TSTP Solution File: SEV152^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV152^5 : 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 : n011.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 04:12:09 EDT 2024
% Result : Theorem 3.35s 0.84s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 73
% Syntax : Number of formulae : 496 ( 28 unt; 44 typ; 0 def)
% Number of atoms : 4489 ( 429 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 12390 ( 658 ~;1280 |; 804 &;7101 @)
% ( 28 <=>;1185 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 614 ( 614 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 70 usr; 67 con; 0-2 aty)
% (1334 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1575 (1401 ^ 173 !; 0 ?;1575 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: a ).
thf(func_def_21,type,
sK3: a ).
thf(func_def_22,type,
sK4: a > a > $o ).
thf(func_def_23,type,
sK5: a > a > $o ).
thf(func_def_24,type,
sK6: a > $o ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a ).
thf(func_def_27,type,
sK9: a > $o ).
thf(func_def_28,type,
sK10: a ).
thf(func_def_29,type,
sK11: a ).
thf(func_def_30,type,
sK12: a ).
thf(func_def_31,type,
sK13: a > $o ).
thf(func_def_32,type,
sK14: a ).
thf(func_def_33,type,
sK15: a ).
thf(func_def_34,type,
sK16: a ).
thf(func_def_35,type,
sK17: a ).
thf(func_def_36,type,
sK18: a ).
thf(func_def_37,type,
sK19: a ).
thf(func_def_38,type,
sK20: a ).
thf(func_def_39,type,
sK21: a ).
thf(func_def_40,type,
sK22: a ).
thf(func_def_41,type,
sK23: a ).
thf(func_def_42,type,
sK24: a ).
thf(func_def_43,type,
sK25: a ).
thf(func_def_44,type,
sK26: a ).
thf(func_def_45,type,
sK27: a ).
thf(func_def_46,type,
sK28: a ).
thf(func_def_47,type,
sK29: a ).
thf(func_def_48,type,
sK30: a ).
thf(func_def_49,type,
sK31: a ).
thf(func_def_50,type,
sK32: a ).
thf(func_def_51,type,
sK33: a ).
thf(func_def_52,type,
sK34: a ).
thf(func_def_53,type,
sK35: a ).
thf(func_def_54,type,
sK36: a ).
thf(func_def_55,type,
sK37: a ).
thf(func_def_56,type,
sK38: a ).
thf(func_def_57,type,
sK39: a ).
thf(func_def_58,type,
sK40: a ).
thf(func_def_59,type,
sK41: a ).
thf(func_def_60,type,
sK42: a ).
thf(f7709,plain,
$false,
inference(avatar_sat_refutation,[],[f41,f53,f137,f286,f396,f428,f454,f658,f881,f892,f899,f902,f2607,f3356,f3425,f4997,f5723,f5731,f5739,f5804,f5977,f6003,f6019,f6648,f6755,f6810,f7471,f7526,f7706]) ).
thf(f7706,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_111 ),
inference(avatar_contradiction_clause,[],[f7705]) ).
thf(f7705,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_111 ),
inference(trivial_inequality_removal,[],[f7704]) ).
thf(f7704,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_111 ),
inference(forward_demodulation,[],[f7703,f7599]) ).
thf(f7599,plain,
( ( $false
= ( sK9 @ sK40 ) )
| ~ spl0_111 ),
inference(boolean_simplification,[],[f7598]) ).
thf(f7598,plain,
( ( $false
= ( $true
=> ( sK9 @ sK40 ) ) )
| ~ spl0_111 ),
inference(backward_demodulation,[],[f7571,f7593]) ).
thf(f7593,plain,
( ( ( ( sK9 @ sK41 )
& ( sK4 @ sK41 @ sK40 ) )
= $true )
| ~ spl0_111 ),
inference(binary_proxy_clausification,[],[f7571]) ).
thf(f7571,plain,
( ( $false
= ( ( ( sK9 @ sK41 )
& ( sK4 @ sK41 @ sK40 ) )
=> ( sK9 @ sK40 ) ) )
| ~ spl0_111 ),
inference(beta_eta_normalization,[],[f7570]) ).
thf(f7570,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK9 @ Y0 )
& ( sK4 @ Y0 @ sK40 ) )
=> ( sK9 @ sK40 ) )
@ sK41 ) )
| ~ spl0_111 ),
inference(sigma_clausification,[],[f7547]) ).
thf(f7547,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ Y0 )
& ( sK4 @ Y0 @ sK40 ) )
=> ( sK9 @ sK40 ) ) ) )
| ~ spl0_111 ),
inference(beta_eta_normalization,[],[f7545]) ).
thf(f7545,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK9 @ Y0 ) ) )
@ sK40 ) )
| ~ spl0_111 ),
inference(sigma_clausification,[],[f7470]) ).
thf(f7470,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK9 @ Y0 ) ) ) )
= $false )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f7469]) ).
thf(f7469,plain,
( spl0_111
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK9 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
thf(f7703,plain,
( ( ( sK9 @ sK40 )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_111 ),
inference(boolean_simplification,[],[f7702]) ).
thf(f7702,plain,
( ( $true
= ( $true
=> ( sK9 @ sK40 ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_111 ),
inference(forward_demodulation,[],[f7701,f7680]) ).
thf(f7680,plain,
( ( $true
= ( sK9 @ sK42 ) )
| ~ spl0_111 ),
inference(binary_proxy_clausification,[],[f7672]) ).
thf(f7672,plain,
( ( ( ( sK9 @ sK42 )
& ( sK4 @ sK42 @ sK40 ) )
= $true )
| ~ spl0_111 ),
inference(not_proxy_clausification,[],[f7643]) ).
thf(f7643,plain,
( ( $false
= ( ~ ( ( sK9 @ sK42 )
& ( sK4 @ sK42 @ sK40 ) ) ) )
| ~ spl0_111 ),
inference(beta_eta_normalization,[],[f7642]) ).
thf(f7642,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK9 @ Y0 )
& ( sK4 @ Y0 @ sK40 ) )
@ sK42 )
= $false )
| ~ spl0_111 ),
inference(sigma_clausification,[],[f7601]) ).
thf(f7601,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK9 @ Y0 )
& ( sK4 @ Y0 @ sK40 ) ) )
= $false )
| ~ spl0_111 ),
inference(boolean_simplification,[],[f7600]) ).
thf(f7600,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ Y0 )
& ( sK4 @ Y0 @ sK40 ) )
=> $false ) )
= $false )
| ~ spl0_111 ),
inference(backward_demodulation,[],[f7547,f7599]) ).
thf(f7701,plain,
( ( $true
= ( ( sK9 @ sK42 )
=> ( sK9 @ sK40 ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_111 ),
inference(boolean_simplification,[],[f7700]) ).
thf(f7700,plain,
( ( ( ( ( sK9 @ sK42 )
& $true )
=> ( sK9 @ sK40 ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_111 ),
inference(boolean_simplification,[],[f7687]) ).
thf(f7687,plain,
( ( $true
= ( ( ( sK9 @ sK42 )
& ( ( sK5 @ sK42 @ sK40 )
| $true ) )
=> ( sK9 @ sK40 ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_111 ),
inference(superposition,[],[f7023,f7685]) ).
thf(f7685,plain,
( ( ( sK4 @ sK42 @ sK40 )
= $true )
| ~ spl0_111 ),
inference(boolean_simplification,[],[f7684]) ).
thf(f7684,plain,
( ( $true
= ( $true
& ( sK4 @ sK42 @ sK40 ) ) )
| ~ spl0_111 ),
inference(backward_demodulation,[],[f7672,f7680]) ).
thf(f7023,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK9 @ X2 )
& ( ( sK5 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) ) )
=> ( sK9 @ X1 ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f7022]) ).
thf(f7022,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK9 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK9 @ X1 ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f7008]) ).
thf(f7008,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK9 @ X1 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f7007]) ).
thf(f7007,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK9 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f6884]) ).
thf(f6884,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK9 @ Y0 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f6830]) ).
thf(f6830,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK9 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f6815]) ).
thf(f6815,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK9 @ Y0 ) ) ) ) )
=> ( sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f6814]) ).
thf(f6814,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ sK9 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[],[f6813]) ).
thf(f6813,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f6812]) ).
thf(f6812,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f6811]) ).
thf(f6811,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| $true )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f6064,f136]) ).
thf(f136,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f135,plain,
( spl0_6
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f6064,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f6063]) ).
thf(f6063,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f6044]) ).
thf(f6044,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f6043]) ).
thf(f6043,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK7 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f49]) ).
thf(f49,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f48,plain,
( spl0_3
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f7526,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_110 ),
inference(avatar_contradiction_clause,[],[f7525]) ).
thf(f7525,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_110 ),
inference(trivial_inequality_removal,[],[f7524]) ).
thf(f7524,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_110 ),
inference(boolean_simplification,[],[f7523]) ).
thf(f7523,plain,
( ( $true = ~ $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_110 ),
inference(boolean_simplification,[],[f7522]) ).
thf(f7522,plain,
( ( $true
= ( ~ ( ( sK5 @ sK7 @ sK39 )
| $true ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_110 ),
inference(forward_demodulation,[],[f7521,f7509]) ).
thf(f7509,plain,
( ( $true
= ( sK4 @ sK7 @ sK39 ) )
| ~ spl0_110 ),
inference(binary_proxy_clausification,[],[f7505]) ).
thf(f7505,plain,
( ( $false
= ( ( sK4 @ sK7 @ sK39 )
=> ( sK9 @ sK39 ) ) )
| ~ spl0_110 ),
inference(beta_eta_normalization,[],[f7503]) ).
thf(f7503,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK4 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) )
@ sK39 ) )
| ~ spl0_110 ),
inference(sigma_clausification,[],[f7467]) ).
thf(f7467,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) ) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f7466]) ).
thf(f7466,plain,
( spl0_110
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
thf(f7521,plain,
( ( $true
= ( ~ ( ( sK5 @ sK7 @ sK39 )
| ( sK4 @ sK7 @ sK39 ) ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_110 ),
inference(boolean_simplification,[],[f7517]) ).
thf(f7517,plain,
( ( ( ( ( sK5 @ sK7 @ sK39 )
| ( sK4 @ sK7 @ sK39 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_110 ),
inference(superposition,[],[f6902,f7514]) ).
thf(f7514,plain,
( ( $false
= ( sK9 @ sK39 ) )
| ~ spl0_110 ),
inference(boolean_simplification,[],[f7513]) ).
thf(f7513,plain,
( ( $false
= ( $true
=> ( sK9 @ sK39 ) ) )
| ~ spl0_110 ),
inference(backward_demodulation,[],[f7505,f7509]) ).
thf(f6902,plain,
( ! [X1: a] :
( $true
= ( ( ( sK5 @ sK7 @ X1 )
| ( sK4 @ sK7 @ X1 ) )
=> ( sK9 @ X1 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f6901]) ).
thf(f6901,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK9 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f6887]) ).
thf(f6887,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK9 @ Y0 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f6886]) ).
thf(f6886,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK9 @ Y0 ) ) )
& $true ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[],[f6830,f6884]) ).
thf(f7471,plain,
( spl0_110
| spl0_111
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f7462,f135,f48,f7469,f7466]) ).
thf(f7462,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK9 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f7448]) ).
thf(f7448,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK9 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(not_proxy_clausification,[],[f6865]) ).
thf(f6865,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK9 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f6860]) ).
thf(f6860,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK9 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f6836,f6829]) ).
thf(f6829,plain,
( ( $false
= ( sK9 @ sK8 ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f6815]) ).
thf(f6836,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK7 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK8 ) )
= $true )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f6835]) ).
thf(f6835,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 ) )
| ~ spl0_6 ),
inference(pi_clausification,[],[f136]) ).
thf(f6810,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_99 ),
inference(avatar_contradiction_clause,[],[f6809]) ).
thf(f6809,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_99 ),
inference(trivial_inequality_removal,[],[f6808]) ).
thf(f6808,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_99 ),
inference(boolean_simplification,[],[f6807]) ).
thf(f6807,plain,
( ( $true = ~ $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_99 ),
inference(boolean_simplification,[],[f6806]) ).
thf(f6806,plain,
( ( $true
= ( ~ ( $true
| ( sK4 @ sK7 @ sK38 ) ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_99 ),
inference(forward_demodulation,[],[f6801,f6792]) ).
thf(f6792,plain,
( ( $true
= ( sK5 @ sK7 @ sK38 ) )
| ~ spl0_99 ),
inference(binary_proxy_clausification,[],[f6779]) ).
thf(f6779,plain,
( ( $false
= ( ( sK5 @ sK7 @ sK38 )
=> ( sK9 @ sK38 ) ) )
| ~ spl0_99 ),
inference(beta_eta_normalization,[],[f6776]) ).
thf(f6776,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) )
@ sK38 ) )
| ~ spl0_99 ),
inference(sigma_clausification,[],[f6644]) ).
thf(f6644,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) ) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f6643]) ).
thf(f6643,plain,
( spl0_99
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
thf(f6801,plain,
( ( $true
= ( ~ ( ( sK5 @ sK7 @ sK38 )
| ( sK4 @ sK7 @ sK38 ) ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_99 ),
inference(boolean_simplification,[],[f6797]) ).
thf(f6797,plain,
( ( ( ( ( sK5 @ sK7 @ sK38 )
| ( sK4 @ sK7 @ sK38 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_99 ),
inference(superposition,[],[f6573,f6791]) ).
thf(f6791,plain,
( ( $false
= ( sK9 @ sK38 ) )
| ~ spl0_99 ),
inference(binary_proxy_clausification,[],[f6779]) ).
thf(f6573,plain,
( ! [X1: a] :
( $true
= ( ( ( sK5 @ sK7 @ X1 )
| ( sK4 @ sK7 @ X1 ) )
=> ( sK9 @ X1 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f6572]) ).
thf(f6572,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK9 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f6104]) ).
thf(f6104,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK9 @ Y0 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f6098]) ).
thf(f6098,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK9 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f6080]) ).
thf(f6080,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK9 @ Y0 ) ) ) ) )
=> ( sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f6079]) ).
thf(f6079,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ sK9 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f6067]) ).
thf(f6067,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f6066]) ).
thf(f6066,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f6065]) ).
thf(f6065,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f6064,f133]) ).
thf(f133,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f132,plain,
( spl0_5
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f6755,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_100 ),
inference(avatar_contradiction_clause,[],[f6754]) ).
thf(f6754,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_100 ),
inference(trivial_inequality_removal,[],[f6753]) ).
thf(f6753,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_100 ),
inference(forward_demodulation,[],[f6752,f6691]) ).
thf(f6691,plain,
( ( ( sK9 @ sK35 )
= $false )
| ~ spl0_100 ),
inference(boolean_simplification,[],[f6690]) ).
thf(f6690,plain,
( ( $false
= ( $true
=> ( sK9 @ sK35 ) ) )
| ~ spl0_100 ),
inference(backward_demodulation,[],[f6678,f6689]) ).
thf(f6689,plain,
( ( ( ( sK5 @ sK36 @ sK35 )
& ( sK9 @ sK36 ) )
= $true )
| ~ spl0_100 ),
inference(binary_proxy_clausification,[],[f6678]) ).
thf(f6678,plain,
( ( ( ( ( sK5 @ sK36 @ sK35 )
& ( sK9 @ sK36 ) )
=> ( sK9 @ sK35 ) )
= $false )
| ~ spl0_100 ),
inference(beta_eta_normalization,[],[f6677]) ).
thf(f6677,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK35 )
& ( sK9 @ Y0 ) )
=> ( sK9 @ sK35 ) )
@ sK36 ) )
| ~ spl0_100 ),
inference(sigma_clausification,[],[f6665]) ).
thf(f6665,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK35 )
& ( sK9 @ Y0 ) )
=> ( sK9 @ sK35 ) ) ) )
| ~ spl0_100 ),
inference(beta_eta_normalization,[],[f6660]) ).
thf(f6660,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK9 @ Y1 ) )
=> ( sK9 @ Y0 ) ) )
@ sK35 ) )
| ~ spl0_100 ),
inference(sigma_clausification,[],[f6647]) ).
thf(f6647,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK9 @ Y1 ) )
=> ( sK9 @ Y0 ) ) ) )
= $false )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f6646]) ).
thf(f6646,plain,
( spl0_100
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK9 @ Y1 ) )
=> ( sK9 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
thf(f6752,plain,
( ( ( sK9 @ sK35 )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_100 ),
inference(boolean_simplification,[],[f6751]) ).
thf(f6751,plain,
( ( $true
= ( $true
=> ( sK9 @ sK35 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_100 ),
inference(forward_demodulation,[],[f6748,f6727]) ).
thf(f6727,plain,
( ( ( sK9 @ sK37 )
= $true )
| ~ spl0_100 ),
inference(binary_proxy_clausification,[],[f6715]) ).
thf(f6715,plain,
( ( ( ( sK5 @ sK37 @ sK35 )
& ( sK9 @ sK37 ) )
= $true )
| ~ spl0_100 ),
inference(not_proxy_clausification,[],[f6704]) ).
thf(f6704,plain,
( ( $false
= ( ~ ( ( sK5 @ sK37 @ sK35 )
& ( sK9 @ sK37 ) ) ) )
| ~ spl0_100 ),
inference(beta_eta_normalization,[],[f6703]) ).
thf(f6703,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK5 @ Y0 @ sK35 )
& ( sK9 @ Y0 ) )
@ sK37 ) )
| ~ spl0_100 ),
inference(sigma_clausification,[],[f6693]) ).
thf(f6693,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK5 @ Y0 @ sK35 )
& ( sK9 @ Y0 ) ) ) )
| ~ spl0_100 ),
inference(boolean_simplification,[],[f6692]) ).
thf(f6692,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK35 )
& ( sK9 @ Y0 ) )
=> $false ) ) )
| ~ spl0_100 ),
inference(backward_demodulation,[],[f6665,f6691]) ).
thf(f6748,plain,
( ( $true
= ( ( sK9 @ sK37 )
=> ( sK9 @ sK35 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_100 ),
inference(boolean_simplification,[],[f6747]) ).
thf(f6747,plain,
( ( $true
= ( ( ( sK9 @ sK37 )
& $true )
=> ( sK9 @ sK35 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_100 ),
inference(boolean_simplification,[],[f6739]) ).
thf(f6739,plain,
( ( $true
= ( ( ( sK9 @ sK37 )
& ( $true
| ( sK4 @ sK37 @ sK35 ) ) )
=> ( sK9 @ sK35 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_100 ),
inference(superposition,[],[f6137,f6730]) ).
thf(f6730,plain,
( ( ( sK5 @ sK37 @ sK35 )
= $true )
| ~ spl0_100 ),
inference(boolean_simplification,[],[f6729]) ).
thf(f6729,plain,
( ( $true
= ( ( sK5 @ sK37 @ sK35 )
& $true ) )
| ~ spl0_100 ),
inference(backward_demodulation,[],[f6715,f6727]) ).
thf(f6137,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK9 @ X2 )
& ( ( sK5 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) ) )
=> ( sK9 @ X1 ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f6136]) ).
thf(f6136,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK9 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK9 @ X1 ) )
@ X2 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f6124]) ).
thf(f6124,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK9 @ X1 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f6123]) ).
thf(f6123,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK9 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f6106]) ).
thf(f6106,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK9 @ Y0 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f6105]) ).
thf(f6105,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK9 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f6098,f6104]) ).
thf(f6648,plain,
( spl0_99
| spl0_100
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f6639,f132,f48,f6646,f6643]) ).
thf(f6639,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK9 @ Y1 ) )
=> ( sK9 @ Y0 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f6602]) ).
thf(f6602,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK9 @ Y1 ) )
=> ( sK9 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(not_proxy_clausification,[],[f6102]) ).
thf(f6102,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK9 @ Y1 ) )
=> ( sK9 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f6101]) ).
thf(f6101,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( sK9 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK9 @ Y1 ) )
=> ( sK9 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f701,f6100]) ).
thf(f6100,plain,
( ( $false
= ( sK9 @ sK8 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f6099]) ).
thf(f6099,plain,
( ( $false
= ( $true
=> ( sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f6080,f6098]) ).
thf(f701,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK7 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK8 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f700]) ).
thf(f700,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[],[f133]) ).
thf(f6019,plain,
( ~ spl0_13
| ~ spl0_91 ),
inference(avatar_contradiction_clause,[],[f6018]) ).
thf(f6018,plain,
( $false
| ~ spl0_13
| ~ spl0_91 ),
inference(trivial_inequality_removal,[],[f6017]) ).
thf(f6017,plain,
( ( $false = $true )
| ~ spl0_13
| ~ spl0_91 ),
inference(backward_demodulation,[],[f5938,f6016]) ).
thf(f6016,plain,
( ( $false
= ( sK6 @ sK33 ) )
| ~ spl0_13
| ~ spl0_91 ),
inference(trivial_inequality_removal,[],[f6015]) ).
thf(f6015,plain,
( ( $false
= ( sK6 @ sK33 ) )
| ( $false = $true )
| ~ spl0_13
| ~ spl0_91 ),
inference(forward_demodulation,[],[f6014,f5908]) ).
thf(f5908,plain,
( ( $false
= ( sK6 @ sK34 ) )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f5907]) ).
thf(f5907,plain,
( ( $false
= ( $true
=> ( sK6 @ sK34 ) ) )
| ~ spl0_13 ),
inference(backward_demodulation,[],[f5893,f5906]) ).
thf(f5906,plain,
( ( $true
= ( ( ( sK4 @ sK33 @ sK34 )
| ( sK5 @ sK33 @ sK34 ) )
& ( sK6 @ sK33 ) ) )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f5893]) ).
thf(f5893,plain,
( ( $false
= ( ( ( ( sK4 @ sK33 @ sK34 )
| ( sK5 @ sK33 @ sK34 ) )
& ( sK6 @ sK33 ) )
=> ( sK6 @ sK34 ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f5892]) ).
thf(f5892,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK4 @ sK33 @ Y0 )
| ( sK5 @ sK33 @ Y0 ) )
& ( sK6 @ sK33 ) )
=> ( sK6 @ Y0 ) )
@ sK34 ) )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f5891]) ).
thf(f5891,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK4 @ sK33 @ Y0 )
| ( sK5 @ sK33 @ Y0 ) )
& ( sK6 @ sK33 ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f5887]) ).
thf(f5887,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK33 ) )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f450]) ).
thf(f450,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f449]) ).
thf(f449,plain,
( spl0_13
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f6014,plain,
( ( ( sK6 @ sK34 )
= $true )
| ( $false
= ( sK6 @ sK33 ) )
| ~ spl0_91 ),
inference(boolean_simplification,[],[f6013]) ).
thf(f6013,plain,
( ( ( sK6 @ sK34 )
= $true )
| ( $false
= ( ( sK6 @ sK33 )
& $true ) )
| ~ spl0_91 ),
inference(boolean_simplification,[],[f6007]) ).
thf(f6007,plain,
( ( $false
= ( ( sK6 @ sK33 )
& ( ( sK5 @ sK33 @ sK34 )
| $true ) ) )
| ( ( sK6 @ sK34 )
= $true )
| ~ spl0_91 ),
inference(superposition,[],[f90,f5973]) ).
thf(f5973,plain,
( ( $true
= ( sK4 @ sK33 @ sK34 ) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f5972]) ).
thf(f5972,plain,
( spl0_91
<=> ( $true
= ( sK4 @ sK33 @ sK34 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
thf(f90,plain,
! [X2: a,X1: a] :
( ( $false
= ( ( sK6 @ X2 )
& ( ( sK5 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) ) ) )
| ( $true
= ( sK6 @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f89]) ).
thf(f89,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 )
& ( ( sK5 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) ) )
=> ( sK6 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f88]) ).
thf(f88,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f83]) ).
thf(f83,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f82]) ).
thf(f82,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f33]) ).
thf(f33,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f32]) ).
thf(f32,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[],[f27,f30]) ).
thf(f30,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK5 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f27]) ).
thf(f27,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK5 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK5 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK3 ) ) ),
inference(beta_eta_normalization,[],[f24]) ).
thf(f24,plain,
( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK5 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) )
@ sK6 ) ),
inference(sigma_clausification,[],[f18]) ).
thf(f18,plain,
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK5 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( $false
= ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK2 @ Y1 )
| ( sK4 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK5 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) ) ) ) ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y1 @ Y5 )
| ( Y0 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK4 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK4 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( sK4 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ sK2 @ Y2 )
| ( sK4 @ sK2 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( Y0 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK2 @ Y2 )
| ( Y0 @ sK2 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK3 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y5 @ Y6 )
| ( sK4 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y1 @ Y5 )
| ( Y0 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK4 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK4 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( sK4 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ sK2 @ Y2 )
| ( sK4 @ sK2 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( Y0 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK2 @ Y2 )
| ( Y0 @ sK2 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y2 @ Y6 )
| ( Y1 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y3 @ Y6 )
| ( Y1 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( Y0 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ sK2 @ Y3 )
| ( Y0 @ sK2 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( Y1 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ sK2 @ Y3 )
| ( Y1 @ sK2 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK3 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y2 @ Y6 )
| ( Y1 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y3 @ Y6 )
| ( Y1 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( Y0 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ sK2 @ Y3 )
| ( Y0 @ sK2 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( Y1 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ sK2 @ Y3 )
| ( Y1 @ sK2 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK3 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y3 @ Y6 )
| ( Y1 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y2 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y3 @ Y7 )
| ( Y2 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y1 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y1 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ sK2 @ Y4 )
| ( Y1 @ sK2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( Y1 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y2 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ sK2 @ Y4 )
| ( Y2 @ sK2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y3 @ Y6 )
| ( Y1 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y2 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y3 @ Y7 )
| ( Y2 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y1 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y1 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ sK2 @ Y4 )
| ( Y1 @ sK2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( Y1 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y2 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ sK2 @ Y4 )
| ( Y2 @ sK2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y3 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y3 @ Y4 @ Y7 )
| ( Y2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y3 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y4 @ Y8 )
| ( Y3 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y5 @ Y8 )
| ( Y3 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y2 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y0 @ Y5 )
| ( Y2 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y2 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y3 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y0 @ Y5 )
| ( Y3 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y3 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y3 @ Y4 @ Y7 )
| ( Y2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y3 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y4 @ Y8 )
| ( Y3 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y5 @ Y8 )
| ( Y3 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y2 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y0 @ Y5 )
| ( Y2 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y2 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y3 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y0 @ Y5 )
| ( Y3 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y3 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y3 @ Y4 @ Y7 )
| ( Y2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y3 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y4 @ Y8 )
| ( Y3 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y5 @ Y8 )
| ( Y3 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y2 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y0 @ Y5 )
| ( Y2 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y2 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y3 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y0 @ Y5 )
| ( Y3 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y3 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y3 @ Y4 @ Y7 )
| ( Y2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y3 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y4 @ Y8 )
| ( Y3 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y5 @ Y8 )
| ( Y3 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y2 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y0 @ Y5 )
| ( Y2 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y2 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y3 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y0 @ Y5 )
| ( Y3 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > a > $o,X2: a,X3: a] :
( ( ( ! [X4: a,X5: a,X6: a] :
( ( ! [X7: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( ( X0 @ X9 @ X8 )
| ( X1 @ X9 @ X8 ) )
& ( X7 @ X9 ) )
=> ( X7 @ X8 ) )
& ! [X10: a] :
( ( ( X0 @ X5 @ X10 )
| ( X1 @ X5 @ X10 ) )
=> ( X7 @ X10 ) ) )
=> ( X7 @ X6 ) )
& ! [X11: a > $o] :
( ( ! [X12: a] :
( ( ( X0 @ X6 @ X12 )
| ( X1 @ X6 @ X12 ) )
=> ( X11 @ X12 ) )
& ! [X13: a,X14: a] :
( ( ( X11 @ X14 )
& ( ( X1 @ X14 @ X13 )
| ( X0 @ X14 @ X13 ) ) )
=> ( X11 @ X13 ) ) )
=> ( X11 @ X4 ) ) )
=> ! [X15: a > $o] :
( ( ! [X16: a] :
( ( ( X1 @ X5 @ X16 )
| ( X0 @ X5 @ X16 ) )
=> ( X15 @ X16 ) )
& ! [X17: a,X18: a] :
( ( ( X15 @ X17 )
& ( ( X0 @ X17 @ X18 )
| ( X1 @ X17 @ X18 ) ) )
=> ( X15 @ X18 ) ) )
=> ( X15 @ X4 ) ) )
& ! [X19: a,X20: a] :
( ( ! [X21: a > $o] :
( ( ! [X22: a,X23: a] :
( ( ( X1 @ X22 @ X23 )
& ( X21 @ X22 ) )
=> ( X21 @ X23 ) )
& ! [X24: a] :
( ( X1 @ X20 @ X24 )
=> ( X21 @ X24 ) ) )
=> ( X21 @ X19 ) )
| ! [X25: a > $o] :
( ( ! [X26: a,X27: a] :
( ( ( X25 @ X26 )
& ( X0 @ X26 @ X27 ) )
=> ( X25 @ X27 ) )
& ! [X28: a] :
( ( X0 @ X20 @ X28 )
=> ( X25 @ X28 ) ) )
=> ( X25 @ X19 ) ) )
=> ! [X29: a > $o] :
( ( ! [X30: a,X31: a] :
( ( ( ( X1 @ X30 @ X31 )
| ( X0 @ X30 @ X31 ) )
& ( X29 @ X30 ) )
=> ( X29 @ X31 ) )
& ! [X32: a] :
( ( ( X1 @ X20 @ X32 )
| ( X0 @ X20 @ X32 ) )
=> ( X29 @ X32 ) ) )
=> ( X29 @ X19 ) ) ) )
=> ! [X33: a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( X33 @ X35 )
& ( ( X0 @ X35 @ X34 )
| ( X1 @ X35 @ X34 ) ) )
=> ( X33 @ X34 ) )
& ! [X36: a] :
( ( ( X1 @ X3 @ X36 )
| ( X0 @ X3 @ X36 ) )
=> ( X33 @ X36 ) ) )
=> ( X33 @ X2 ) ) )
=> ! [X37: a > $o] :
( ( ! [X38: a] :
( ( ( X0 @ X3 @ X38 )
| ( X1 @ X3 @ X38 ) )
=> ( X37 @ X38 ) )
& ! [X39: a,X40: a] :
( ( ( ( X1 @ X39 @ X40 )
| ( X0 @ X39 @ X40 ) )
& ( X37 @ X39 ) )
=> ( X37 @ X40 ) ) )
=> ( X37 @ X2 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > a > $o,X3: a,X2: a] :
( ( ( ! [X10: a,X4: a,X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X0 @ X4 @ X7 )
| ( X1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
& ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X0 @ X5 @ X7 )
| ( X1 @ X5 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
& ! [X5: a,X4: a] :
( ( ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X1 @ X4 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X0 @ X8 @ X9 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X0 @ X4 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X2 @ X7 )
| ( X0 @ X2 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X3 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X0 @ X2 @ X7 )
| ( X1 @ X2 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a > a > $o,X3: a,X2: a] :
( ( ( ! [X10: a,X4: a,X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X0 @ X4 @ X7 )
| ( X1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
& ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X0 @ X5 @ X7 )
| ( X1 @ X5 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
& ! [X5: a,X4: a] :
( ( ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X1 @ X4 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X0 @ X8 @ X9 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X0 @ X4 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X2 @ X7 )
| ( X0 @ X2 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X3 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X0 @ X2 @ X7 )
| ( X1 @ X2 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM251D_pme) ).
thf(f5938,plain,
( ( $true
= ( sK6 @ sK33 ) )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f5906]) ).
thf(f6003,plain,
( ~ spl0_13
| ~ spl0_92 ),
inference(avatar_contradiction_clause,[],[f6002]) ).
thf(f6002,plain,
( $false
| ~ spl0_13
| ~ spl0_92 ),
inference(trivial_inequality_removal,[],[f6001]) ).
thf(f6001,plain,
( ( $false = $true )
| ~ spl0_13
| ~ spl0_92 ),
inference(backward_demodulation,[],[f5938,f6000]) ).
thf(f6000,plain,
( ( $false
= ( sK6 @ sK33 ) )
| ~ spl0_13
| ~ spl0_92 ),
inference(trivial_inequality_removal,[],[f5999]) ).
thf(f5999,plain,
( ( $false
= ( sK6 @ sK33 ) )
| ( $false = $true )
| ~ spl0_13
| ~ spl0_92 ),
inference(forward_demodulation,[],[f5984,f5908]) ).
thf(f5984,plain,
( ( ( sK6 @ sK34 )
= $true )
| ( $false
= ( sK6 @ sK33 ) )
| ~ spl0_92 ),
inference(boolean_simplification,[],[f5983]) ).
thf(f5983,plain,
( ( $false
= ( ( sK6 @ sK33 )
& $true ) )
| ( ( sK6 @ sK34 )
= $true )
| ~ spl0_92 ),
inference(boolean_simplification,[],[f5981]) ).
thf(f5981,plain,
( ( ( sK6 @ sK34 )
= $true )
| ( $false
= ( ( sK6 @ sK33 )
& ( $true
| ( sK4 @ sK33 @ sK34 ) ) ) )
| ~ spl0_92 ),
inference(superposition,[],[f90,f5976]) ).
thf(f5976,plain,
( ( $true
= ( sK5 @ sK33 @ sK34 ) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f5975]) ).
thf(f5975,plain,
( spl0_92
<=> ( $true
= ( sK5 @ sK33 @ sK34 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
thf(f5977,plain,
( spl0_91
| spl0_92
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f5970,f449,f5975,f5972]) ).
thf(f5970,plain,
( ( $true
= ( sK5 @ sK33 @ sK34 ) )
| ( $true
= ( sK4 @ sK33 @ sK34 ) )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f5941]) ).
thf(f5941,plain,
( ( $true
= ( ( sK4 @ sK33 @ sK34 )
| ( sK5 @ sK33 @ sK34 ) ) )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f5940]) ).
thf(f5940,plain,
( ( ( ( ( sK4 @ sK33 @ sK34 )
| ( sK5 @ sK33 @ sK34 ) )
& $true )
= $true )
| ~ spl0_13 ),
inference(backward_demodulation,[],[f5906,f5938]) ).
thf(f5804,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f5803]) ).
thf(f5803,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f5802]) ).
thf(f5802,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f5752,f5797]) ).
thf(f5797,plain,
( ( ( ( sK13 @ sK14 )
=> ( sK13 @ sK15 ) )
= $false )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f5796]) ).
thf(f5796,plain,
( ( $false
= ( ( $true
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f5795]) ).
thf(f5795,plain,
( ( $false
= ( ( ( ( sK5 @ sK14 @ sK15 )
| $true )
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f5794,f395]) ).
thf(f395,plain,
( ( $true
= ( sK4 @ sK14 @ sK15 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f394]) ).
thf(f394,plain,
( spl0_10
<=> ( $true
= ( sK4 @ sK14 @ sK15 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f5794,plain,
( ( $false
= ( ( ( ( sK5 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f5793]) ).
thf(f5793,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ Y0 ) )
@ sK15 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f5763]) ).
thf(f5763,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f5759]) ).
thf(f5759,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) )
@ sK14 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f282]) ).
thf(f282,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f281,plain,
( spl0_7
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f5752,plain,
( ( ( ( sK13 @ sK14 )
=> ( sK13 @ sK15 ) )
= $true )
| ~ spl0_4
| ~ spl0_10 ),
inference(boolean_simplification,[],[f5751]) ).
thf(f5751,plain,
( ( $true
= ( ( $true
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_4
| ~ spl0_10 ),
inference(boolean_simplification,[],[f5744]) ).
thf(f5744,plain,
( ( $true
= ( ( ( $true
| ( sK5 @ sK14 @ sK15 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f1087,f395]) ).
thf(f1087,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( ( sK4 @ X2 @ X1 )
| ( sK5 @ X2 @ X1 ) )
& ( sK13 @ X2 ) )
=> ( sK13 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1086]) ).
thf(f1086,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f1054]) ).
thf(f1054,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1053]) ).
thf(f1053,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f1038]) ).
thf(f1038,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f1037]) ).
thf(f1037,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& $true )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f975,f1035]) ).
thf(f1035,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK11 @ Y0 )
| ( sK4 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f975]) ).
thf(f975,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK11 @ Y0 )
| ( sK4 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f959]) ).
thf(f959,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK11 @ Y0 )
| ( sK4 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
=> ( sK13 @ sK12 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f958]) ).
thf(f958,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f941]) ).
thf(f941,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f928]) ).
thf(f928,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK10 @ Y1 )
| ( sK5 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f927]) ).
thf(f927,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK10 @ Y2 )
| ( sK5 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK11 @ Y2 )
| ( sK4 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f911]) ).
thf(f911,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK10 @ Y2 )
| ( sK5 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK11 @ Y2 )
| ( sK4 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f910]) ).
thf(f910,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ sK10 @ Y3 )
| ( sK5 @ sK10 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f909]) ).
thf(f909,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ sK10 @ Y3 )
| ( sK5 @ sK10 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f908]) ).
thf(f908,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK10 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f52]) ).
thf(f52,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f51,plain,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f5739,plain,
( ~ spl0_4
| ~ spl0_59
| ~ spl0_89 ),
inference(avatar_contradiction_clause,[],[f5738]) ).
thf(f5738,plain,
( $false
| ~ spl0_4
| ~ spl0_59
| ~ spl0_89 ),
inference(trivial_inequality_removal,[],[f5737]) ).
thf(f5737,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_59
| ~ spl0_89 ),
inference(boolean_simplification,[],[f5736]) ).
thf(f5736,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_59
| ~ spl0_89 ),
inference(boolean_simplification,[],[f5735]) ).
thf(f5735,plain,
( ( ( ~ ( ( sK5 @ sK11 @ sK32 )
| $true ) )
= $true )
| ~ spl0_4
| ~ spl0_59
| ~ spl0_89 ),
inference(forward_demodulation,[],[f5442,f5719]) ).
thf(f5719,plain,
( ( ( sK4 @ sK11 @ sK32 )
= $true )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f5718]) ).
thf(f5718,plain,
( spl0_89
<=> ( ( sK4 @ sK11 @ sK32 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
thf(f5442,plain,
( ( $true
= ( ~ ( ( sK5 @ sK11 @ sK32 )
| ( sK4 @ sK11 @ sK32 ) ) ) )
| ~ spl0_4
| ~ spl0_59 ),
inference(boolean_simplification,[],[f5434]) ).
thf(f5434,plain,
( ( $true
= ( ( ( sK5 @ sK11 @ sK32 )
| ( sK4 @ sK11 @ sK32 ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_59 ),
inference(superposition,[],[f1210,f5425]) ).
thf(f5425,plain,
( ( $false
= ( sK13 @ sK32 ) )
| ~ spl0_59 ),
inference(binary_proxy_clausification,[],[f5393]) ).
thf(f5393,plain,
( ( $false
= ( ( ( sK4 @ sK11 @ sK32 )
| ( sK5 @ sK11 @ sK32 ) )
=> ( sK13 @ sK32 ) ) )
| ~ spl0_59 ),
inference(beta_eta_normalization,[],[f5389]) ).
thf(f5389,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ sK32 ) )
| ~ spl0_59 ),
inference(sigma_clausification,[],[f2606]) ).
thf(f2606,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f2605]) ).
thf(f2605,plain,
( spl0_59
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
thf(f1210,plain,
( ! [X1: a] :
( ( ( ( sK5 @ sK11 @ X1 )
| ( sK4 @ sK11 @ X1 ) )
=> ( sK13 @ X1 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1209]) ).
thf(f1209,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK5 @ sK11 @ Y0 )
| ( sK4 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f1035]) ).
thf(f5731,plain,
( ~ spl0_4
| ~ spl0_59
| ~ spl0_90 ),
inference(avatar_contradiction_clause,[],[f5730]) ).
thf(f5730,plain,
( $false
| ~ spl0_4
| ~ spl0_59
| ~ spl0_90 ),
inference(trivial_inequality_removal,[],[f5729]) ).
thf(f5729,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_59
| ~ spl0_90 ),
inference(boolean_simplification,[],[f5728]) ).
thf(f5728,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_59
| ~ spl0_90 ),
inference(boolean_simplification,[],[f5726]) ).
thf(f5726,plain,
( ( ( ~ ( $true
| ( sK4 @ sK11 @ sK32 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_59
| ~ spl0_90 ),
inference(backward_demodulation,[],[f5442,f5722]) ).
thf(f5722,plain,
( ( $true
= ( sK5 @ sK11 @ sK32 ) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f5721]) ).
thf(f5721,plain,
( spl0_90
<=> ( $true
= ( sK5 @ sK11 @ sK32 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
thf(f5723,plain,
( spl0_89
| spl0_90
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f5714,f2605,f5721,f5718]) ).
thf(f5714,plain,
( ( ( sK4 @ sK11 @ sK32 )
= $true )
| ( $true
= ( sK5 @ sK11 @ sK32 ) )
| ~ spl0_59 ),
inference(binary_proxy_clausification,[],[f5426]) ).
thf(f5426,plain,
( ( $true
= ( ( sK4 @ sK11 @ sK32 )
| ( sK5 @ sK11 @ sK32 ) ) )
| ~ spl0_59 ),
inference(binary_proxy_clausification,[],[f5393]) ).
thf(f4997,plain,
( spl0_59
| spl0_58
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f4994,f423,f284,f51,f2602,f2605]) ).
thf(f2602,plain,
( spl0_58
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
thf(f284,plain,
( spl0_8
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f423,plain,
( spl0_11
<=> ( $true
= ( sK4 @ sK10 @ sK16 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f4994,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f4962]) ).
thf(f4962,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(not_proxy_clausification,[],[f3513]) ).
thf(f3513,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f3505]) ).
thf(f3505,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f1166,f3485]) ).
thf(f3485,plain,
( ( $false
= ( sK13 @ sK10 ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(not_proxy_clausification,[],[f3484]) ).
thf(f3484,plain,
( ( ( ~ ( sK13 @ sK10 ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f3483]) ).
thf(f3483,plain,
( ( $true
= ( ( sK13 @ sK10 )
=> $false ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f3476,f3455]) ).
thf(f3455,plain,
( ( $false
= ( sK13 @ sK16 ) )
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f3454]) ).
thf(f3454,plain,
( ( $false
= ( $true
=> ( sK13 @ sK16 ) ) )
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f3453]) ).
thf(f3453,plain,
( ( $false
= ( ( $true
| ( sK5 @ sK10 @ sK16 ) )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f3450,f424]) ).
thf(f424,plain,
( ( $true
= ( sK4 @ sK10 @ sK16 ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f423]) ).
thf(f3450,plain,
( ( $false
= ( ( ( sK4 @ sK10 @ sK16 )
| ( sK5 @ sK10 @ sK16 ) )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f3448]) ).
thf(f3448,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ sK16 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f285]) ).
thf(f285,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f3476,plain,
( ( $true
= ( ( sK13 @ sK10 )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[],[f3475]) ).
thf(f3475,plain,
( ( $true
= ( ( $true
& ( sK13 @ sK10 ) )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[],[f3470]) ).
thf(f3470,plain,
( ( $true
= ( ( ( $true
| ( sK5 @ sK10 @ sK16 ) )
& ( sK13 @ sK10 ) )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f1087,f424]) ).
thf(f1166,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK10 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1165]) ).
thf(f1165,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f980]) ).
thf(f980,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f942]) ).
thf(f942,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK10 @ Y1 )
| ( sK5 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f928]) ).
thf(f3425,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f3424]) ).
thf(f3424,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f3423]) ).
thf(f3423,plain,
( ( $false = $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(boolean_simplification,[],[f3422]) ).
thf(f3422,plain,
( ( $false
= ( ( sK13 @ sK14 )
=> $true ) )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f3421,f654]) ).
thf(f654,plain,
( ( ( sK13 @ sK15 )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f653]) ).
thf(f653,plain,
( spl0_17
<=> ( ( sK13 @ sK15 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f3421,plain,
( ( ( ( sK13 @ sK14 )
=> ( sK13 @ sK15 ) )
= $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f3420]) ).
thf(f3420,plain,
( ( $false
= ( ( $true
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f3419]) ).
thf(f3419,plain,
( ( $false
= ( ( ( $true
| ( sK4 @ sK14 @ sK15 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f3418,f392]) ).
thf(f392,plain,
( ( $true
= ( sK5 @ sK14 @ sK15 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f391]) ).
thf(f391,plain,
( spl0_9
<=> ( $true
= ( sK5 @ sK14 @ sK15 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f3418,plain,
( ( $false
= ( ( ( ( sK5 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f3417]) ).
thf(f3417,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ Y0 ) )
@ sK15 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f3383]) ).
thf(f3383,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f3381]) ).
thf(f3381,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) )
@ sK14 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f282]) ).
thf(f3356,plain,
( ~ spl0_4
| ~ spl0_58 ),
inference(avatar_contradiction_clause,[],[f3355]) ).
thf(f3355,plain,
( $false
| ~ spl0_4
| ~ spl0_58 ),
inference(trivial_inequality_removal,[],[f3354]) ).
thf(f3354,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_58 ),
inference(forward_demodulation,[],[f3353,f2795]) ).
thf(f2795,plain,
( ( $false
= ( sK13 @ sK25 ) )
| ~ spl0_58 ),
inference(binary_proxy_clausification,[],[f2763]) ).
thf(f2763,plain,
( ( $false
= ( ( ( sK13 @ sK24 )
& ( ( sK4 @ sK24 @ sK25 )
| ( sK5 @ sK24 @ sK25 ) ) )
=> ( sK13 @ sK25 ) ) )
| ~ spl0_58 ),
inference(beta_eta_normalization,[],[f2762]) ).
thf(f2762,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK13 @ sK24 )
& ( ( sK4 @ sK24 @ Y0 )
| ( sK5 @ sK24 @ Y0 ) ) )
=> ( sK13 @ Y0 ) )
@ sK25 ) )
| ~ spl0_58 ),
inference(sigma_clausification,[],[f2627]) ).
thf(f2627,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ sK24 )
& ( ( sK4 @ sK24 @ Y0 )
| ( sK5 @ sK24 @ Y0 ) ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_58 ),
inference(beta_eta_normalization,[],[f2623]) ).
thf(f2623,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) )
@ sK24 ) )
| ~ spl0_58 ),
inference(sigma_clausification,[],[f2603]) ).
thf(f2603,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f2602]) ).
thf(f3353,plain,
( ( ( sK13 @ sK25 )
= $true )
| ~ spl0_4
| ~ spl0_58 ),
inference(boolean_simplification,[],[f3352]) ).
thf(f3352,plain,
( ( ( $true
=> ( sK13 @ sK25 ) )
= $true )
| ~ spl0_4
| ~ spl0_58 ),
inference(forward_demodulation,[],[f3351,f3328]) ).
thf(f3328,plain,
( ( $true
= ( sK13 @ sK24 ) )
| ~ spl0_58 ),
inference(binary_proxy_clausification,[],[f2796]) ).
thf(f2796,plain,
( ( $true
= ( ( sK13 @ sK24 )
& ( ( sK4 @ sK24 @ sK25 )
| ( sK5 @ sK24 @ sK25 ) ) ) )
| ~ spl0_58 ),
inference(binary_proxy_clausification,[],[f2763]) ).
thf(f3351,plain,
( ( $true
= ( ( sK13 @ sK24 )
=> ( sK13 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_58 ),
inference(boolean_simplification,[],[f3350]) ).
thf(f3350,plain,
( ( $true
= ( ( $true
& ( sK13 @ sK24 ) )
=> ( sK13 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_58 ),
inference(superposition,[],[f1087,f3330]) ).
thf(f3330,plain,
( ( $true
= ( ( sK4 @ sK24 @ sK25 )
| ( sK5 @ sK24 @ sK25 ) ) )
| ~ spl0_58 ),
inference(boolean_simplification,[],[f3329]) ).
thf(f3329,plain,
( ( $true
= ( $true
& ( ( sK4 @ sK24 @ sK25 )
| ( sK5 @ sK24 @ sK25 ) ) ) )
| ~ spl0_58 ),
inference(backward_demodulation,[],[f2796,f3328]) ).
thf(f2607,plain,
( spl0_58
| spl0_59
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f2598,f426,f284,f51,f2605,f2602]) ).
thf(f426,plain,
( spl0_12
<=> ( ( sK5 @ sK10 @ sK16 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f2598,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f2568]) ).
thf(f2568,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(not_proxy_clausification,[],[f1174]) ).
thf(f1174,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1173]) ).
thf(f1173,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f1166,f1167]) ).
thf(f1167,plain,
( ( $false
= ( sK13 @ sK10 ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(not_proxy_clausification,[],[f1151]) ).
thf(f1151,plain,
( ( ( ~ ( sK13 @ sK10 ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1150]) ).
thf(f1150,plain,
( ( $true
= ( ( sK13 @ sK10 )
=> $false ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1122,f1095]) ).
thf(f1095,plain,
( ( $false
= ( sK13 @ sK16 ) )
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1094]) ).
thf(f1094,plain,
( ( $false
= ( $true
=> ( sK13 @ sK16 ) ) )
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1093]) ).
thf(f1093,plain,
( ( $false
= ( ( ( sK4 @ sK10 @ sK16 )
| $true )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1092,f427]) ).
thf(f427,plain,
( ( ( sK5 @ sK10 @ sK16 )
= $true )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f426]) ).
thf(f1092,plain,
( ( $false
= ( ( ( sK4 @ sK10 @ sK16 )
| ( sK5 @ sK10 @ sK16 ) )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1088]) ).
thf(f1088,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ sK16 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f285]) ).
thf(f1122,plain,
( ( $true
= ( ( sK13 @ sK10 )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_4
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1121]) ).
thf(f1121,plain,
( ( $true
= ( ( $true
& ( sK13 @ sK10 ) )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_4
| ~ spl0_12 ),
inference(boolean_simplification,[],[f1106]) ).
thf(f1106,plain,
( ( $true
= ( ( ( ( sK4 @ sK10 @ sK16 )
| $true )
& ( sK13 @ sK10 ) )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f1087,f427]) ).
thf(f902,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f901]) ).
thf(f901,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f900]) ).
thf(f900,plain,
( ( $false = $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_18 ),
inference(backward_demodulation,[],[f703,f657]) ).
thf(f657,plain,
( ( $false
= ( sK13 @ sK14 ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f656]) ).
thf(f656,plain,
( spl0_18
<=> ( $false
= ( sK13 @ sK14 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f703,plain,
( ( ( sK13 @ sK14 )
= $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f693]) ).
thf(f693,plain,
( ( ( ( sK13 @ sK14 )
=> ( sK13 @ sK15 ) )
= $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f692]) ).
thf(f692,plain,
( ( $false
= ( ( $true
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f691]) ).
thf(f691,plain,
( ( $false
= ( ( ( $true
| ( sK4 @ sK14 @ sK15 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f690,f392]) ).
thf(f690,plain,
( ( $false
= ( ( ( ( sK5 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f689]) ).
thf(f689,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ Y0 ) )
@ sK15 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f686]) ).
thf(f686,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f685]) ).
thf(f685,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) )
@ sK14 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f282]) ).
thf(f899,plain,
( ~ spl0_14
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f898]) ).
thf(f898,plain,
( $false
| ~ spl0_14
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f897]) ).
thf(f897,plain,
( ( $false = $true )
| ~ spl0_14
| ~ spl0_21 ),
inference(boolean_simplification,[],[f896]) ).
thf(f896,plain,
( ( $true = ~ $true )
| ~ spl0_14
| ~ spl0_21 ),
inference(boolean_simplification,[],[f893]) ).
thf(f893,plain,
( ( $true
= ( ~ ( $true
| ( sK5 @ sK2 @ sK17 ) ) ) )
| ~ spl0_14
| ~ spl0_21 ),
inference(backward_demodulation,[],[f865,f877]) ).
thf(f877,plain,
( ( $true
= ( sK4 @ sK2 @ sK17 ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f876]) ).
thf(f876,plain,
( spl0_21
<=> ( $true
= ( sK4 @ sK2 @ sK17 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f865,plain,
( ( $true
= ( ~ ( ( sK4 @ sK2 @ sK17 )
| ( sK5 @ sK2 @ sK17 ) ) ) )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f862]) ).
thf(f862,plain,
( ( $true
= ( ( ( sK4 @ sK2 @ sK17 )
| ( sK5 @ sK2 @ sK17 ) )
=> $false ) )
| ~ spl0_14 ),
inference(superposition,[],[f45,f851]) ).
thf(f851,plain,
( ( $false
= ( sK6 @ sK17 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f809]) ).
thf(f809,plain,
( ( $false
= ( ( ( sK5 @ sK2 @ sK17 )
| ( sK4 @ sK2 @ sK17 ) )
=> ( sK6 @ sK17 ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f808]) ).
thf(f808,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK5 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ sK17 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f453]) ).
thf(f453,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f452]) ).
thf(f452,plain,
( spl0_14
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f45,plain,
! [X1: a] :
( $true
= ( ( ( sK4 @ sK2 @ X1 )
| ( sK5 @ sK2 @ X1 ) )
=> ( sK6 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK5 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[],[f30]) ).
thf(f892,plain,
( ~ spl0_14
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f891]) ).
thf(f891,plain,
( $false
| ~ spl0_14
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f890]) ).
thf(f890,plain,
( ( $false = $true )
| ~ spl0_14
| ~ spl0_22 ),
inference(boolean_simplification,[],[f889]) ).
thf(f889,plain,
( ( $true = ~ $true )
| ~ spl0_14
| ~ spl0_22 ),
inference(boolean_simplification,[],[f886]) ).
thf(f886,plain,
( ( $true
= ( ~ ( ( sK4 @ sK2 @ sK17 )
| $true ) ) )
| ~ spl0_14
| ~ spl0_22 ),
inference(backward_demodulation,[],[f865,f880]) ).
thf(f880,plain,
( ( ( sK5 @ sK2 @ sK17 )
= $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f879]) ).
thf(f879,plain,
( spl0_22
<=> ( ( sK5 @ sK2 @ sK17 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f881,plain,
( spl0_21
| spl0_22
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f870,f452,f879,f876]) ).
thf(f870,plain,
( ( $true
= ( sK4 @ sK2 @ sK17 ) )
| ( ( sK5 @ sK2 @ sK17 )
= $true )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f852]) ).
thf(f852,plain,
( ( ( ( sK5 @ sK2 @ sK17 )
| ( sK4 @ sK2 @ sK17 ) )
= $true )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f809]) ).
thf(f658,plain,
( spl0_17
| spl0_18
| ~ spl0_4
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f651,f391,f51,f656,f653]) ).
thf(f651,plain,
( ( $false
= ( sK13 @ sK14 ) )
| ( ( sK13 @ sK15 )
= $true )
| ~ spl0_4
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f623]) ).
thf(f623,plain,
( ( ( ( sK13 @ sK14 )
=> ( sK13 @ sK15 ) )
= $true )
| ~ spl0_4
| ~ spl0_9 ),
inference(boolean_simplification,[],[f622]) ).
thf(f622,plain,
( ( $true
= ( ( $true
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_4
| ~ spl0_9 ),
inference(boolean_simplification,[],[f615]) ).
thf(f615,plain,
( ( $true
= ( ( ( ( sK4 @ sK14 @ sK15 )
| $true )
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[],[f589,f392]) ).
thf(f589,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( ( sK4 @ X2 @ X1 )
| ( sK5 @ X2 @ X1 ) )
& ( sK13 @ X2 ) )
=> ( sK13 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f588]) ).
thf(f588,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f576]) ).
thf(f576,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f575]) ).
thf(f575,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f521]) ).
thf(f521,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f517]) ).
thf(f517,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK11 @ Y0 )
| ( sK4 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f504]) ).
thf(f504,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK11 @ Y0 )
| ( sK4 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
=> ( sK13 @ sK12 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f503]) ).
thf(f503,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f496]) ).
thf(f496,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f495]) ).
thf(f495,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f487,f494]) ).
thf(f494,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK10 @ Y1 )
| ( sK5 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f487]) ).
thf(f487,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK10 @ Y1 )
| ( sK5 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f486]) ).
thf(f486,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK10 @ Y2 )
| ( sK5 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK11 @ Y2 )
| ( sK4 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f476]) ).
thf(f476,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK10 @ Y2 )
| ( sK5 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK11 @ Y2 )
| ( sK4 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f475]) ).
thf(f475,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ sK10 @ Y3 )
| ( sK5 @ sK10 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f464]) ).
thf(f464,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ sK10 @ Y3 )
| ( sK5 @ sK10 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f463]) ).
thf(f463,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK10 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f52]) ).
thf(f454,plain,
( spl0_13
| spl0_14
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f445,f36,f452,f449]) ).
thf(f36,plain,
( spl0_1
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK2 @ Y1 )
| ( sK4 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f445,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f442]) ).
thf(f442,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f440]) ).
thf(f440,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f436]) ).
thf(f436,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f434,f29]) ).
thf(f29,plain,
( $false
= ( sK6 @ sK3 ) ),
inference(boolean_simplification,[],[f28]) ).
thf(f28,plain,
( $false
= ( $true
=> ( sK6 @ sK3 ) ) ),
inference(backward_demodulation,[],[f25,f27]) ).
thf(f434,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK3 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f433]) ).
thf(f433,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK2 @ Y1 )
| ( sK4 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f37]) ).
thf(f37,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK2 @ Y1 )
| ( sK4 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f428,plain,
( spl0_11
| spl0_12
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f419,f284,f426,f423]) ).
thf(f419,plain,
( ( ( sK5 @ sK10 @ sK16 )
= $true )
| ( $true
= ( sK4 @ sK10 @ sK16 ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f405]) ).
thf(f405,plain,
( ( $true
= ( ( sK4 @ sK10 @ sK16 )
| ( sK5 @ sK10 @ sK16 ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f403]) ).
thf(f403,plain,
( ( $false
= ( ( ( sK4 @ sK10 @ sK16 )
| ( sK5 @ sK10 @ sK16 ) )
=> ( sK13 @ sK16 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f399]) ).
thf(f399,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ sK16 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f285]) ).
thf(f396,plain,
( spl0_9
| spl0_10
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f387,f281,f394,f391]) ).
thf(f387,plain,
( ( $true
= ( sK5 @ sK14 @ sK15 ) )
| ( $true
= ( sK4 @ sK14 @ sK15 ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f365]) ).
thf(f365,plain,
( ( $true
= ( ( sK5 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) ) )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f364]) ).
thf(f364,plain,
( ( $true
= ( ( ( sK5 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
& $true ) )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f310,f362]) ).
thf(f362,plain,
( ( ( sK13 @ sK14 )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f310]) ).
thf(f310,plain,
( ( $true
= ( ( ( sK5 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
& ( sK13 @ sK14 ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f308]) ).
thf(f308,plain,
( ( $false
= ( ( ( ( sK5 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ sK15 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f307]) ).
thf(f307,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ Y0 ) )
@ sK15 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f306]) ).
thf(f306,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
& ( sK13 @ sK14 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f302]) ).
thf(f302,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) )
@ sK14 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f282]) ).
thf(f286,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f277,f51,f284,f281]) ).
thf(f277,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f258]) ).
thf(f258,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f205,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f204]) ).
thf(f204,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[],[f193,f167]) ).
thf(f167,plain,
( ( ( sK13 @ sK12 )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f166]) ).
thf(f166,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK11 @ Y0 )
| ( sK4 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
=> ( sK13 @ sK12 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f165]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f159]) ).
thf(f159,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f158]) ).
thf(f158,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK10 @ Y1 )
| ( sK5 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK11 @ Y1 )
| ( sK4 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f157]) ).
thf(f157,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK10 @ Y2 )
| ( sK5 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK11 @ Y2 )
| ( sK4 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f156]) ).
thf(f156,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK10 @ Y2 )
| ( sK5 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK11 @ Y2 )
| ( sK4 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f155]) ).
thf(f155,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ sK10 @ Y3 )
| ( sK5 @ sK10 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f154]) ).
thf(f154,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK4 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ sK10 @ Y3 )
| ( sK5 @ sK10 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK10 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f153]) ).
thf(f153,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK10 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f52]) ).
thf(f193,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK10 @ Y0 )
| ( sK5 @ sK10 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK12 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f192]) ).
thf(f192,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK10 @ Y1 )
| ( sK5 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f174]) ).
thf(f174,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK10 @ Y1 )
| ( sK5 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f160]) ).
thf(f160,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK10 @ Y1 )
| ( sK5 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK10 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f158]) ).
thf(f137,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f130,f48,f135,f132]) ).
thf(f130,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f73]) ).
thf(f73,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f65]) ).
thf(f65,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f64]) ).
thf(f64,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f60]) ).
thf(f60,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f59]) ).
thf(f59,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK7 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f49]) ).
thf(f53,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f46,f39,f51,f48]) ).
thf(f39,plain,
( spl0_2
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f46,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f40]) ).
thf(f40,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f41,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f34,f39,f36]) ).
thf(f34,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK2 @ Y1 )
| ( sK4 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f19]) ).
thf(f19,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK4 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y1 @ Y4 )
| ( sK5 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK2 @ Y1 )
| ( sK4 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV152^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 18:24:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a TH0_THM_NEQ_NAR problem
% 0.13/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 % (4050)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.38 % (4044)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.38 % (4046)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)
% 0.20/0.38 % (4045)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)
% 0.20/0.38 % (4049)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)
% 0.20/0.38 % (4048)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)
% 0.20/0.38 % (4048)Instruction limit reached!
% 0.20/0.38 % (4048)------------------------------
% 0.20/0.38 % (4048)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (4045)Instruction limit reached!
% 0.20/0.38 % (4045)------------------------------
% 0.20/0.38 % (4045)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (4048)Termination reason: Unknown
% 0.20/0.38 % (4048)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (4048)Memory used [KB]: 1023
% 0.20/0.38 % (4048)Time elapsed: 0.004 s
% 0.20/0.38 % (4048)Instructions burned: 3 (million)
% 0.20/0.38 % (4048)------------------------------
% 0.20/0.38 % (4048)------------------------------
% 0.20/0.38 % (4050)Instruction limit reached!
% 0.20/0.38 % (4050)------------------------------
% 0.20/0.38 % (4050)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (4050)Termination reason: Unknown
% 0.20/0.38 % (4050)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (4050)Memory used [KB]: 5628
% 0.20/0.38 % (4050)Time elapsed: 0.019 s
% 0.20/0.38 % (4050)Instructions burned: 18 (million)
% 0.20/0.38 % (4050)------------------------------
% 0.20/0.38 % (4050)------------------------------
% 0.20/0.38 % (4045)Termination reason: Unknown
% 0.20/0.38 % (4045)Termination phase: Preprocessing 3
% 0.20/0.38
% 0.20/0.38 % (4045)Memory used [KB]: 1023
% 0.20/0.38 % (4045)Time elapsed: 0.007 s
% 0.20/0.38 % (4045)Instructions burned: 4 (million)
% 0.20/0.38 % (4045)------------------------------
% 0.20/0.38 % (4045)------------------------------
% 0.20/0.39 % (4047)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.39 % (4047)Instruction limit reached!
% 0.20/0.39 % (4047)------------------------------
% 0.20/0.39 % (4047)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (4047)Termination reason: Unknown
% 0.20/0.39 % (4047)Termination phase: Preprocessing 2
% 0.20/0.39
% 0.20/0.39 % (4047)Memory used [KB]: 1023
% 0.20/0.39 % (4047)Time elapsed: 0.004 s
% 0.20/0.39 % (4047)Instructions burned: 3 (million)
% 0.20/0.39 % (4047)------------------------------
% 0.20/0.39 % (4047)------------------------------
% 0.20/0.39 % (4051)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)
% 0.20/0.39 % (4051)Instruction limit reached!
% 0.20/0.39 % (4051)------------------------------
% 0.20/0.39 % (4051)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (4051)Termination reason: Unknown
% 0.20/0.39 % (4051)Termination phase: Preprocessing 3
% 0.20/0.39
% 0.20/0.39 % (4051)Memory used [KB]: 1023
% 0.20/0.39 % (4051)Time elapsed: 0.004 s
% 0.20/0.39 % (4051)Instructions burned: 4 (million)
% 0.20/0.39 % (4051)------------------------------
% 0.20/0.39 % (4051)------------------------------
% 0.20/0.39 % (4046)Instruction limit reached!
% 0.20/0.39 % (4046)------------------------------
% 0.20/0.39 % (4046)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (4046)Termination reason: Unknown
% 0.20/0.39 % (4046)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (4046)Memory used [KB]: 5756
% 0.20/0.39 % (4046)Time elapsed: 0.019 s
% 0.20/0.39 % (4046)Instructions burned: 28 (million)
% 0.20/0.39 % (4046)------------------------------
% 0.20/0.39 % (4046)------------------------------
% 0.20/0.40 % (4052)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)
% 0.20/0.40 % (4053)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)
% 0.20/0.40 % (4054)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)
% 0.20/0.40 % (4054)Instruction limit reached!
% 0.20/0.40 % (4054)------------------------------
% 0.20/0.40 % (4054)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (4054)Termination reason: Unknown
% 0.20/0.40 % (4054)Termination phase: Naming
% 0.20/0.40
% 0.20/0.40 % (4054)Memory used [KB]: 1023
% 0.20/0.40 % (4054)Time elapsed: 0.004 s
% 0.20/0.40 % (4054)Instructions burned: 3 (million)
% 0.20/0.40 % (4054)------------------------------
% 0.20/0.40 % (4054)------------------------------
% 0.20/0.40 % (4053)Instruction limit reached!
% 0.20/0.40 % (4053)------------------------------
% 0.20/0.40 % (4053)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (4053)Termination reason: Unknown
% 0.20/0.40 % (4053)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (4053)Memory used [KB]: 5756
% 0.20/0.40 % (4053)Time elapsed: 0.009 s
% 0.20/0.40 % (4053)Instructions burned: 15 (million)
% 0.20/0.40 % (4053)------------------------------
% 0.20/0.40 % (4053)------------------------------
% 0.20/0.41 % (4056)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.41 % (4055)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)
% 0.20/0.41 % (4057)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.41 % (4052)Instruction limit reached!
% 0.20/0.41 % (4052)------------------------------
% 0.20/0.41 % (4052)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (4052)Termination reason: Unknown
% 0.20/0.41 % (4052)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (4052)Memory used [KB]: 5628
% 0.20/0.41 % (4052)Time elapsed: 0.017 s
% 0.20/0.41 % (4052)Instructions burned: 38 (million)
% 0.20/0.41 % (4052)------------------------------
% 0.20/0.41 % (4052)------------------------------
% 0.20/0.41 % (4056)Instruction limit reached!
% 0.20/0.41 % (4056)------------------------------
% 0.20/0.41 % (4056)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (4056)Termination reason: Unknown
% 0.20/0.41 % (4056)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (4056)Memory used [KB]: 1151
% 0.20/0.41 % (4056)Time elapsed: 0.006 s
% 0.20/0.41 % (4056)Instructions burned: 7 (million)
% 0.20/0.41 % (4056)------------------------------
% 0.20/0.41 % (4056)------------------------------
% 0.20/0.41 % (4058)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.42 % (4057)Instruction limit reached!
% 0.20/0.42 % (4057)------------------------------
% 0.20/0.42 % (4057)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (4057)Termination reason: Unknown
% 0.20/0.42 % (4057)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (4057)Memory used [KB]: 1151
% 0.20/0.42 % (4057)Time elapsed: 0.010 s
% 0.20/0.42 % (4057)Instructions burned: 17 (million)
% 0.20/0.42 % (4057)------------------------------
% 0.20/0.42 % (4057)------------------------------
% 0.20/0.42 % (4058)Instruction limit reached!
% 0.20/0.42 % (4058)------------------------------
% 0.20/0.42 % (4058)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (4058)Termination reason: Unknown
% 0.20/0.42 % (4058)Termination phase: Preprocessing 3
% 0.20/0.42
% 0.20/0.42 % (4058)Memory used [KB]: 1023
% 0.20/0.42 % (4058)Time elapsed: 0.004 s
% 0.20/0.42 % (4058)Instructions burned: 4 (million)
% 0.20/0.42 % (4058)------------------------------
% 0.20/0.42 % (4058)------------------------------
% 0.20/0.42 % (4059)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.42 % (4059)Instruction limit reached!
% 0.20/0.42 % (4059)------------------------------
% 0.20/0.42 % (4059)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (4059)Termination reason: Unknown
% 0.20/0.42 % (4059)Termination phase: Preprocessing 2
% 0.20/0.42
% 0.20/0.42 % (4059)Memory used [KB]: 1023
% 0.20/0.42 % (4059)Time elapsed: 0.003 s
% 0.20/0.42 % (4059)Instructions burned: 3 (million)
% 0.20/0.42 % (4059)------------------------------
% 0.20/0.42 % (4059)------------------------------
% 0.20/0.43 % (4061)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.43 % (4060)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.43 % (4061)Instruction limit reached!
% 0.20/0.43 % (4061)------------------------------
% 0.20/0.43 % (4061)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (4061)Termination reason: Unknown
% 0.20/0.43 % (4061)Termination phase: Property scanning
% 0.20/0.43
% 0.20/0.43 % (4061)Memory used [KB]: 1023
% 0.20/0.43 % (4061)Time elapsed: 0.004 s
% 0.20/0.43 % (4061)Instructions burned: 4 (million)
% 0.20/0.43 % (4061)------------------------------
% 0.20/0.43 % (4061)------------------------------
% 0.20/0.43 % (4060)Instruction limit reached!
% 0.20/0.43 % (4060)------------------------------
% 0.20/0.43 % (4060)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (4060)Termination reason: Unknown
% 0.20/0.43 % (4060)Termination phase: Property scanning
% 0.20/0.43
% 0.20/0.43 % (4060)Memory used [KB]: 1151
% 0.20/0.43 % (4060)Time elapsed: 0.005 s
% 0.20/0.43 % (4060)Instructions burned: 8 (million)
% 0.20/0.43 % (4060)------------------------------
% 0.20/0.43 % (4060)------------------------------
% 0.20/0.43 % (4062)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.43 % (4063)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.43 % (4062)Instruction limit reached!
% 0.20/0.43 % (4062)------------------------------
% 0.20/0.43 % (4062)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (4062)Termination reason: Unknown
% 0.20/0.43 % (4062)Termination phase: Preprocessing 3
% 0.20/0.43
% 0.20/0.43 % (4062)Memory used [KB]: 1023
% 0.20/0.43 % (4062)Time elapsed: 0.004 s
% 0.20/0.43 % (4062)Instructions burned: 4 (million)
% 0.20/0.43 % (4062)------------------------------
% 0.20/0.43 % (4062)------------------------------
% 0.20/0.44 % (4064)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.44 % (4063)Instruction limit reached!
% 0.20/0.44 % (4063)------------------------------
% 0.20/0.44 % (4063)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (4063)Termination reason: Unknown
% 0.20/0.44 % (4063)Termination phase: Saturation
% 0.20/0.44
% 0.20/0.44 % (4063)Memory used [KB]: 5756
% 0.20/0.44 % (4063)Time elapsed: 0.012 s
% 0.20/0.44 % (4063)Instructions burned: 18 (million)
% 0.20/0.44 % (4063)------------------------------
% 0.20/0.44 % (4063)------------------------------
% 0.20/0.44 % (4065)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.45 % (4066)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.20/0.45 % (4065)Instruction limit reached!
% 0.20/0.45 % (4065)------------------------------
% 0.20/0.45 % (4065)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (4065)Termination reason: Unknown
% 0.20/0.45 % (4065)Termination phase: Preprocessing 3
% 0.20/0.45
% 0.20/0.45 % (4065)Memory used [KB]: 1023
% 0.20/0.45 % (4065)Time elapsed: 0.005 s
% 0.20/0.45 % (4065)Instructions burned: 6 (million)
% 0.20/0.45 % (4065)------------------------------
% 0.20/0.45 % (4065)------------------------------
% 0.20/0.45 % (4067)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.20/0.46 % (4068)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.46 % (4068)Instruction limit reached!
% 0.20/0.46 % (4068)------------------------------
% 0.20/0.46 % (4068)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (4068)Termination reason: Unknown
% 0.20/0.46 % (4068)Termination phase: Property scanning
% 0.20/0.46
% 0.20/0.46 % (4068)Memory used [KB]: 1023
% 0.20/0.46 % (4068)Time elapsed: 0.004 s
% 0.20/0.46 % (4068)Instructions burned: 6 (million)
% 0.20/0.46 % (4068)------------------------------
% 0.20/0.46 % (4068)------------------------------
% 0.20/0.46 % (4067)Instruction limit reached!
% 0.20/0.46 % (4067)------------------------------
% 0.20/0.46 % (4067)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (4067)Termination reason: Unknown
% 0.20/0.46 % (4067)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (4067)Memory used [KB]: 5884
% 0.20/0.46 % (4067)Time elapsed: 0.013 s
% 0.20/0.46 % (4067)Instructions burned: 21 (million)
% 0.20/0.46 % (4067)------------------------------
% 0.20/0.46 % (4067)------------------------------
% 0.20/0.46 % (4069)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.46 % (4069)Instruction limit reached!
% 0.20/0.46 % (4069)------------------------------
% 0.20/0.46 % (4069)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (4069)Termination reason: Unknown
% 0.20/0.46 % (4069)Termination phase: Property scanning
% 0.20/0.46
% 0.20/0.46 % (4069)Memory used [KB]: 1023
% 0.20/0.46 % (4069)Time elapsed: 0.003 s
% 0.20/0.46 % (4069)Instructions burned: 6 (million)
% 0.20/0.46 % (4069)------------------------------
% 0.20/0.46 % (4069)------------------------------
% 0.20/0.47 % (4070)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.20/0.47 % (4071)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.20/0.47 % (4072)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.20/0.47 % (4044)Instruction limit reached!
% 0.20/0.47 % (4044)------------------------------
% 0.20/0.47 % (4044)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47 % (4044)Termination reason: Unknown
% 0.20/0.47 % (4044)Termination phase: Saturation
% 0.20/0.47
% 0.20/0.47 % (4044)Memory used [KB]: 6652
% 0.20/0.47 % (4072)Instruction limit reached!
% 0.20/0.47 % (4072)------------------------------
% 0.20/0.47 % (4072)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47 % (4044)Time elapsed: 0.111 s
% 0.20/0.47 % (4044)Instructions burned: 183 (million)
% 0.20/0.47 % (4044)------------------------------
% 0.20/0.47 % (4044)------------------------------
% 0.20/0.47 % (4072)Termination reason: Unknown
% 0.20/0.47 % (4072)Termination phase: Saturation
% 0.20/0.47
% 0.20/0.47 % (4072)Memory used [KB]: 5500
% 0.20/0.47 % (4072)Time elapsed: 0.006 s
% 0.20/0.47 % (4072)Instructions burned: 19 (million)
% 0.20/0.47 % (4072)------------------------------
% 0.20/0.47 % (4072)------------------------------
% 0.20/0.48 % (4073)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.20/0.49 % (4074)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.20/0.50 % (4074)Instruction limit reached!
% 0.20/0.50 % (4074)------------------------------
% 0.20/0.50 % (4074)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.50 % (4074)Termination reason: Unknown
% 0.20/0.50 % (4074)Termination phase: Saturation
% 0.20/0.50
% 0.20/0.50 % (4074)Memory used [KB]: 5756
% 0.20/0.50 % (4074)Time elapsed: 0.011 s
% 0.20/0.50 % (4074)Instructions burned: 19 (million)
% 0.20/0.50 % (4074)------------------------------
% 0.20/0.50 % (4074)------------------------------
% 0.20/0.50 % (4049)Instruction limit reached!
% 0.20/0.50 % (4049)------------------------------
% 0.20/0.50 % (4049)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.50 % (4049)Termination reason: Unknown
% 0.20/0.50 % (4049)Termination phase: Saturation
% 0.20/0.50
% 0.20/0.50 % (4049)Memory used [KB]: 6396
% 0.20/0.50 % (4049)Time elapsed: 0.127 s
% 0.20/0.50 % (4049)Instructions burned: 275 (million)
% 0.20/0.50 % (4049)------------------------------
% 0.20/0.50 % (4049)------------------------------
% 0.20/0.51 % (4075)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.20/0.51 % (4075)Instruction limit reached!
% 0.20/0.51 % (4075)------------------------------
% 0.20/0.51 % (4075)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.51 % (4075)Termination reason: Unknown
% 0.20/0.51 % (4075)Termination phase: Preprocessing 3
% 0.20/0.51
% 0.20/0.51 % (4075)Memory used [KB]: 1023
% 0.20/0.51 % (4075)Time elapsed: 0.003 s
% 0.20/0.51 % (4075)Instructions burned: 5 (million)
% 0.20/0.51 % (4075)------------------------------
% 0.20/0.51 % (4075)------------------------------
% 0.20/0.52 % (4077)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.20/0.52 % (4076)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 1.37/0.53 % (4076)Instruction limit reached!
% 1.37/0.53 % (4076)------------------------------
% 1.37/0.53 % (4076)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.37/0.53 % (4076)Termination reason: Unknown
% 1.37/0.53 % (4076)Termination phase: Saturation
% 1.37/0.53
% 1.37/0.53 % (4076)Memory used [KB]: 5756
% 1.37/0.53 % (4076)Time elapsed: 0.018 s
% 1.37/0.53 % (4076)Instructions burned: 30 (million)
% 1.37/0.53 % (4076)------------------------------
% 1.37/0.53 % (4076)------------------------------
% 1.50/0.55 % (4078)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 1.50/0.56 % (4077)Instruction limit reached!
% 1.50/0.56 % (4077)------------------------------
% 1.50/0.56 % (4077)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.56 % (4077)Termination reason: Unknown
% 1.50/0.56 % (4077)Termination phase: Saturation
% 1.50/0.56
% 1.50/0.56 % (4077)Memory used [KB]: 6268
% 1.50/0.56 % (4077)Time elapsed: 0.039 s
% 1.50/0.56 % (4077)Instructions burned: 127 (million)
% 1.50/0.56 % (4077)------------------------------
% 1.50/0.56 % (4077)------------------------------
% 1.50/0.56 % (4079)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 1.50/0.56 % (4079)Instruction limit reached!
% 1.50/0.56 % (4079)------------------------------
% 1.50/0.56 % (4079)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.56 % (4079)Termination reason: Unknown
% 1.50/0.56 % (4079)Termination phase: shuffling
% 1.50/0.56
% 1.50/0.56 % (4079)Memory used [KB]: 1023
% 1.50/0.56 % (4079)Time elapsed: 0.002 s
% 1.50/0.56 % (4079)Instructions burned: 3 (million)
% 1.50/0.56 % (4079)------------------------------
% 1.50/0.56 % (4079)------------------------------
% 1.50/0.57 % (4080)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 1.50/0.58 % (4080)Instruction limit reached!
% 1.50/0.58 % (4080)------------------------------
% 1.50/0.58 % (4080)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.58 % (4080)Termination reason: Unknown
% 1.50/0.58 % (4080)Termination phase: Saturation
% 1.50/0.58
% 1.50/0.58 % (4080)Memory used [KB]: 5628
% 1.50/0.58 % (4080)Time elapsed: 0.007 s
% 1.50/0.58 % (4080)Instructions burned: 20 (million)
% 1.50/0.58 % (4080)------------------------------
% 1.50/0.58 % (4080)------------------------------
% 1.50/0.58 % (4081)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2997ds/86Mi)
% 1.50/0.60 % (4070)Instruction limit reached!
% 1.50/0.60 % (4070)------------------------------
% 1.50/0.60 % (4070)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.60 % (4070)Termination reason: Unknown
% 1.50/0.60 % (4070)Termination phase: Saturation
% 1.50/0.60
% 1.50/0.60 % (4070)Memory used [KB]: 6780
% 1.50/0.60 % (4070)Time elapsed: 0.130 s
% 1.50/0.60 % (4070)Instructions burned: 378 (million)
% 1.50/0.60 % (4070)------------------------------
% 1.50/0.60 % (4070)------------------------------
% 1.50/0.60 % (4078)Instruction limit reached!
% 1.50/0.60 % (4078)------------------------------
% 1.50/0.60 % (4078)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.60 % (4078)Termination reason: Unknown
% 1.50/0.60 % (4078)Termination phase: Saturation
% 1.50/0.60
% 1.50/0.60 % (4078)Memory used [KB]: 6140
% 1.50/0.60 % (4078)Time elapsed: 0.056 s
% 1.50/0.60 % (4078)Instructions burned: 101 (million)
% 1.50/0.60 % (4078)------------------------------
% 1.50/0.60 % (4078)------------------------------
% 1.50/0.60 % (4082)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2997ds/107Mi)
% 1.50/0.61 % (4081)Instruction limit reached!
% 1.50/0.61 % (4081)------------------------------
% 1.50/0.61 % (4081)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.61 % (4081)Termination reason: Unknown
% 1.50/0.61 % (4081)Termination phase: Saturation
% 1.50/0.61
% 1.50/0.61 % (4081)Memory used [KB]: 6140
% 1.50/0.61 % (4081)Time elapsed: 0.027 s
% 1.50/0.61 % (4081)Instructions burned: 87 (million)
% 1.50/0.61 % (4081)------------------------------
% 1.50/0.61 % (4081)------------------------------
% 1.50/0.61 % (4083)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 1.50/0.62 % (4084)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on theBenchmark for (2997ds/448Mi)
% 2.09/0.63 % (4083)Instruction limit reached!
% 2.09/0.63 % (4083)------------------------------
% 2.09/0.63 % (4083)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.09/0.63 % (4083)Termination reason: Unknown
% 2.09/0.63 % (4083)Termination phase: Saturation
% 2.09/0.63
% 2.09/0.63 % (4083)Memory used [KB]: 5628
% 2.09/0.63 % (4083)Time elapsed: 0.013 s
% 2.09/0.63 % (4083)Instructions burned: 39 (million)
% 2.09/0.63 % (4083)------------------------------
% 2.09/0.63 % (4083)------------------------------
% 2.09/0.64 % (4085)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2997ds/46Mi)
% 2.09/0.64 % (4082)Instruction limit reached!
% 2.09/0.64 % (4082)------------------------------
% 2.09/0.64 % (4082)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.09/0.64 % (4082)Termination reason: Unknown
% 2.09/0.64 % (4082)Termination phase: Saturation
% 2.09/0.64
% 2.09/0.64 % (4082)Memory used [KB]: 6268
% 2.09/0.64 % (4082)Time elapsed: 0.040 s
% 2.09/0.64 % (4082)Instructions burned: 108 (million)
% 2.09/0.64 % (4082)------------------------------
% 2.09/0.64 % (4082)------------------------------
% 2.09/0.65 % (4086)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on theBenchmark for (2997ds/98Mi)
% 2.09/0.67 % (4085)Instruction limit reached!
% 2.09/0.67 % (4085)------------------------------
% 2.09/0.67 % (4085)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.09/0.67 % (4085)Termination reason: Unknown
% 2.09/0.67 % (4085)Termination phase: Saturation
% 2.09/0.67
% 2.09/0.67 % (4085)Memory used [KB]: 5884
% 2.09/0.67 % (4085)Time elapsed: 0.026 s
% 2.09/0.67 % (4085)Instructions burned: 46 (million)
% 2.09/0.67 % (4085)------------------------------
% 2.09/0.67 % (4085)------------------------------
% 2.45/0.68 % (4086)Instruction limit reached!
% 2.45/0.68 % (4086)------------------------------
% 2.45/0.68 % (4086)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.45/0.68 % (4086)Termination reason: Unknown
% 2.45/0.68 % (4086)Termination phase: Saturation
% 2.45/0.68
% 2.45/0.68 % (4086)Memory used [KB]: 1279
% 2.45/0.68 % (4086)Time elapsed: 0.032 s
% 2.45/0.68 % (4086)Instructions burned: 98 (million)
% 2.45/0.68 % (4086)------------------------------
% 2.45/0.68 % (4086)------------------------------
% 2.45/0.68 % (4087)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on theBenchmark for (2997ds/507Mi)
% 2.45/0.69 % (4088)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on theBenchmark for (2996ds/149Mi)
% 2.45/0.72 % (4071)Instruction limit reached!
% 2.45/0.72 % (4071)------------------------------
% 2.45/0.72 % (4071)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.45/0.72 % (4071)Termination reason: Unknown
% 2.45/0.72 % (4071)Termination phase: Saturation
% 2.45/0.72
% 2.45/0.72 % (4071)Memory used [KB]: 7036
% 2.45/0.72 % (4071)Time elapsed: 0.250 s
% 2.45/0.72 % (4071)Instructions burned: 779 (million)
% 2.45/0.72 % (4071)------------------------------
% 2.45/0.72 % (4071)------------------------------
% 2.45/0.72 % (4089)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2996ds/39Mi)
% 2.45/0.73 % (4088)Instruction limit reached!
% 2.45/0.73 % (4088)------------------------------
% 2.45/0.73 % (4088)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.45/0.73 % (4088)Termination reason: Unknown
% 2.45/0.73 % (4088)Termination phase: Property scanning
% 2.45/0.73
% 2.45/0.73 % (4088)Memory used [KB]: 2174
% 2.45/0.73 % (4088)Time elapsed: 0.038 s
% 2.45/0.73 % (4088)Instructions burned: 151 (million)
% 2.45/0.73 % (4088)------------------------------
% 2.45/0.73 % (4088)------------------------------
% 2.45/0.74 % (4090)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2996ds/6Mi)
% 2.45/0.74 % (4089)Instruction limit reached!
% 2.45/0.74 % (4089)------------------------------
% 2.45/0.74 % (4089)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.45/0.74 % (4089)Termination reason: Unknown
% 2.45/0.74 % (4089)Termination phase: Saturation
% 2.45/0.74
% 2.45/0.74 % (4089)Memory used [KB]: 5756
% 2.45/0.74 % (4089)Time elapsed: 0.037 s
% 2.45/0.74 % (4089)Instructions burned: 41 (million)
% 2.45/0.74 % (4089)------------------------------
% 2.45/0.74 % (4089)------------------------------
% 2.45/0.74 % (4090)Instruction limit reached!
% 2.45/0.74 % (4090)------------------------------
% 2.45/0.74 % (4090)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.45/0.74 % (4090)Termination reason: Unknown
% 2.45/0.74 % (4090)Termination phase: Saturation
% 2.45/0.74
% 2.45/0.74 % (4090)Memory used [KB]: 9978
% 2.45/0.74 % (4090)Time elapsed: 0.003 s
% 2.45/0.74 % (4090)Instructions burned: 7 (million)
% 2.45/0.74 % (4090)------------------------------
% 2.45/0.74 % (4090)------------------------------
% 2.89/0.75 % (4091)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on theBenchmark for (2996ds/1087Mi)
% 2.89/0.75 % (4092)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2996ds/47Mi)
% 2.89/0.75 % (4084)Instruction limit reached!
% 2.89/0.75 % (4084)------------------------------
% 2.89/0.75 % (4084)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.89/0.75 % (4084)Termination reason: Unknown
% 2.89/0.75 % (4084)Termination phase: Saturation
% 2.89/0.75
% 2.89/0.75 % (4084)Memory used [KB]: 6780
% 2.89/0.75 % (4084)Time elapsed: 0.132 s
% 2.89/0.75 % (4084)Instructions burned: 450 (million)
% 2.89/0.75 % (4084)------------------------------
% 2.89/0.75 % (4084)------------------------------
% 2.89/0.76 % (4093)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on theBenchmark for (2996ds/44Mi)
% 2.89/0.76 % (4064)Refutation not found, non-redundant clauses discarded% (4064)------------------------------
% 2.89/0.76 % (4064)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.89/0.76 % (4064)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.89/0.76
% 2.89/0.76 % (4064)Memory used [KB]: 7547
% 2.89/0.76 % (4064)Time elapsed: 0.325 s
% 2.89/0.76 % (4064)Instructions burned: 702 (million)
% 2.89/0.76 % (4064)------------------------------
% 2.89/0.76 % (4064)------------------------------
% 2.89/0.76 % (4092)Instruction limit reached!
% 2.89/0.76 % (4092)------------------------------
% 2.89/0.76 % (4092)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.89/0.76 % (4092)Termination reason: Unknown
% 2.89/0.76 % (4092)Termination phase: Saturation
% 2.89/0.76
% 2.89/0.76 % (4092)Memory used [KB]: 5756
% 2.89/0.76 % (4092)Time elapsed: 0.017 s
% 2.89/0.76 % (4092)Instructions burned: 48 (million)
% 2.89/0.76 % (4092)------------------------------
% 2.89/0.76 % (4092)------------------------------
% 2.89/0.77 % (4093)Instruction limit reached!
% 2.89/0.77 % (4093)------------------------------
% 2.89/0.77 % (4093)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.89/0.77 % (4093)Termination reason: Unknown
% 2.89/0.77 % (4093)Termination phase: Saturation
% 2.89/0.77
% 2.89/0.77 % (4093)Memory used [KB]: 1151
% 2.89/0.77 % (4093)Time elapsed: 0.012 s
% 2.89/0.77 % (4093)Instructions burned: 45 (million)
% 2.89/0.77 % (4093)------------------------------
% 2.89/0.77 % (4093)------------------------------
% 3.18/0.77 % (4095)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2995ds/62Mi)
% 3.18/0.78 % (4096)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2995ds/31Mi)
% 3.18/0.78 % (4094)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on theBenchmark for (2995ds/432Mi)
% 3.18/0.78 % (4096)Instruction limit reached!
% 3.18/0.78 % (4096)------------------------------
% 3.18/0.78 % (4096)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.18/0.78 % (4096)Termination reason: Unknown
% 3.18/0.78 % (4096)Termination phase: Saturation
% 3.18/0.78
% 3.18/0.78 % (4096)Memory used [KB]: 5756
% 3.18/0.78 % (4096)Time elapsed: 0.011 s
% 3.18/0.78 % (4096)Instructions burned: 32 (million)
% 3.18/0.78 % (4096)------------------------------
% 3.18/0.78 % (4096)------------------------------
% 3.18/0.79 % (4095)Instruction limit reached!
% 3.18/0.79 % (4095)------------------------------
% 3.18/0.79 % (4095)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.18/0.79 % (4095)Termination reason: Unknown
% 3.18/0.79 % (4095)Termination phase: Saturation
% 3.18/0.79
% 3.18/0.79 % (4095)Memory used [KB]: 5756
% 3.18/0.79 % (4095)Time elapsed: 0.021 s
% 3.18/0.79 % (4095)Instructions burned: 63 (million)
% 3.18/0.79 % (4095)------------------------------
% 3.18/0.79 % (4095)------------------------------
% 3.18/0.79 % (4097)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2995ds/96Mi)
% 3.18/0.80 % (4073)Refutation not found, non-redundant clauses discarded% (4073)------------------------------
% 3.18/0.80 % (4073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.18/0.80 % (4073)Termination reason: Refutation not found, non-redundant clauses discarded
% 3.18/0.80
% 3.18/0.80 % (4073)Memory used [KB]: 7291
% 3.18/0.80 % (4073)Time elapsed: 0.328 s
% 3.18/0.80 % (4073)Instructions burned: 869 (million)
% 3.18/0.80 % (4073)------------------------------
% 3.18/0.80 % (4073)------------------------------
% 3.18/0.80 % (4098)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on theBenchmark for (2995ds/453Mi)
% 3.18/0.81 % (4099)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2995ds/71Mi)
% 3.35/0.82 % (4097)Instruction limit reached!
% 3.35/0.82 % (4097)------------------------------
% 3.35/0.82 % (4097)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.82 % (4097)Termination reason: Unknown
% 3.35/0.82 % (4097)Termination phase: Saturation
% 3.35/0.82
% 3.35/0.82 % (4097)Memory used [KB]: 6140
% 3.35/0.82 % (4097)Time elapsed: 0.031 s
% 3.35/0.82 % (4097)Instructions burned: 96 (million)
% 3.35/0.82 % (4097)------------------------------
% 3.35/0.82 % (4097)------------------------------
% 3.35/0.83 % (4055)First to succeed.
% 3.35/0.83 % (4100)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on theBenchmark for (2995ds/83Mi)
% 3.35/0.83 % (4099)Instruction limit reached!
% 3.35/0.83 % (4099)------------------------------
% 3.35/0.83 % (4099)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.83 % (4099)Termination reason: Unknown
% 3.35/0.83 % (4099)Termination phase: Saturation
% 3.35/0.83
% 3.35/0.83 % (4099)Memory used [KB]: 6012
% 3.35/0.83 % (4099)Time elapsed: 0.026 s
% 3.35/0.83 % (4099)Instructions burned: 71 (million)
% 3.35/0.83 % (4099)------------------------------
% 3.35/0.83 % (4099)------------------------------
% 3.35/0.84 % (4055)Refutation found. Thanks to Tanya!
% 3.35/0.84 % SZS status Theorem for theBenchmark
% 3.35/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/0.85 % (4055)------------------------------
% 3.35/0.85 % (4055)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.85 % (4055)Termination reason: Refutation
% 3.35/0.85
% 3.35/0.85 % (4055)Memory used [KB]: 8955
% 3.35/0.85 % (4055)Time elapsed: 0.437 s
% 3.35/0.85 % (4055)Instructions burned: 829 (million)
% 3.35/0.85 % (4055)------------------------------
% 3.35/0.85 % (4055)------------------------------
% 3.35/0.85 % (4043)Success in time 0.492 s
% 3.35/0.85 % Vampire---4.8 exiting
%------------------------------------------------------------------------------