183)Instructions burned: 8 (million)
% 0.21/0.45 % (15183)------------------------------
% 0.21/0.45 % (15183)------------------------------
% 0.21/0.45 % (15185)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.46 % (15181)Instruction limit reached!
% 0.21/0.46 % (15181)------------------------------
% 0.21/0.46 % (15181)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (15181)Termination reason: Unknown
% 0.21/0.46 % (15181)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (15181)Memory used [KB]: 5628
% 0.21/0.46 % (15181)Time elapsed: 0.012 s
% 0.21/0.46 % (15181)Instructions burned: 18 (million)
% 0.21/0.46 % (15181)------------------------------
% 0.21/0.46 % (15181)------------------------------
% 0.21/0.46 % (15186)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.47 % (15186)Instruction limit reached!
% 0.21/0.47 % (15186)------------------------------
% 0.21/0.47 % (15186)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (15186)Termination reason: Unknown
% 0.21/0.47 % (15186)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (15186)Memory used [KB]: 5500
% 0.21/0.47 % (15186)Time elapsed: 0.004 s
% 0.21/0.47 % (15186)Instructions burned: 8 (million)
% 0.21/0.47 % (15186)------------------------------
% 0.21/0.47 % (15186)------------------------------
% 0.21/0.47 % (15185)Instruction limit reached!
% 0.21/0.47 % (15185)------------------------------
% 0.21/0.47 % (15185)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (15185)Termination reason: Unknown
% 0.21/0.47 % (15185)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (15185)Memory used [KB]: 5756
% 0.21/0.47 % (15185)Time elapsed: 0.014 s
% 0.21/0.47 % (15185)Instructions burned: 21 (million)
% 0.21/0.47 % (15185)------------------------------
% 0.21/0.47 % (15185)------------------------------
% 0.21/0.47 % (15188)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.21/0.47 % (15187)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.48 % (15187)Instruction limit reached!
% 0.21/0.48 % (15187)------------------------------
% 0.21/0.48 % (15187)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (15187)Termination reason: Unknown
% 0.21/0.48 % (15187)Termination phase: SInE selection
% 0.21/0.48
% 0.21/0.48 % (15187)Memory used [KB]: 1023
% 0.21/0.48 % (15187)Time elapsed: 0.005 s
% 0.21/0.48 % (15187)Instructions burned: 6 (million)
% 0.21/0.48 % (15187)------------------------------
% 0.21/0.48 % (15187)------------------------------
% 0.21/0.48 % (15162)Instruction limit reached!
% 0.21/0.48 % (15162)------------------------------
% 0.21/0.48 % (15162)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (15162)Termination reason: Unknown
% 0.21/0.48 % (15162)Termination phase: Saturation
% 0.21/0.48
% 0.21/0.48 % (15162)Memory used [KB]: 6268
% 0.21/0.48 % (15162)Time elapsed: 0.102 s
% 0.21/0.48 % (15162)Instructions burned: 183 (million)
% 0.21/0.48 % (15162)------------------------------
% 0.21/0.48 % (15162)------------------------------
% 0.21/0.48 % (15189)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)
% 0.21/0.49 % (15190)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)
% 0.21/0.50 % (15192)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.21/0.50 % (15190)Instruction limit reached!
% 0.21/0.50 % (15190)------------------------------
% 0.21/0.50 % (15190)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50 % (15190)Termination reason: Unknown
% 0.21/0.50 % (15190)Termination phase: Saturation
% 0.21/0.50
% 0.21/0.50 % (15190)Memory used [KB]: 5500
% 0.21/0.50 % (15190)Time elapsed: 0.012 s
% 0.21/0.50 % (15190)Instructions burned: 19 (million)
% 0.21/0.50 % (15190)------------------------------
% 0.21/0.50 % (15190)------------------------------
% 0.21/0.52 % (15193)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.21/0.53 % (15193)Instruction limit reached!
% 0.21/0.53 % (15193)------------------------------
% 0.21/0.53 % (15193)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53 % (15193)Termination reason: Unknown
% 0.21/0.53 % (15193)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (15193)Memory used [KB]: 5756
% 0.21/0.53 % (15193)Time elapsed: 0.034 s
% 0.21/0.53 % (15193)Instructions burned: 17 (million)
% 0.21/0.53 % (15193)------------------------------
% 0.21/0.53 % (15193)------------------------------
% 0.21/0.54 % (15167)Instruction limit reached!
% 0.21/0.54 % (15167)------------------------------
% 0.21/0.54 % (15167)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.54 % (15167)Termination reason: Unknown
% 0.21/0.54 % (15167)Termination phase: Saturation
% 0.21/0.54
% 0.21/0.54 % (15167)Memory used [KB]: 6396
% 0.21/0.54 % (15167)Time elapsed: 0.161 s
% 0.21/0.54 % (15167)Instructions burned: 276 (million)
% 0.21/0.54 % (15167)------------------------------
% 0.21/0.54 % (15167)------------------------------
% 0.21/0.55 % (15194)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.21/0.55 % (15194)Instruction limit reached!
% 0.21/0.55 % (15194)------------------------------
% 0.21/0.55 % (15194)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.55 % (15194)Termination reason: Unknown
% 0.21/0.55 % (15194)Termination phase: Property scanning
% 0.21/0.55
% 0.21/0.55 % (15194)Memory used [KB]: 1023
% 0.21/0.55 % (15194)Time elapsed: 0.004 s
% 0.21/0.55 % (15194)Instructions burned: 3 (million)
% 0.21/0.55 % (15194)------------------------------
% 0.21/0.55 % (15194)------------------------------
% 0.21/0.56 % (15195)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.21/0.57 % (15195)Instruction limit reached!
% 0.21/0.57 % (15195)------------------------------
% 0.21/0.57 % (15195)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.57 % (15195)Termination reason: Unknown
% 0.21/0.57 % (15195)Termination phase: Saturation
% 0.21/0.57
% 0.21/0.57 % (15195)Memory used [KB]: 5756
% 0.21/0.57 % (15195)Time elapsed: 0.013 s
% 0.21/0.57 % (15195)Instructions burned: 31 (million)
% 0.21/0.57 % (15195)------------------------------
% 0.21/0.57 % (15195)------------------------------
% 0.21/0.57 % (15196)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)
% 0.21/0.58 % (15197)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)
% 0.21/0.58 % (15173)First to succeed.
% 1.88/0.61 % (15173)Refutation found. Thanks to Tanya!
% 1.88/0.61 % SZS status Theorem for theBenchmark
% 1.88/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 2.01/0.62 % (15173)------------------------------
% 2.01/0.62 % (15173)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.01/0.62 % (15173)Termination reason: Refutation
% 2.01/0.62
% 2.01/0.62 % (15173)Memory used [KB]: 6908
% 2.01/0.62 % (15173)Time elapsed: 0.211 s
% 2.01/0.62 % (15173)Instructions burned: 310 (million)
% 2.01/0.62 % (15173)------------------------------
% 2.01/0.62 % (15173)------------------------------
% 2.01/0.62 % (15161)Success in time 0.23 s
% 2.01/0.62 % Vampire---4.8 exiting
%------------------------------------------------------------------------------