TSTP Solution File: SEV150^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV150^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n012.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 10.69s 1.65s
% Output : Refutation 10.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 85
% Syntax : Number of formulae : 508 ( 16 unt; 59 typ; 0 def)
% Number of atoms : 4331 ( 429 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 11209 ( 839 ~;1037 |; 787 &;6072 @)
% ( 25 <=>;1145 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 638 ( 638 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 82 usr; 61 con; 0-2 aty)
% (1304 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1537 (1408 ^ 128 !; 0 ?;1537 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_22,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK2: a > a > $o ).
thf(func_def_24,type,
sK3: a > a > $o ).
thf(func_def_25,type,
sK4: a ).
thf(func_def_26,type,
sK5: a ).
thf(func_def_27,type,
sK6: a > $o ).
thf(func_def_28,type,
sK7: a ).
thf(func_def_29,type,
sK8: a ).
thf(func_def_30,type,
sK9: a ).
thf(func_def_31,type,
sK10: a ).
thf(func_def_32,type,
sK11: a > $o ).
thf(func_def_33,type,
sK12: a ).
thf(func_def_34,type,
sK13: a ).
thf(func_def_35,type,
sK14: a ).
thf(func_def_36,type,
sK15: a ).
thf(func_def_37,type,
sK16: a > $o ).
thf(func_def_38,type,
sK17: a > $o ).
thf(func_def_39,type,
sK18: a > $o ).
thf(func_def_40,type,
sK19: a > $o ).
thf(func_def_41,type,
sK20: a > $o ).
thf(func_def_42,type,
sK21: a > $o ).
thf(func_def_43,type,
sK22: a ).
thf(func_def_44,type,
sK23: a ).
thf(func_def_45,type,
sK24: a ).
thf(func_def_46,type,
sK25: a > $o ).
thf(func_def_47,type,
sK26: a > $o ).
thf(func_def_48,type,
sK27: a > $o ).
thf(func_def_49,type,
sK28: a ).
thf(func_def_50,type,
sK29: a > $o ).
thf(func_def_51,type,
sK30: a > $o ).
thf(func_def_52,type,
sK31: a ).
thf(func_def_53,type,
sK32: ( a > $o ) > a ).
thf(func_def_54,type,
sK33: a > $o ).
thf(func_def_55,type,
sK34: ( a > $o ) > a ).
thf(func_def_56,type,
sK35: a > $o ).
thf(func_def_57,type,
sK36: a ).
thf(func_def_58,type,
sK37: a > $o ).
thf(func_def_59,type,
sK38: a ).
thf(func_def_60,type,
sK39: a ).
thf(func_def_61,type,
sK40: ( a > $o ) > a ).
thf(func_def_62,type,
sK41: a ).
thf(func_def_63,type,
sK42: a ).
thf(func_def_64,type,
sK43: a ).
thf(func_def_65,type,
sK44: a > $o ).
thf(func_def_66,type,
sK45: a > $o ).
thf(func_def_67,type,
sK46: a ).
thf(func_def_68,type,
sK47: a ).
thf(func_def_69,type,
sK48: a ).
thf(func_def_70,type,
sK49: a ).
thf(func_def_71,type,
sK50: a ).
thf(func_def_72,type,
sK51: a ).
thf(func_def_73,type,
sK52: a ).
thf(func_def_74,type,
sK53: a ).
thf(func_def_75,type,
sK54: a ).
thf(func_def_76,type,
sK55: a ).
thf(func_def_77,type,
sK56: a ).
thf(func_def_78,type,
sK57: a ).
thf(f11721,plain,
$false,
inference(avatar_sat_refutation,[],[f27,f34,f131,f188,f260,f302,f350,f408,f1098,f1345,f1427,f2005,f3684,f9592,f9596,f9942,f10354,f10472,f10501,f10578,f10633,f10730,f11163,f11512,f11659,f11720]) ).
thf(f11720,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_200 ),
inference(avatar_contradiction_clause,[],[f11719]) ).
thf(f11719,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_200 ),
inference(trivial_inequality_removal,[],[f11718]) ).
thf(f11718,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_200 ),
inference(boolean_simplification,[],[f11717]) ).
thf(f11717,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_200 ),
inference(boolean_simplification,[],[f11716]) ).
thf(f11716,plain,
( ( $true
= ( ~ ( ( sK2 @ sK7 @ sK57 )
| $true ) ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_200 ),
inference(forward_demodulation,[],[f11710,f11696]) ).
thf(f11696,plain,
( ( $true
= ( sK3 @ sK7 @ sK57 ) )
| ~ spl0_200 ),
inference(binary_proxy_clausification,[],[f11677]) ).
thf(f11677,plain,
( ( $false
= ( ( sK3 @ sK7 @ sK57 )
=> ( sK6 @ sK57 ) ) )
| ~ spl0_200 ),
inference(beta_eta_normalization,[],[f11673]) ).
thf(f11673,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK57 ) )
| ~ spl0_200 ),
inference(sigma_clausification,[],[f11508]) ).
thf(f11508,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f11507]) ).
thf(f11507,plain,
( spl0_200
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
thf(f11710,plain,
( ( ( ~ ( ( sK2 @ sK7 @ sK57 )
| ( sK3 @ sK7 @ sK57 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_200 ),
inference(boolean_simplification,[],[f11706]) ).
thf(f11706,plain,
( ( $true
= ( ( ( sK2 @ sK7 @ sK57 )
| ( sK3 @ sK7 @ sK57 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_200 ),
inference(superposition,[],[f11205,f11695]) ).
thf(f11695,plain,
( ( $false
= ( sK6 @ sK57 ) )
| ~ spl0_200 ),
inference(binary_proxy_clausification,[],[f11677]) ).
thf(f11205,plain,
( ! [X0: a] :
( $true
= ( ( ( sK2 @ sK7 @ X0 )
| ( sK3 @ sK7 @ X0 ) )
=> ( sK6 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f11202]) ).
thf(f11202,plain,
( ! [X0: a] :
( ( ( $true
& ( ( sK2 @ sK7 @ X0 )
| ( sK3 @ sK7 @ X0 ) ) )
=> ( sK6 @ X0 ) )
= $true )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f9689,f11181]) ).
thf(f11181,plain,
( ( $true
= ( sK6 @ sK7 ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f11174]) ).
thf(f11174,plain,
( ( $false
= ( ( sK6 @ sK7 )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f11173]) ).
thf(f11173,plain,
( ( $false
= ( ( $true
& ( sK6 @ sK7 ) )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f11172]) ).
thf(f11172,plain,
( ( $false
= ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| $true )
& ( sK6 @ sK7 ) )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(backward_demodulation,[],[f10751,f187]) ).
thf(f187,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f186]) ).
thf(f186,plain,
( spl0_8
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f10751,plain,
( ( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
& ( sK6 @ sK7 ) )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f10750]) ).
thf(f10750,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK7 ) )
=> ( sK6 @ Y0 ) )
@ sK8 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f10737]) ).
thf(f10737,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK7 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f10734]) ).
thf(f10734,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK7 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f127]) ).
thf(f127,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f126,plain,
( spl0_5
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f9689,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK6 @ X2 )
& ( ( sK2 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) ) )
=> ( sK6 @ X1 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f9688]) ).
thf(f9688,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f9681]) ).
thf(f9681,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f9680]) ).
thf(f9680,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f9632]) ).
thf(f9632,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f9608]) ).
thf(f9608,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f9606]) ).
thf(f9606,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK5 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f9605]) ).
thf(f9605,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f23]) ).
thf(f23,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f22,plain,
( spl0_1
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f11659,plain,
( ~ spl0_1
| ~ spl0_201 ),
inference(avatar_contradiction_clause,[],[f11658]) ).
thf(f11658,plain,
( $false
| ~ spl0_1
| ~ spl0_201 ),
inference(trivial_inequality_removal,[],[f11657]) ).
thf(f11657,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_201 ),
inference(forward_demodulation,[],[f11656,f11555]) ).
thf(f11555,plain,
( ( $false
= ( sK6 @ sK54 ) )
| ~ spl0_201 ),
inference(binary_proxy_clausification,[],[f11542]) ).
thf(f11542,plain,
( ( $false
= ( ( ( sK3 @ sK55 @ sK54 )
& ( sK6 @ sK55 ) )
=> ( sK6 @ sK54 ) ) )
| ~ spl0_201 ),
inference(beta_eta_normalization,[],[f11541]) ).
thf(f11541,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK54 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK54 ) )
@ sK55 ) )
| ~ spl0_201 ),
inference(sigma_clausification,[],[f11526]) ).
thf(f11526,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK54 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK54 ) ) )
= $false )
| ~ spl0_201 ),
inference(beta_eta_normalization,[],[f11524]) ).
thf(f11524,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) )
@ sK54 ) )
| ~ spl0_201 ),
inference(sigma_clausification,[],[f11511]) ).
thf(f11511,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f11510]) ).
thf(f11510,plain,
( spl0_201
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
thf(f11656,plain,
( ( $true
= ( sK6 @ sK54 ) )
| ~ spl0_1
| ~ spl0_201 ),
inference(boolean_simplification,[],[f11655]) ).
thf(f11655,plain,
( ( ( $true
=> ( sK6 @ sK54 ) )
= $true )
| ~ spl0_1
| ~ spl0_201 ),
inference(forward_demodulation,[],[f11654,f11634]) ).
thf(f11634,plain,
( ( ( sK6 @ sK56 )
= $true )
| ~ spl0_201 ),
inference(binary_proxy_clausification,[],[f11617]) ).
thf(f11617,plain,
( ( $true
= ( ( sK3 @ sK56 @ sK54 )
& ( sK6 @ sK56 ) ) )
| ~ spl0_201 ),
inference(not_proxy_clausification,[],[f11612]) ).
thf(f11612,plain,
( ( $false
= ( ~ ( ( sK3 @ sK56 @ sK54 )
& ( sK6 @ sK56 ) ) ) )
| ~ spl0_201 ),
inference(beta_eta_normalization,[],[f11611]) ).
thf(f11611,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK3 @ Y0 @ sK54 )
& ( sK6 @ Y0 ) )
@ sK56 ) )
| ~ spl0_201 ),
inference(sigma_clausification,[],[f11559]) ).
thf(f11559,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK3 @ Y0 @ sK54 )
& ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_201 ),
inference(boolean_simplification,[],[f11558]) ).
thf(f11558,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ sK54 )
& ( sK6 @ Y0 ) )
=> $false ) )
= $false )
| ~ spl0_201 ),
inference(backward_demodulation,[],[f11526,f11555]) ).
thf(f11654,plain,
( ( ( ( sK6 @ sK56 )
=> ( sK6 @ sK54 ) )
= $true )
| ~ spl0_1
| ~ spl0_201 ),
inference(boolean_simplification,[],[f11653]) ).
thf(f11653,plain,
( ( $true
= ( ( ( sK6 @ sK56 )
& $true )
=> ( sK6 @ sK54 ) ) )
| ~ spl0_1
| ~ spl0_201 ),
inference(boolean_simplification,[],[f11652]) ).
thf(f11652,plain,
( ( ( ( ( sK6 @ sK56 )
& ( ( sK2 @ sK56 @ sK54 )
| $true ) )
=> ( sK6 @ sK54 ) )
= $true )
| ~ spl0_1
| ~ spl0_201 ),
inference(superposition,[],[f9689,f11637]) ).
thf(f11637,plain,
( ( $true
= ( sK3 @ sK56 @ sK54 ) )
| ~ spl0_201 ),
inference(boolean_simplification,[],[f11636]) ).
thf(f11636,plain,
( ( ( ( sK3 @ sK56 @ sK54 )
& $true )
= $true )
| ~ spl0_201 ),
inference(backward_demodulation,[],[f11617,f11634]) ).
thf(f11512,plain,
( spl0_200
| spl0_201
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f11503,f186,f126,f11510,f11507]) ).
thf(f11503,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f11484]) ).
thf(f11484,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f11242]) ).
thf(f11242,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f11234]) ).
thf(f11234,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f11220,f11180]) ).
thf(f11180,plain,
( ( ( sK6 @ sK8 )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f11174]) ).
thf(f11220,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK7 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK8 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f11219]) ).
thf(f11219,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[],[f187]) ).
thf(f11163,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f11162]) ).
thf(f11162,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f11161]) ).
thf(f11161,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(boolean_simplification,[],[f11160]) ).
thf(f11160,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(boolean_simplification,[],[f11159]) ).
thf(f11159,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK7 @ sK53 ) ) ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f11140,f11094]) ).
thf(f11094,plain,
( ( $true
= ( sK2 @ sK7 @ sK53 ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f11078]) ).
thf(f11078,plain,
( ( $false
= ( ( sK2 @ sK7 @ sK53 )
=> ( sK6 @ sK53 ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f11076]) ).
thf(f11076,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK53 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f256]) ).
thf(f256,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f255,plain,
( spl0_11
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f11140,plain,
( ( $true
= ( ~ ( ( sK2 @ sK7 @ sK53 )
| ( sK3 @ sK7 @ sK53 ) ) ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(boolean_simplification,[],[f11126]) ).
thf(f11126,plain,
( ( $true
= ( ( ( sK2 @ sK7 @ sK53 )
| ( sK3 @ sK7 @ sK53 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(superposition,[],[f10787,f11096]) ).
thf(f11096,plain,
( ( ( sK6 @ sK53 )
= $false )
| ~ spl0_11 ),
inference(boolean_simplification,[],[f11095]) ).
thf(f11095,plain,
( ( $false
= ( $true
=> ( sK6 @ sK53 ) ) )
| ~ spl0_11 ),
inference(backward_demodulation,[],[f11078,f11094]) ).
thf(f10787,plain,
( ! [X0: a] :
( $true
= ( ( ( sK2 @ sK7 @ X0 )
| ( sK3 @ sK7 @ X0 ) )
=> ( sK6 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f10784]) ).
thf(f10784,plain,
( ! [X0: a] :
( ( ( $true
& ( ( sK2 @ sK7 @ X0 )
| ( sK3 @ sK7 @ X0 ) ) )
=> ( sK6 @ X0 ) )
= $true )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f9689,f10768]) ).
thf(f10768,plain,
( ( $true
= ( sK6 @ sK7 ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f10754]) ).
thf(f10754,plain,
( ( $false
= ( ( sK6 @ sK7 )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f10753]) ).
thf(f10753,plain,
( ( $false
= ( ( $true
& ( sK6 @ sK7 ) )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f10752]) ).
thf(f10752,plain,
( ( ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
& ( sK6 @ sK7 ) )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f10751,f184]) ).
thf(f184,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f183]) ).
thf(f183,plain,
( spl0_7
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f10730,plain,
( ~ spl0_1
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f10729]) ).
thf(f10729,plain,
( $false
| ~ spl0_1
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f10728]) ).
thf(f10728,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_12 ),
inference(forward_demodulation,[],[f10727,f10667]) ).
thf(f10667,plain,
( ( $false
= ( sK6 @ sK9 ) )
| ~ spl0_12 ),
inference(boolean_simplification,[],[f10666]) ).
thf(f10666,plain,
( ( $false
= ( $true
=> ( sK6 @ sK9 ) ) )
| ~ spl0_12 ),
inference(backward_demodulation,[],[f10651,f10665]) ).
thf(f10665,plain,
( ( ( ( sK2 @ sK10 @ sK9 )
& ( sK6 @ sK10 ) )
= $true )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f10651]) ).
thf(f10651,plain,
( ( $false
= ( ( ( sK2 @ sK10 @ sK9 )
& ( sK6 @ sK10 ) )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f10650]) ).
thf(f10650,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f10638]) ).
thf(f10638,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK9 ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f10636]) ).
thf(f10636,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) )
@ sK9 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f259]) ).
thf(f259,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f258]) ).
thf(f258,plain,
( spl0_12
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f10727,plain,
( ( $true
= ( sK6 @ sK9 ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[],[f10726]) ).
thf(f10726,plain,
( ( $true
= ( $true
=> ( sK6 @ sK9 ) ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(forward_demodulation,[],[f10725,f10710]) ).
thf(f10710,plain,
( ( $true
= ( sK6 @ sK15 ) )
| ~ spl0_12 ),
inference(boolean_simplification,[],[f10709]) ).
thf(f10709,plain,
( ( ( $true
& ( sK6 @ sK15 ) )
= $true )
| ~ spl0_12 ),
inference(backward_demodulation,[],[f10704,f10708]) ).
thf(f10708,plain,
( ( ( sK2 @ sK15 @ sK9 )
= $true )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f10704]) ).
thf(f10704,plain,
( ( $true
= ( ( sK2 @ sK15 @ sK9 )
& ( sK6 @ sK15 ) ) )
| ~ spl0_12 ),
inference(not_proxy_clausification,[],[f10691]) ).
thf(f10691,plain,
( ( $false
= ( ~ ( ( sK2 @ sK15 @ sK9 )
& ( sK6 @ sK15 ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f10690]) ).
thf(f10690,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) )
@ sK15 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f10669]) ).
thf(f10669,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(boolean_simplification,[],[f10668]) ).
thf(f10668,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) )
=> $false ) ) )
| ~ spl0_12 ),
inference(backward_demodulation,[],[f10638,f10667]) ).
thf(f10725,plain,
( ( ( ( sK6 @ sK15 )
=> ( sK6 @ sK9 ) )
= $true )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[],[f10724]) ).
thf(f10724,plain,
( ( $true
= ( ( ( sK6 @ sK15 )
& $true )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[],[f10723]) ).
thf(f10723,plain,
( ( $true
= ( ( ( sK6 @ sK15 )
& ( $true
| ( sK3 @ sK15 @ sK9 ) ) )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f9689,f10708]) ).
thf(f10633,plain,
( ~ spl0_1
| ~ spl0_199 ),
inference(avatar_contradiction_clause,[],[f10632]) ).
thf(f10632,plain,
( $false
| ~ spl0_1
| ~ spl0_199 ),
inference(trivial_inequality_removal,[],[f10631]) ).
thf(f10631,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_199 ),
inference(boolean_simplification,[],[f10630]) ).
thf(f10630,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_199 ),
inference(boolean_simplification,[],[f10629]) ).
thf(f10629,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK4 @ sK52 ) ) ) )
| ~ spl0_1
| ~ spl0_199 ),
inference(forward_demodulation,[],[f10622,f10611]) ).
thf(f10611,plain,
( ( ( sK2 @ sK4 @ sK52 )
= $true )
| ~ spl0_199 ),
inference(binary_proxy_clausification,[],[f10597]) ).
thf(f10597,plain,
( ( ( ( sK2 @ sK4 @ sK52 )
=> ( sK6 @ sK52 ) )
= $false )
| ~ spl0_199 ),
inference(beta_eta_normalization,[],[f10593]) ).
thf(f10593,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK52 )
= $false )
| ~ spl0_199 ),
inference(sigma_clausification,[],[f10577]) ).
thf(f10577,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f10576]) ).
thf(f10576,plain,
( spl0_199
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
thf(f10622,plain,
( ( $true
= ( ~ ( ( sK2 @ sK4 @ sK52 )
| ( sK3 @ sK4 @ sK52 ) ) ) )
| ~ spl0_1
| ~ spl0_199 ),
inference(boolean_simplification,[],[f10621]) ).
thf(f10621,plain,
( ( $true
= ( ( ( sK2 @ sK4 @ sK52 )
| ( sK3 @ sK4 @ sK52 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_199 ),
inference(superposition,[],[f9636,f10610]) ).
thf(f10610,plain,
( ( ( sK6 @ sK52 )
= $false )
| ~ spl0_199 ),
inference(binary_proxy_clausification,[],[f10597]) ).
thf(f9636,plain,
( ! [X1: a] :
( $true
= ( ( ( sK2 @ sK4 @ X1 )
| ( sK3 @ sK4 @ X1 ) )
=> ( sK6 @ X1 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f9635]) ).
thf(f9635,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f9634]) ).
thf(f9634,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f9633]) ).
thf(f9633,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f9608,f9632]) ).
thf(f10578,plain,
( spl0_199
| spl0_12
| ~ spl0_6
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f10572,f9937,f129,f258,f10576]) ).
thf(f129,plain,
( spl0_6
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f9937,plain,
( spl0_181
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
thf(f10572,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_6
| ~ spl0_181 ),
inference(binary_proxy_clausification,[],[f10560]) ).
thf(f10560,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_6
| ~ spl0_181 ),
inference(not_proxy_clausification,[],[f10543]) ).
thf(f10543,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_181 ),
inference(boolean_simplification,[],[f10532]) ).
thf(f10532,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_6
| ~ spl0_181 ),
inference(superposition,[],[f10516,f9810]) ).
thf(f9810,plain,
( ( $false
= ( sK6 @ sK46 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f9801]) ).
thf(f9801,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) ) )
=> ( sK6 @ sK46 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f9799]) ).
thf(f9799,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) )
@ sK46 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f130]) ).
thf(f130,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f129]) ).
thf(f10516,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK46 ) ) )
| ~ spl0_181 ),
inference(beta_eta_normalization,[],[f10515]) ).
thf(f10515,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) )
@ X1 )
= $true )
| ~ spl0_181 ),
inference(pi_clausification,[],[f9938]) ).
thf(f9938,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) )
= $true )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f9937]) ).
thf(f10501,plain,
( ~ spl0_1
| ~ spl0_196 ),
inference(avatar_contradiction_clause,[],[f10500]) ).
thf(f10500,plain,
( $false
| ~ spl0_1
| ~ spl0_196 ),
inference(trivial_inequality_removal,[],[f10499]) ).
thf(f10499,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_196 ),
inference(boolean_simplification,[],[f10498]) ).
thf(f10498,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_196 ),
inference(boolean_simplification,[],[f10497]) ).
thf(f10497,plain,
( ( ( ~ ( ( sK2 @ sK4 @ sK51 )
| $true ) )
= $true )
| ~ spl0_1
| ~ spl0_196 ),
inference(forward_demodulation,[],[f10493,f10481]) ).
thf(f10481,plain,
( ( $true
= ( sK3 @ sK4 @ sK51 ) )
| ~ spl0_196 ),
inference(binary_proxy_clausification,[],[f10479]) ).
thf(f10479,plain,
( ( $false
= ( ( sK3 @ sK4 @ sK51 )
=> ( sK6 @ sK51 ) ) )
| ~ spl0_196 ),
inference(beta_eta_normalization,[],[f10475]) ).
thf(f10475,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK51 ) )
| ~ spl0_196 ),
inference(sigma_clausification,[],[f10353]) ).
thf(f10353,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f10352]) ).
thf(f10352,plain,
( spl0_196
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
thf(f10493,plain,
( ( $true
= ( ~ ( ( sK2 @ sK4 @ sK51 )
| ( sK3 @ sK4 @ sK51 ) ) ) )
| ~ spl0_1
| ~ spl0_196 ),
inference(boolean_simplification,[],[f10489]) ).
thf(f10489,plain,
( ( $true
= ( ( ( sK2 @ sK4 @ sK51 )
| ( sK3 @ sK4 @ sK51 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_196 ),
inference(superposition,[],[f9636,f10483]) ).
thf(f10483,plain,
( ( $false
= ( sK6 @ sK51 ) )
| ~ spl0_196 ),
inference(boolean_simplification,[],[f10482]) ).
thf(f10482,plain,
( ( $false
= ( $true
=> ( sK6 @ sK51 ) ) )
| ~ spl0_196 ),
inference(backward_demodulation,[],[f10479,f10481]) ).
thf(f10472,plain,
( ~ spl0_1
| ~ spl0_195 ),
inference(avatar_contradiction_clause,[],[f10471]) ).
thf(f10471,plain,
( $false
| ~ spl0_1
| ~ spl0_195 ),
inference(trivial_inequality_removal,[],[f10470]) ).
thf(f10470,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_195 ),
inference(forward_demodulation,[],[f10469,f10397]) ).
thf(f10397,plain,
( ( $false
= ( sK6 @ sK48 ) )
| ~ spl0_195 ),
inference(binary_proxy_clausification,[],[f10384]) ).
thf(f10384,plain,
( ( $false
= ( ( ( sK6 @ sK49 )
& ( sK3 @ sK49 @ sK48 ) )
=> ( sK6 @ sK48 ) ) )
| ~ spl0_195 ),
inference(beta_eta_normalization,[],[f10383]) ).
thf(f10383,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ sK48 ) )
=> ( sK6 @ sK48 ) )
@ sK49 )
= $false )
| ~ spl0_195 ),
inference(sigma_clausification,[],[f10370]) ).
thf(f10370,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ sK48 ) )
=> ( sK6 @ sK48 ) ) )
= $false )
| ~ spl0_195 ),
inference(beta_eta_normalization,[],[f10366]) ).
thf(f10366,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
@ sK48 )
= $false )
| ~ spl0_195 ),
inference(sigma_clausification,[],[f10350]) ).
thf(f10350,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f10349]) ).
thf(f10349,plain,
( spl0_195
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
thf(f10469,plain,
( ( $true
= ( sK6 @ sK48 ) )
| ~ spl0_1
| ~ spl0_195 ),
inference(boolean_simplification,[],[f10468]) ).
thf(f10468,plain,
( ( $true
= ( $true
=> ( sK6 @ sK48 ) ) )
| ~ spl0_1
| ~ spl0_195 ),
inference(forward_demodulation,[],[f10467,f10421]) ).
thf(f10421,plain,
( ( $true
= ( sK6 @ sK49 ) )
| ~ spl0_195 ),
inference(binary_proxy_clausification,[],[f10398]) ).
thf(f10398,plain,
( ( ( ( sK6 @ sK49 )
& ( sK3 @ sK49 @ sK48 ) )
= $true )
| ~ spl0_195 ),
inference(binary_proxy_clausification,[],[f10384]) ).
thf(f10467,plain,
( ( ( ( sK6 @ sK49 )
=> ( sK6 @ sK48 ) )
= $true )
| ~ spl0_1
| ~ spl0_195 ),
inference(boolean_simplification,[],[f10466]) ).
thf(f10466,plain,
( ( $true
= ( ( ( sK6 @ sK49 )
& $true )
=> ( sK6 @ sK48 ) ) )
| ~ spl0_1
| ~ spl0_195 ),
inference(boolean_simplification,[],[f10465]) ).
thf(f10465,plain,
( ( ( ( ( sK6 @ sK49 )
& ( ( sK2 @ sK49 @ sK48 )
| $true ) )
=> ( sK6 @ sK48 ) )
= $true )
| ~ spl0_1
| ~ spl0_195 ),
inference(superposition,[],[f9689,f10423]) ).
thf(f10423,plain,
( ( $true
= ( sK3 @ sK49 @ sK48 ) )
| ~ spl0_195 ),
inference(boolean_simplification,[],[f10422]) ).
thf(f10422,plain,
( ( $true
= ( $true
& ( sK3 @ sK49 @ sK48 ) ) )
| ~ spl0_195 ),
inference(backward_demodulation,[],[f10398,f10421]) ).
thf(f10354,plain,
( spl0_195
| spl0_196
| ~ spl0_6
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f10345,f9940,f129,f10352,f10349]) ).
thf(f9940,plain,
( spl0_182
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
thf(f10345,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_6
| ~ spl0_182 ),
inference(binary_proxy_clausification,[],[f10330]) ).
thf(f10330,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_6
| ~ spl0_182 ),
inference(not_proxy_clausification,[],[f10014]) ).
thf(f10014,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_6
| ~ spl0_182 ),
inference(boolean_simplification,[],[f10013]) ).
thf(f10013,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_6
| ~ spl0_182 ),
inference(superposition,[],[f9954,f9810]) ).
thf(f9954,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK46 ) ) )
| ~ spl0_182 ),
inference(beta_eta_normalization,[],[f9953]) ).
thf(f9953,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) )
@ X1 ) )
| ~ spl0_182 ),
inference(pi_clausification,[],[f9941]) ).
thf(f9941,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) ) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f9940]) ).
thf(f9942,plain,
( spl0_181
| spl0_182
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f9935,f129,f9940,f9937]) ).
thf(f9935,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) )
= $true )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f9811]) ).
thf(f9811,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK46 ) ) ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f9801]) ).
thf(f9596,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f9595]) ).
thf(f9595,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f9594]) ).
thf(f9594,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(backward_demodulation,[],[f33,f23]) ).
thf(f33,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f32,plain,
( spl0_4
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f9592,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f9591]) ).
thf(f9591,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f9590]) ).
thf(f9590,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_demodulation,[],[f9578,f4650]) ).
thf(f4650,plain,
( ( $false
= ( sK35 @ sK12 ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(boolean_simplification,[],[f4649]) ).
thf(f4649,plain,
( ( ( $true
=> ( sK35 @ sK12 ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(backward_demodulation,[],[f4613,f4648]) ).
thf(f4648,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK14 @ Y0 )
=> ( sK35 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK35 @ Y1 ) )
=> ( sK35 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f4613]) ).
thf(f4613,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK14 @ Y0 )
=> ( sK35 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK35 @ Y1 ) )
=> ( sK35 @ Y0 ) ) ) ) )
=> ( sK35 @ sK12 ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f4609]) ).
thf(f4609,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK35 )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(sigma_clausification,[],[f3978]) ).
thf(f3978,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f3788]) ).
thf(f3788,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(boolean_simplification,[],[f3786]) ).
thf(f3786,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
& $true )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[],[f3752,f3718]) ).
thf(f3718,plain,
( ( ( sK11 @ sK14 )
= $true )
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(not_proxy_clausification,[],[f3709]) ).
thf(f3709,plain,
( ( ( ~ ( sK11 @ sK14 ) )
= $false )
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(boolean_simplification,[],[f3708]) ).
thf(f3708,plain,
( ( $false
= ( ~ ( ( sK11 @ sK14 )
& $true ) ) )
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(boolean_simplification,[],[f3707]) ).
thf(f3707,plain,
( ( $false
= ( ~ ( ( sK11 @ sK14 )
& ( $true
| ( sK3 @ sK14 @ sK12 ) ) ) ) )
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_demodulation,[],[f3706,f346]) ).
thf(f346,plain,
( ( ( sK2 @ sK14 @ sK12 )
= $true )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f345]) ).
thf(f345,plain,
( spl0_15
<=> ( ( sK2 @ sK14 @ sK12 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f3706,plain,
( ( $false
= ( ~ ( ( sK11 @ sK14 )
& ( ( sK2 @ sK14 @ sK12 )
| ( sK3 @ sK14 @ sK12 ) ) ) ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f3705]) ).
thf(f3705,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
@ sK14 )
= $false )
| ~ spl0_14
| ~ spl0_19 ),
inference(sigma_clausification,[],[f3695]) ).
thf(f3695,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_14
| ~ spl0_19 ),
inference(boolean_simplification,[],[f3694]) ).
thf(f3694,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
=> $false ) )
= $false )
| ~ spl0_14
| ~ spl0_19 ),
inference(backward_demodulation,[],[f1437,f3693]) ).
thf(f3693,plain,
( ( $false
= ( sK11 @ sK12 ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(boolean_simplification,[],[f3692]) ).
thf(f3692,plain,
( ( ( $true
=> ( sK11 @ sK12 ) )
= $false )
| ~ spl0_14
| ~ spl0_19 ),
inference(backward_demodulation,[],[f3687,f3691]) ).
thf(f3691,plain,
( ( $true
= ( sK11 @ sK13 ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f3687]) ).
thf(f3687,plain,
( ( $false
= ( ( sK11 @ sK13 )
=> ( sK11 @ sK12 ) ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(boolean_simplification,[],[f3686]) ).
thf(f3686,plain,
( ( $false
= ( ( ( sK11 @ sK13 )
& $true )
=> ( sK11 @ sK12 ) ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(boolean_simplification,[],[f3685]) ).
thf(f3685,plain,
( ( $false
= ( ( ( sK11 @ sK13 )
& ( $true
| ( sK3 @ sK13 @ sK12 ) ) )
=> ( sK11 @ sK12 ) ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(backward_demodulation,[],[f1447,f404]) ).
thf(f404,plain,
( ( $true
= ( sK2 @ sK13 @ sK12 ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f403]) ).
thf(f403,plain,
( spl0_19
<=> ( $true
= ( sK2 @ sK13 @ sK12 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f1447,plain,
( ( ( ( ( sK11 @ sK13 )
& ( ( sK2 @ sK13 @ sK12 )
| ( sK3 @ sK13 @ sK12 ) ) )
=> ( sK11 @ sK12 ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f1446]) ).
thf(f1446,plain,
( ( ( ^ [Y0: a] :
( ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
=> ( sK11 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f1437]) ).
thf(f1437,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
=> ( sK11 @ sK12 ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f1434]) ).
thf(f1434,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK11 @ Y0 ) ) )
@ sK12 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f301]) ).
thf(f301,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK11 @ Y0 ) ) ) )
= $false )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f300,plain,
( spl0_14
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK11 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f3752,plain,
( ! [X0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
& ( sK11 @ X0 ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_19 ),
inference(not_proxy_clausification,[],[f3700]) ).
thf(f3700,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
& ( sK11 @ X0 ) ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_19 ),
inference(boolean_simplification,[],[f3696]) ).
thf(f3696,plain,
( ! [X0: a] :
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
& ( sK11 @ X0 ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_19 ),
inference(superposition,[],[f364,f3693]) ).
thf(f364,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X1 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ X2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X1 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ X2 ) ) ) )
& ( sK11 @ X1 ) )
=> ( sK11 @ X2 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f363]) ).
thf(f363,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ X1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ X1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK11 @ X1 ) )
=> ( sK11 @ Y0 ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f362]) ).
thf(f362,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ X1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ X1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK11 @ X1 ) )
=> ( sK11 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f361]) ).
thf(f361,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK11 @ Y0 ) )
=> ( sK11 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f356]) ).
thf(f356,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK11 @ Y0 ) )
=> ( sK11 @ Y1 ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f355]) ).
thf(f355,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK11 @ Y0 ) )
=> ( sK11 @ Y1 ) ) ) )
& $true )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f285,f353]) ).
thf(f353,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f285]) ).
thf(f285,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK11 @ Y0 ) )
=> ( sK11 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f275]) ).
thf(f275,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK11 @ Y0 ) )
=> ( sK11 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y0 ) ) ) )
=> ( sK11 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f274]) ).
thf(f274,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK11 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f26]) ).
thf(f26,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f25,plain,
( spl0_2
<=> ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f9578,plain,
( ( $true
= ( sK35 @ sK12 ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(boolean_simplification,[],[f9568]) ).
thf(f9568,plain,
( ( $true
= ( $true
=> ( sK35 @ sK12 ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[],[f9548,f346]) ).
thf(f9548,plain,
( ! [X1: a] :
( $true
= ( ( sK2 @ sK14 @ X1 )
=> ( sK35 @ X1 ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f9547]) ).
thf(f9547,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ sK14 @ Y0 )
=> ( sK35 @ Y0 ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(pi_clausification,[],[f5841]) ).
thf(f5841,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK14 @ Y0 )
=> ( sK35 @ Y0 ) ) )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f4648]) ).
thf(f3684,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f3683]) ).
thf(f3683,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f3682]) ).
thf(f3682,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(boolean_simplification,[],[f3681]) ).
thf(f3681,plain,
( ( $true = ~ $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f3673,f407]) ).
thf(f407,plain,
( ( $true
= ( sK3 @ sK13 @ sK12 ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f406]) ).
thf(f406,plain,
( spl0_20
<=> ( $true
= ( sK3 @ sK13 @ sK12 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f3673,plain,
( ( $true
= ( ~ ( sK3 @ sK13 @ sK12 ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(boolean_simplification,[],[f3666]) ).
thf(f3666,plain,
( ( ( ( sK3 @ sK13 @ sK12 )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f3661,f2928]) ).
thf(f2928,plain,
( ( ( sK37 @ sK12 )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(boolean_simplification,[],[f2927]) ).
thf(f2927,plain,
( ( ( $true
=> ( sK37 @ sK12 ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f2897,f2926]) ).
thf(f2926,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK37 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK37 @ Y1 ) )
=> ( sK37 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f2897]) ).
thf(f2897,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK37 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK37 @ Y1 ) )
=> ( sK37 @ Y0 ) ) ) ) )
=> ( sK37 @ sK12 ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f2893]) ).
thf(f2893,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK37 ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(sigma_clausification,[],[f2874]) ).
thf(f2874,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(boolean_simplification,[],[f2873]) ).
thf(f2873,plain,
( ( ( $false
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f2325,f2865]) ).
thf(f2865,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f2325]) ).
thf(f2325,plain,
( ( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(boolean_simplification,[],[f2316]) ).
thf(f2316,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
& $true ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f2283,f2014]) ).
thf(f2014,plain,
( ( $true
= ( sK11 @ sK13 ) )
| ~ spl0_14
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f2008]) ).
thf(f2008,plain,
( ( $false
= ( ( sK11 @ sK13 )
=> ( sK11 @ sK12 ) ) )
| ~ spl0_14
| ~ spl0_20 ),
inference(boolean_simplification,[],[f2007]) ).
thf(f2007,plain,
( ( $false
= ( ( ( sK11 @ sK13 )
& $true )
=> ( sK11 @ sK12 ) ) )
| ~ spl0_14
| ~ spl0_20 ),
inference(boolean_simplification,[],[f2006]) ).
thf(f2006,plain,
( ( ( ( ( sK11 @ sK13 )
& ( ( sK2 @ sK13 @ sK12 )
| $true ) )
=> ( sK11 @ sK12 ) )
= $false )
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1447,f407]) ).
thf(f2283,plain,
( ! [X0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
& ( sK11 @ X0 ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(not_proxy_clausification,[],[f2027]) ).
thf(f2027,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
& ( sK11 @ X0 ) ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(boolean_simplification,[],[f2021]) ).
thf(f2021,plain,
( ! [X0: a] :
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ X0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
& ( sK11 @ X0 ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f364,f2013]) ).
thf(f2013,plain,
( ( $false
= ( sK11 @ sK12 ) )
| ~ spl0_14
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f2008]) ).
thf(f3661,plain,
( ! [X1: a] :
( $true
= ( ( sK3 @ sK13 @ X1 )
=> ( sK37 @ X1 ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f3660]) ).
thf(f3660,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK37 @ Y0 ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(pi_clausification,[],[f3645]) ).
thf(f3645,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK37 @ Y0 ) ) )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(boolean_simplification,[],[f3644]) ).
thf(f3644,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK37 @ Y0 ) ) )
& $true )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f2926,f3642]) ).
thf(f3642,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK37 @ Y1 ) )
=> ( sK37 @ Y0 ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f2926]) ).
thf(f2005,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f2004]) ).
thf(f2004,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f2003]) ).
thf(f2003,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1996,f1716]) ).
thf(f1716,plain,
( ( ( sK25 @ sK12 )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1715]) ).
thf(f1715,plain,
( ( ( $true
=> ( sK25 @ sK12 ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(backward_demodulation,[],[f1697,f1714]) ).
thf(f1714,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK14 @ Y0 )
=> ( sK25 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK25 @ Y1 ) )
=> ( sK25 @ Y0 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f1697]) ).
thf(f1697,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK14 @ Y0 )
=> ( sK25 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK25 @ Y1 ) )
=> ( sK25 @ Y0 ) ) ) ) )
=> ( sK25 @ sK12 ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f1692]) ).
thf(f1692,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK25 )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(sigma_clausification,[],[f1683]) ).
thf(f1683,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1682]) ).
thf(f1682,plain,
( ( ( $false
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(backward_demodulation,[],[f1643,f1676]) ).
thf(f1676,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f1643]) ).
thf(f1643,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(not_proxy_clausification,[],[f1509]) ).
thf(f1509,plain,
( ( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1502]) ).
thf(f1502,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(superposition,[],[f1481,f1451]) ).
thf(f1451,plain,
( ( $false
= ( sK11 @ sK12 ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f1450]) ).
thf(f1450,plain,
( ( $false
= ( ( sK11 @ sK13 )
=> ( sK11 @ sK12 ) ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1449]) ).
thf(f1449,plain,
( ( $false
= ( ( ( sK11 @ sK13 )
& $true )
=> ( sK11 @ sK12 ) ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1448]) ).
thf(f1448,plain,
( ( $false
= ( ( ( sK11 @ sK13 )
& ( $true
| ( sK3 @ sK13 @ sK12 ) ) )
=> ( sK11 @ sK12 ) ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1447,f404]) ).
thf(f1481,plain,
( ! [X0: a] :
( $true
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ X0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ X0 ) ) ) )
=> ( sK11 @ X0 ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1477]) ).
thf(f1477,plain,
( ! [X0: a] :
( $true
= ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ X0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK14 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ X0 ) ) ) )
& $true )
=> ( sK11 @ X0 ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(superposition,[],[f364,f1473]) ).
thf(f1473,plain,
( ( ( sK11 @ sK14 )
= $true )
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(not_proxy_clausification,[],[f1463]) ).
thf(f1463,plain,
( ( ( ~ ( sK11 @ sK14 ) )
= $false )
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1462]) ).
thf(f1462,plain,
( ( $false
= ( ~ ( ( sK11 @ sK14 )
& $true ) ) )
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1461]) ).
thf(f1461,plain,
( ( ( ~ ( ( sK11 @ sK14 )
& ( ( sK2 @ sK14 @ sK12 )
| $true ) ) )
= $false )
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1460,f349]) ).
thf(f349,plain,
( ( $true
= ( sK3 @ sK14 @ sK12 ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f348]) ).
thf(f348,plain,
( spl0_16
<=> ( $true
= ( sK3 @ sK14 @ sK12 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f1460,plain,
( ( $false
= ( ~ ( ( sK11 @ sK14 )
& ( ( sK2 @ sK14 @ sK12 )
| ( sK3 @ sK14 @ sK12 ) ) ) ) )
| ~ spl0_14
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f1459]) ).
thf(f1459,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
@ sK14 )
= $false )
| ~ spl0_14
| ~ spl0_19 ),
inference(sigma_clausification,[],[f1456]) ).
thf(f1456,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_14
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1454]) ).
thf(f1454,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
=> $false ) )
= $false )
| ~ spl0_14
| ~ spl0_19 ),
inference(backward_demodulation,[],[f1437,f1451]) ).
thf(f1996,plain,
( ( ( sK25 @ sK12 )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1995]) ).
thf(f1995,plain,
( ( ( $true
=> ( sK25 @ sK12 ) )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(superposition,[],[f1986,f349]) ).
thf(f1986,plain,
( ! [X1: a] :
( ( ( sK3 @ sK14 @ X1 )
=> ( sK25 @ X1 ) )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f1985]) ).
thf(f1985,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ sK14 @ Y0 )
=> ( sK25 @ Y0 ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(pi_clausification,[],[f1981]) ).
thf(f1981,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK14 @ Y0 )
=> ( sK25 @ Y0 ) ) )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1980]) ).
thf(f1980,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK14 @ Y0 )
=> ( sK25 @ Y0 ) ) )
& $true )
= $true )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(backward_demodulation,[],[f1714,f1978]) ).
thf(f1978,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK25 @ Y1 ) )
=> ( sK25 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_14
| ~ spl0_16
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f1714]) ).
thf(f1427,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f1426]) ).
thf(f1426,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_36 ),
inference(trivial_inequality_removal,[],[f1425]) ).
thf(f1425,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_36 ),
inference(boolean_simplification,[],[f1424]) ).
thf(f1424,plain,
( ( $true = ~ $true )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_36 ),
inference(forward_demodulation,[],[f1419,f1097]) ).
thf(f1097,plain,
( ( $true
= ( sK2 @ sK4 @ sK28 ) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1096]) ).
thf(f1096,plain,
( spl0_36
<=> ( $true
= ( sK2 @ sK4 @ sK28 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
thf(f1419,plain,
( ( ( ~ ( sK2 @ sK4 @ sK28 ) )
= $true )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1417]) ).
thf(f1417,plain,
( ( $true
= ( ( sK2 @ sK4 @ sK28 )
=> $false ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f1412,f1252]) ).
thf(f1252,plain,
( ( $false
= ( sK30 @ sK28 ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1244]) ).
thf(f1244,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK30 @ Y1 ) )
=> ( sK30 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK30 @ Y0 ) ) ) )
=> ( sK30 @ sK28 ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f1241]) ).
thf(f1241,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) )
@ sK30 ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(sigma_clausification,[],[f1146]) ).
thf(f1146,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1135]) ).
thf(f1135,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(not_proxy_clausification,[],[f1087]) ).
thf(f1087,plain,
( ( $true
= ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1085]) ).
thf(f1085,plain,
( ( $true
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f477,f1081]) ).
thf(f1081,plain,
( ( ( sK11 @ sK28 )
= $false )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1080]) ).
thf(f1080,plain,
( ( ( $true
=> ( sK11 @ sK28 ) )
= $false )
| ~ spl0_13 ),
inference(backward_demodulation,[],[f1064,f1079]) ).
thf(f1079,plain,
( ( ( ( sK2 @ sK4 @ sK28 )
| ( sK3 @ sK4 @ sK28 ) )
= $true )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1064]) ).
thf(f1064,plain,
( ( ( ( ( sK2 @ sK4 @ sK28 )
| ( sK3 @ sK4 @ sK28 ) )
=> ( sK11 @ sK28 ) )
= $false )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f1061]) ).
thf(f1061,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK11 @ Y0 ) )
@ sK28 )
= $false )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f298]) ).
thf(f298,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK11 @ Y0 ) ) )
= $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f297,plain,
( spl0_13
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK11 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f477,plain,
( ! [X1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ X1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ X1 ) ) ) )
=> ( sK11 @ X1 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f476]) ).
thf(f476,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK11 @ Y0 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f353]) ).
thf(f1412,plain,
( ! [X1: a] :
( $true
= ( ( sK2 @ sK4 @ X1 )
=> ( sK30 @ X1 ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f1411]) ).
thf(f1411,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK30 @ Y0 ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(pi_clausification,[],[f1398]) ).
thf(f1398,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK30 @ Y0 ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1397]) ).
thf(f1397,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK30 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(backward_demodulation,[],[f1253,f1396]) ).
thf(f1396,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK30 @ Y1 ) )
=> ( sK30 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1253]) ).
thf(f1253,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK30 @ Y1 ) )
=> ( sK30 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK30 @ Y0 ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1244]) ).
thf(f1345,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f1344]) ).
thf(f1344,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_35 ),
inference(trivial_inequality_removal,[],[f1343]) ).
thf(f1343,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1336,f1190]) ).
thf(f1190,plain,
( ( $false
= ( sK29 @ sK28 ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1189]) ).
thf(f1189,plain,
( ( ( $true
=> ( sK29 @ sK28 ) )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(backward_demodulation,[],[f1171,f1188]) ).
thf(f1188,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK29 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK29 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK29 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1171]) ).
thf(f1171,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK29 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK29 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK29 @ Y0 ) ) ) )
=> ( sK29 @ sK28 ) )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f1168]) ).
thf(f1168,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) )
@ sK29 )
= $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(sigma_clausification,[],[f1151]) ).
thf(f1151,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1150]) ).
thf(f1150,plain,
( ( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK28 ) ) )
| $false ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(backward_demodulation,[],[f1135,f1146]) ).
thf(f1336,plain,
( ( $true
= ( sK29 @ sK28 ) )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_35 ),
inference(boolean_simplification,[],[f1332]) ).
thf(f1332,plain,
( ( ( $true
=> ( sK29 @ sK28 ) )
= $true )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_35 ),
inference(superposition,[],[f1325,f1094]) ).
thf(f1094,plain,
( ( $true
= ( sK3 @ sK4 @ sK28 ) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1093]) ).
thf(f1093,plain,
( spl0_35
<=> ( $true
= ( sK3 @ sK4 @ sK28 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
thf(f1325,plain,
( ! [X1: a] :
( $true
= ( ( sK3 @ sK4 @ X1 )
=> ( sK29 @ X1 ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f1324]) ).
thf(f1324,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK29 @ Y0 ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(pi_clausification,[],[f1191]) ).
thf(f1191,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK4 @ Y0 )
=> ( sK29 @ Y0 ) ) ) )
| ~ spl0_2
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1188]) ).
thf(f1098,plain,
( spl0_35
| spl0_36
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f1091,f297,f1096,f1093]) ).
thf(f1091,plain,
( ( $true
= ( sK3 @ sK4 @ sK28 ) )
| ( $true
= ( sK2 @ sK4 @ sK28 ) )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f1079]) ).
thf(f408,plain,
( spl0_19
| spl0_20
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f401,f300,f406,f403]) ).
thf(f401,plain,
( ( $true
= ( sK2 @ sK13 @ sK12 ) )
| ( $true
= ( sK3 @ sK13 @ sK12 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f396]) ).
thf(f396,plain,
( ( $true
= ( ( sK2 @ sK13 @ sK12 )
| ( sK3 @ sK13 @ sK12 ) ) )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f395]) ).
thf(f395,plain,
( ( $true
= ( $true
& ( ( sK2 @ sK13 @ sK12 )
| ( sK3 @ sK13 @ sK12 ) ) ) )
| ~ spl0_14 ),
inference(backward_demodulation,[],[f317,f394]) ).
thf(f394,plain,
( ( $true
= ( sK11 @ sK13 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f317]) ).
thf(f317,plain,
( ( $true
= ( ( sK11 @ sK13 )
& ( ( sK2 @ sK13 @ sK12 )
| ( sK3 @ sK13 @ sK12 ) ) ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f315]) ).
thf(f315,plain,
( ( ( ( ( sK11 @ sK13 )
& ( ( sK2 @ sK13 @ sK12 )
| ( sK3 @ sK13 @ sK12 ) ) )
=> ( sK11 @ sK12 ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f314]) ).
thf(f314,plain,
( ( ( ^ [Y0: a] :
( ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
=> ( sK11 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f313]) ).
thf(f313,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
=> ( sK11 @ sK12 ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f309]) ).
thf(f309,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK11 @ Y0 ) ) )
@ sK12 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f301]) ).
thf(f350,plain,
( spl0_15
| spl0_16
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f343,f300,f348,f345]) ).
thf(f343,plain,
( ( $true
= ( sK3 @ sK14 @ sK12 ) )
| ( ( sK2 @ sK14 @ sK12 )
= $true )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f342]) ).
thf(f342,plain,
( ( $true
= ( ( sK2 @ sK14 @ sK12 )
| ( sK3 @ sK14 @ sK12 ) ) )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f341]) ).
thf(f341,plain,
( ( $true
= ( $true
& ( ( sK2 @ sK14 @ sK12 )
| ( sK3 @ sK14 @ sK12 ) ) ) )
| ~ spl0_14 ),
inference(backward_demodulation,[],[f328,f340]) ).
thf(f340,plain,
( ( ( sK11 @ sK14 )
= $true )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f328]) ).
thf(f328,plain,
( ( $true
= ( ( sK11 @ sK14 )
& ( ( sK2 @ sK14 @ sK12 )
| ( sK3 @ sK14 @ sK12 ) ) ) )
| ~ spl0_14 ),
inference(not_proxy_clausification,[],[f325]) ).
thf(f325,plain,
( ( $false
= ( ~ ( ( sK11 @ sK14 )
& ( ( sK2 @ sK14 @ sK12 )
| ( sK3 @ sK14 @ sK12 ) ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f324]) ).
thf(f324,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
@ sK14 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f320]) ).
thf(f320,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f319]) ).
thf(f319,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK11 @ Y0 )
& ( ( sK2 @ Y0 @ sK12 )
| ( sK3 @ Y0 @ sK12 ) ) )
=> $false ) )
= $false )
| ~ spl0_14 ),
inference(backward_demodulation,[],[f313,f316]) ).
thf(f316,plain,
( ( $false
= ( sK11 @ sK12 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f315]) ).
thf(f302,plain,
( spl0_13
| spl0_14
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f293,f25,f300,f297]) ).
thf(f293,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK11 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK11 @ Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f290]) ).
thf(f290,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK11 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK11 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f289]) ).
thf(f289,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK11 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK11 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f288]) ).
thf(f288,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK11 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK11 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f250,f287]) ).
thf(f287,plain,
( ( $false
= ( sK11 @ sK5 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f286]) ).
thf(f286,plain,
( ( ( $true
=> ( sK11 @ sK5 ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f275,f285]) ).
thf(f250,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK5 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f249]) ).
thf(f249,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f245]) ).
thf(f245,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
!= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f18,f26]) ).
thf(f18,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
!= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK4 @ Y2 )
| ( sK3 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ sK4 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ sK4 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK4 @ Y2 )
| ( sK3 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ sK4 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ sK4 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK4 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f13]) ).
thf(f13,plain,
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK3 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( Y0 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( Y0 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y9 @ Y8 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) )
= ( ^ [X8: a,X9: a] :
! [X10: a > $o] :
( ( ! [X11: a] :
( ( ! [X12: a > $o] :
( ( ! [X13: a] :
( ( X1 @ X8 @ X13 )
=> ( X12 @ X13 ) )
& ! [X14: a,X15: a] :
( ( ( X12 @ X14 )
& ( X1 @ X14 @ X15 ) )
=> ( X12 @ X15 ) ) )
=> ( X12 @ X11 ) )
| ! [X16: a > $o] :
( ( ! [X17: a] :
( ( X0 @ X8 @ X17 )
=> ( X16 @ X17 ) )
& ! [X18: a,X19: a] :
( ( ( X0 @ X18 @ X19 )
& ( X16 @ X18 ) )
=> ( X16 @ X19 ) ) )
=> ( X16 @ X11 ) ) )
=> ( X10 @ X11 ) )
& ! [X20: a,X21: a] :
( ( ( X10 @ X21 )
& ( ! [X22: a > $o] :
( ( ! [X23: a,X24: a] :
( ( ( X22 @ X23 )
& ( X0 @ X23 @ X24 ) )
=> ( X22 @ X24 ) )
& ! [X25: a] :
( ( X0 @ X21 @ X25 )
=> ( X22 @ X25 ) ) )
=> ( X22 @ X20 ) )
| ! [X26: a > $o] :
( ( ! [X27: a,X28: a] :
( ( ( X26 @ X27 )
& ( X1 @ X27 @ X28 ) )
=> ( X26 @ X28 ) )
& ! [X29: a] :
( ( X1 @ X21 @ X29 )
=> ( X26 @ X29 ) ) )
=> ( X26 @ X20 ) ) ) )
=> ( X10 @ X20 ) ) )
=> ( X10 @ X9 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > $o,X0: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X5: a] :
( ( ! [X8: a > $o] :
( ( ! [X9: a] :
( ( X0 @ X2 @ X9 )
=> ( X8 @ X9 ) )
& ! [X6: a,X7: a] :
( ( ( X8 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X8 @ X7 ) ) )
=> ( X8 @ X5 ) )
| ! [X8: a > $o] :
( ( ! [X9: a] :
( ( X1 @ X2 @ X9 )
=> ( X8 @ X9 ) )
& ! [X6: a,X7: a] :
( ( ( X1 @ X6 @ X7 )
& ( X8 @ X6 ) )
=> ( X8 @ X7 ) ) )
=> ( X8 @ X5 ) ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ! [X8: a > $o] :
( ( ! [X10: a,X11: a] :
( ( ( X8 @ X10 )
& ( X1 @ X10 @ X11 ) )
=> ( X8 @ X11 ) )
& ! [X5: a] :
( ( X1 @ X6 @ X5 )
=> ( X8 @ X5 ) ) )
=> ( X8 @ X7 ) )
| ! [X8: a > $o] :
( ( ! [X10: a,X11: a] :
( ( ( X8 @ X10 )
& ( X0 @ X10 @ X11 ) )
=> ( X8 @ X11 ) )
& ! [X5: a] :
( ( X0 @ X6 @ X5 )
=> ( X8 @ X5 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: a > a > $o,X0: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( ! [X5: a] :
( ( ! [X8: a > $o] :
( ( ! [X9: a] :
( ( X0 @ X2 @ X9 )
=> ( X8 @ X9 ) )
& ! [X6: a,X7: a] :
( ( ( X8 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X8 @ X7 ) ) )
=> ( X8 @ X5 ) )
| ! [X8: a > $o] :
( ( ! [X9: a] :
( ( X1 @ X2 @ X9 )
=> ( X8 @ X9 ) )
& ! [X6: a,X7: a] :
( ( ( X1 @ X6 @ X7 )
& ( X8 @ X6 ) )
=> ( X8 @ X7 ) ) )
=> ( X8 @ X5 ) ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ! [X8: a > $o] :
( ( ! [X10: a,X11: a] :
( ( ( X8 @ X10 )
& ( X1 @ X10 @ X11 ) )
=> ( X8 @ X11 ) )
& ! [X5: a] :
( ( X1 @ X6 @ X5 )
=> ( X8 @ X5 ) ) )
=> ( X8 @ X7 ) )
| ! [X8: a > $o] :
( ( ! [X10: a,X11: a] :
( ( ( X8 @ X10 )
& ( X0 @ X10 @ X11 ) )
=> ( X8 @ X11 ) )
& ! [X5: a] :
( ( X0 @ X6 @ X5 )
=> ( X8 @ X5 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM251A_pme) ).
thf(f260,plain,
( spl0_11
| spl0_12
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f251,f183,f126,f258,f255]) ).
thf(f251,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_5
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f246]) ).
thf(f246,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_5
| ~ spl0_7 ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f216,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f215]) ).
thf(f215,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f201,f154]) ).
thf(f154,plain,
( ( ( sK6 @ sK8 )
= $false )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f153]) ).
thf(f153,plain,
( ( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
& ( sK6 @ sK7 ) )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f152]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK7 ) )
=> ( sK6 @ Y0 ) )
@ sK8 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f151]) ).
thf(f151,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK7 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK7 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f147]) ).
thf(f147,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK7 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f127]) ).
thf(f201,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK8 ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f200]) ).
thf(f200,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[],[f184]) ).
thf(f188,plain,
( spl0_7
| spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f181,f126,f186,f183]) ).
thf(f181,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f172]) ).
thf(f172,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f171]) ).
thf(f171,plain,
( ( $true
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
& $true ) )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f155,f169]) ).
thf(f169,plain,
( ( $true
= ( sK6 @ sK7 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f155]) ).
thf(f155,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
& ( sK6 @ sK7 ) )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f153]) ).
thf(f131,plain,
( spl0_5
| spl0_6
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f122,f29,f22,f129,f126]) ).
thf(f29,plain,
( spl0_3
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f122,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f103]) ).
thf(f103,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f56]) ).
thf(f56,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f55]) ).
thf(f55,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f49,f42]) ).
thf(f42,plain,
( ( $false
= ( sK6 @ sK5 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f41,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK4 @ Y0 )
| ( sK3 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK5 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f40]) ).
thf(f40,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f23]) ).
thf(f49,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK5 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f48]) ).
thf(f48,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f30]) ).
thf(f30,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f34,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f19,f32,f29]) ).
thf(f19,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f18]) ).
thf(f27,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f20,f25,f22]) ).
thf(f20,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK4 @ Y1 )
| ( sK3 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $false )
| ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK4 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SEV150^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.31 % Computer : n012.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun May 19 18:23:22 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.31 This is a TH0_THM_EQU_NAR problem
% 0.16/0.31 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.32 % (795)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 (3000ds/27Mi)
% 0.16/0.32 % (796)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.16/0.32 % (797)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 (3000ds/2Mi)
% 0.16/0.32 % (796)Instruction limit reached!
% 0.16/0.32 % (796)------------------------------
% 0.16/0.32 % (796)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32 % (796)Termination reason: Unknown
% 0.16/0.32 % (796)Termination phase: Preprocessing 3
% 0.16/0.32 % (797)Instruction limit reached!
% 0.16/0.32 % (797)------------------------------
% 0.16/0.32 % (797)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32
% 0.16/0.32 % (797)Termination reason: Unknown
% 0.16/0.32 % (797)Termination phase: Property scanning
% 0.16/0.32
% 0.16/0.32 % (797)Memory used [KB]: 1023
% 0.16/0.32 % (797)Time elapsed: 0.002 s
% 0.16/0.32 % (797)Instructions burned: 4 (million)
% 0.16/0.32 % (797)------------------------------
% 0.16/0.32 % (797)------------------------------
% 0.16/0.32 % (796)Memory used [KB]: 1023
% 0.16/0.32 % (796)Time elapsed: 0.002 s
% 0.16/0.32 % (796)Instructions burned: 3 (million)
% 0.16/0.32 % (796)------------------------------
% 0.16/0.32 % (796)------------------------------
% 0.16/0.32 % (793)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.16/0.32 % (794)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 (3000ds/4Mi)
% 0.16/0.32 % (800)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.16/0.32 % (800)Instruction limit reached!
% 0.16/0.32 % (800)------------------------------
% 0.16/0.32 % (800)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32 % (800)Termination reason: Unknown
% 0.16/0.32 % (800)Termination phase: shuffling
% 0.16/0.32
% 0.16/0.32 % (800)Memory used [KB]: 1023
% 0.16/0.32 % (800)Time elapsed: 0.002 s
% 0.16/0.32 % (800)Instructions burned: 3 (million)
% 0.16/0.32 % (800)------------------------------
% 0.16/0.32 % (800)------------------------------
% 0.16/0.32 % (794)Instruction limit reached!
% 0.16/0.32 % (794)------------------------------
% 0.16/0.32 % (794)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32 % (794)Termination reason: Unknown
% 0.16/0.32 % (794)Termination phase: Property scanning
% 0.16/0.32
% 0.16/0.32 % (794)Memory used [KB]: 1023
% 0.16/0.32 % (794)Time elapsed: 0.003 s
% 0.16/0.32 % (794)Instructions burned: 5 (million)
% 0.16/0.32 % (794)------------------------------
% 0.16/0.32 % (794)------------------------------
% 0.16/0.32 % (799)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.16/0.33 % (798)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 (3000ds/275Mi)
% 0.16/0.33 % (795)Instruction limit reached!
% 0.16/0.33 % (795)------------------------------
% 0.16/0.33 % (795)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (795)Termination reason: Unknown
% 0.16/0.33 % (795)Termination phase: Saturation
% 0.16/0.33
% 0.16/0.33 % (795)Memory used [KB]: 5628
% 0.16/0.33 % (795)Time elapsed: 0.009 s
% 0.16/0.33 % (795)Instructions burned: 28 (million)
% 0.16/0.33 % (795)------------------------------
% 0.16/0.33 % (795)------------------------------
% 0.16/0.33 % (801)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)
% 0.16/0.33 % (802)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)
% 0.16/0.33 % (799)Instruction limit reached!
% 0.16/0.33 % (799)------------------------------
% 0.16/0.33 % (799)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (799)Termination reason: Unknown
% 0.16/0.33 % (799)Termination phase: Saturation
% 0.16/0.33
% 0.16/0.33 % (799)Memory used [KB]: 5500
% 0.16/0.33 % (799)Time elapsed: 0.009 s
% 0.16/0.33 % (799)Instructions burned: 18 (million)
% 0.16/0.33 % (799)------------------------------
% 0.16/0.33 % (799)------------------------------
% 0.16/0.33 % (803)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)
% 0.16/0.33 % (804)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)
% 0.16/0.33 % (803)Instruction limit reached!
% 0.16/0.33 % (803)------------------------------
% 0.16/0.33 % (803)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (803)Termination reason: Unknown
% 0.16/0.33 % (803)Termination phase: Preprocessing 3
% 0.16/0.33
% 0.16/0.33 % (803)Memory used [KB]: 1023
% 0.16/0.33 % (803)Time elapsed: 0.002 s
% 0.16/0.33 % (803)Instructions burned: 3 (million)
% 0.16/0.33 % (803)------------------------------
% 0.16/0.33 % (803)------------------------------
% 0.16/0.33 % (802)Instruction limit reached!
% 0.16/0.33 % (802)------------------------------
% 0.16/0.33 % (802)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (802)Termination reason: Unknown
% 0.16/0.33 % (802)Termination phase: Saturation
% 0.16/0.33
% 0.16/0.33 % (802)Memory used [KB]: 5884
% 0.16/0.33 % (802)Time elapsed: 0.006 s
% 0.16/0.33 % (802)Instructions burned: 15 (million)
% 0.16/0.33 % (802)------------------------------
% 0.16/0.33 % (802)------------------------------
% 0.16/0.34 % (805)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.34 % (805)Instruction limit reached!
% 0.16/0.34 % (805)------------------------------
% 0.16/0.34 % (805)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (805)Termination reason: Unknown
% 0.16/0.34 % (805)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (805)Memory used [KB]: 1023
% 0.16/0.34 % (805)Time elapsed: 0.004 s
% 0.16/0.34 % (805)Instructions burned: 8 (million)
% 0.16/0.34 % (805)------------------------------
% 0.16/0.34 % (805)------------------------------
% 0.16/0.34 % (801)Instruction limit reached!
% 0.16/0.34 % (801)------------------------------
% 0.16/0.34 % (801)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (801)Termination reason: Unknown
% 0.16/0.34 % (801)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (801)Memory used [KB]: 5628
% 0.16/0.34 % (801)Time elapsed: 0.012 s
% 0.16/0.34 % (801)Instructions burned: 38 (million)
% 0.16/0.34 % (801)------------------------------
% 0.16/0.34 % (801)------------------------------
% 0.16/0.34 % (808)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)
% 0.16/0.34 % (807)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)
% 0.16/0.34 % (808)Instruction limit reached!
% 0.16/0.34 % (808)------------------------------
% 0.16/0.34 % (808)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (808)Termination reason: Unknown
% 0.16/0.34 % (808)Termination phase: Property scanning
% 0.16/0.34
% 0.16/0.34 % (808)Memory used [KB]: 1023
% 0.16/0.34 % (806)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.16/0.34 % (808)Time elapsed: 0.003 s
% 0.16/0.34 % (808)Instructions burned: 6 (million)
% 0.16/0.34 % (808)------------------------------
% 0.16/0.34 % (808)------------------------------
% 0.16/0.34 % (807)Instruction limit reached!
% 0.16/0.34 % (807)------------------------------
% 0.16/0.34 % (807)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (807)Termination reason: Unknown
% 0.16/0.34 % (807)Termination phase: Preprocessing 1
% 0.16/0.34
% 0.16/0.34 % (807)Memory used [KB]: 1023
% 0.16/0.34 % (807)Time elapsed: 0.002 s
% 0.16/0.34 % (807)Instructions burned: 4 (million)
% 0.16/0.34 % (807)------------------------------
% 0.16/0.34 % (807)------------------------------
% 0.16/0.35 % (809)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)
% 0.16/0.35 % (810)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)
% 0.16/0.35 % (809)Instruction limit reached!
% 0.16/0.35 % (809)------------------------------
% 0.16/0.35 % (809)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (809)Termination reason: Unknown
% 0.16/0.35 % (809)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (809)Memory used [KB]: 5500
% 0.16/0.35 % (809)Time elapsed: 0.004 s
% 0.16/0.35 % (809)Instructions burned: 9 (million)
% 0.16/0.35 % (809)------------------------------
% 0.16/0.35 % (809)------------------------------
% 0.16/0.35 % (810)Instruction limit reached!
% 0.16/0.35 % (810)------------------------------
% 0.16/0.35 % (810)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (810)Termination reason: Unknown
% 0.16/0.35 % (810)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (810)Memory used [KB]: 5500
% 0.16/0.35 % (810)Time elapsed: 0.003 s
% 0.16/0.35 % (810)Instructions burned: 6 (million)
% 0.16/0.35 % (810)------------------------------
% 0.16/0.35 % (810)------------------------------
% 0.16/0.35 % (811)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.16/0.35 % (806)Instruction limit reached!
% 0.16/0.35 % (806)------------------------------
% 0.16/0.35 % (806)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (806)Termination reason: Unknown
% 0.16/0.35 % (806)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (806)Memory used [KB]: 5884
% 0.16/0.35 % (806)Time elapsed: 0.010 s
% 0.16/0.35 % (806)Instructions burned: 17 (million)
% 0.16/0.35 % (806)------------------------------
% 0.16/0.35 % (806)------------------------------
% 0.16/0.35 % (811)Instruction limit reached!
% 0.16/0.35 % (811)------------------------------
% 0.16/0.35 % (811)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (811)Termination reason: Unknown
% 0.16/0.35 % (811)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (811)Memory used [KB]: 5500
% 0.16/0.35 % (811)Time elapsed: 0.003 s
% 0.16/0.35 % (811)Instructions burned: 6 (million)
% 0.16/0.35 % (811)------------------------------
% 0.16/0.35 % (811)------------------------------
% 0.16/0.35 % (812)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)
% 0.16/0.36 % (813)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.16/0.36 % (814)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.16/0.36 % (814)Instruction limit reached!
% 0.16/0.36 % (814)------------------------------
% 0.16/0.36 % (814)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (814)Termination reason: Unknown
% 0.16/0.36 % (814)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (814)Memory used [KB]: 5500
% 0.16/0.36 % (814)Time elapsed: 0.003 s
% 0.16/0.36 % (814)Instructions burned: 6 (million)
% 0.16/0.36 % (814)------------------------------
% 0.16/0.36 % (814)------------------------------
% 0.16/0.36 % (812)Instruction limit reached!
% 0.16/0.36 % (812)------------------------------
% 0.16/0.36 % (812)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (812)Termination reason: Unknown
% 0.16/0.36 % (812)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (812)Memory used [KB]: 5500
% 0.16/0.36 % (812)Time elapsed: 0.007 s
% 0.16/0.36 % (812)Instructions burned: 19 (million)
% 0.16/0.36 % (812)------------------------------
% 0.16/0.36 % (812)------------------------------
% 0.16/0.36 % (816)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)
% 0.16/0.36 % (815)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)
% 0.16/0.37 % (817)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.16/0.37 % (817)Instruction limit reached!
% 0.16/0.37 % (817)------------------------------
% 0.16/0.37 % (817)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (816)Instruction limit reached!
% 0.16/0.37 % (816)------------------------------
% 0.16/0.37 % (816)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (817)Termination reason: Unknown
% 0.16/0.37 % (817)Termination phase: Saturation
% 0.16/0.37
% 0.16/0.37 % (817)Memory used [KB]: 5500
% 0.16/0.37 % (817)Time elapsed: 0.003 s
% 0.16/0.37 % (817)Instructions burned: 5 (million)
% 0.16/0.37 % (817)------------------------------
% 0.16/0.37 % (817)------------------------------
% 0.16/0.37 % (816)Termination reason: Unknown
% 0.16/0.37 % (816)Termination phase: Saturation
% 0.16/0.37
% 0.16/0.37 % (816)Memory used [KB]: 5628
% 0.16/0.37 % (816)Time elapsed: 0.009 s
% 0.16/0.37 % (816)Instructions burned: 22 (million)
% 0.16/0.37 % (816)------------------------------
% 0.16/0.37 % (816)------------------------------
% 0.16/0.37 % (818)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)
% 0.17/0.37 % (818)Instruction limit reached!
% 0.17/0.37 % (818)------------------------------
% 0.17/0.37 % (818)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (818)Termination reason: Unknown
% 0.17/0.37 % (818)Termination phase: Saturation
% 0.17/0.37
% 0.17/0.37 % (818)Memory used [KB]: 5500
% 0.17/0.37 % (818)Time elapsed: 0.003 s
% 0.17/0.37 % (818)Instructions burned: 6 (million)
% 0.17/0.37 % (818)------------------------------
% 0.17/0.37 % (818)------------------------------
% 0.17/0.38 % (819)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.17/0.38 % (820)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)
% 0.17/0.38 % (821)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)
% 0.17/0.38 % (793)Instruction limit reached!
% 0.17/0.38 % (793)------------------------------
% 0.17/0.38 % (793)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.38 % (793)Termination reason: Unknown
% 0.17/0.38 % (793)Termination phase: Saturation
% 0.17/0.38
% 0.17/0.38 % (793)Memory used [KB]: 6396
% 0.17/0.38 % (793)Time elapsed: 0.064 s
% 0.17/0.38 % (793)Instructions burned: 183 (million)
% 0.17/0.38 % (793)------------------------------
% 0.17/0.38 % (793)------------------------------
% 0.17/0.39 % (821)Instruction limit reached!
% 0.17/0.39 % (821)------------------------------
% 0.17/0.39 % (821)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.39 % (821)Termination reason: Unknown
% 0.17/0.39 % (821)Termination phase: Saturation
% 0.17/0.39
% 0.17/0.39 % (821)Memory used [KB]: 5500
% 0.17/0.39 % (821)Time elapsed: 0.007 s
% 0.17/0.39 % (821)Instructions burned: 19 (million)
% 0.17/0.39 % (821)------------------------------
% 0.17/0.39 % (821)------------------------------
% 0.17/0.39 % (822)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.17/0.40 % (823)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.17/0.40 % (823)Instruction limit reached!
% 0.17/0.40 % (823)------------------------------
% 0.17/0.40 % (823)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (823)Termination reason: Unknown
% 0.17/0.40 % (823)Termination phase: Saturation
% 0.17/0.40
% 0.17/0.40 % (823)Memory used [KB]: 5884
% 0.17/0.40 % (823)Time elapsed: 0.007 s
% 0.17/0.40 % (823)Instructions burned: 18 (million)
% 0.17/0.40 % (823)------------------------------
% 0.17/0.40 % (823)------------------------------
% 0.17/0.41 % (824)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.41 % (824)Instruction limit reached!
% 0.17/0.41 % (824)------------------------------
% 0.17/0.41 % (824)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (824)Termination reason: Unknown
% 0.17/0.41 % (824)Termination phase: Preprocessing 2
% 0.17/0.41
% 0.17/0.41 % (824)Memory used [KB]: 1023
% 0.17/0.41 % (824)Time elapsed: 0.003 s
% 0.17/0.41 % (824)Instructions burned: 4 (million)
% 0.17/0.41 % (824)------------------------------
% 0.17/0.41 % (824)------------------------------
% 0.17/0.42 % (825)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.17/0.43 % (825)Refutation not found, incomplete strategy
% 0.17/0.43 % (825)------------------------------
% 0.17/0.43 % (825)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.43 % (825)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.43
% 0.17/0.43
% 0.17/0.43 % (825)Memory used [KB]: 5500
% 0.17/0.43 % (825)Time elapsed: 0.010 s
% 0.17/0.43 % (825)Instructions burned: 14 (million)
% 0.17/0.43 % (825)------------------------------
% 0.17/0.43 % (825)------------------------------
% 0.17/0.44 % (828)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)
% 0.17/0.46 % (798)Instruction limit reached!
% 0.17/0.46 % (798)------------------------------
% 0.17/0.46 % (798)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.46 % (798)Termination reason: Unknown
% 0.17/0.46 % (798)Termination phase: Saturation
% 0.17/0.46
% 0.17/0.46 % (798)Memory used [KB]: 6780
% 0.17/0.46 % (798)Time elapsed: 0.131 s
% 0.17/0.46 % (798)Instructions burned: 276 (million)
% 0.17/0.46 % (798)------------------------------
% 0.17/0.46 % (798)------------------------------
% 0.17/0.47 % (840)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.17/0.48 % (828)Instruction limit reached!
% 0.17/0.48 % (828)------------------------------
% 0.17/0.48 % (828)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.48 % (828)Termination reason: Unknown
% 0.17/0.48 % (828)Termination phase: Saturation
% 0.17/0.48
% 0.17/0.48 % (828)Memory used [KB]: 6012
% 0.17/0.48 % (828)Time elapsed: 0.042 s
% 0.17/0.48 % (828)Instructions burned: 128 (million)
% 0.17/0.48 % (828)------------------------------
% 0.17/0.48 % (828)------------------------------
% 0.17/0.49 % (851)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)
% 0.17/0.49 % (851)Instruction limit reached!
% 0.17/0.49 % (851)------------------------------
% 0.17/0.49 % (851)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.49 % (851)Termination reason: Unknown
% 0.17/0.49 % (851)Termination phase: Property scanning
% 0.17/0.49
% 0.17/0.49 % (851)Memory used [KB]: 1023
% 0.17/0.49 % (851)Time elapsed: 0.002 s
% 0.17/0.49 % (851)Instructions burned: 3 (million)
% 0.17/0.49 % (851)------------------------------
% 0.17/0.49 % (851)------------------------------
% 0.17/0.50 % (840)Instruction limit reached!
% 0.17/0.50 % (840)------------------------------
% 0.17/0.50 % (840)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.50 % (840)Termination reason: Unknown
% 0.17/0.50 % (840)Termination phase: Saturation
% 0.17/0.50
% 0.17/0.50 % (840)Memory used [KB]: 5756
% 0.17/0.50 % (840)Time elapsed: 0.032 s
% 0.17/0.50 % (840)Instructions burned: 100 (million)
% 0.17/0.50 % (840)------------------------------
% 0.17/0.50 % (840)------------------------------
% 0.17/0.50 % (819)Instruction limit reached!
% 0.17/0.50 % (819)------------------------------
% 0.17/0.50 % (819)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.50 % (819)Termination reason: Unknown
% 0.17/0.50 % (819)Termination phase: Saturation
% 0.17/0.50
% 0.17/0.50 % (819)Memory used [KB]: 7036
% 0.17/0.50 % (819)Time elapsed: 0.123 s
% 0.17/0.50 % (819)Instructions burned: 379 (million)
% 0.17/0.50 % (819)------------------------------
% 0.17/0.50 % (819)------------------------------
% 0.17/0.50 % (853)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)
% 0.17/0.50 % (853)Refutation not found, incomplete strategy
% 0.17/0.50 % (853)------------------------------
% 0.17/0.50 % (853)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.50 % (853)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.50
% 0.17/0.50
% 0.17/0.50 % (853)Memory used [KB]: 5500
% 0.17/0.50 % (853)Time elapsed: 0.003 s
% 0.17/0.50 % (853)Instructions burned: 7 (million)
% 0.17/0.50 % (853)------------------------------
% 0.17/0.50 % (853)------------------------------
% 0.17/0.51 % (855)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 (2998ds/86Mi)
% 0.17/0.51 % (856)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 (2998ds/107Mi)
% 0.17/0.51 % (858)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 (2998ds/39Mi)
% 0.17/0.52 % (858)Instruction limit reached!
% 0.17/0.52 % (858)------------------------------
% 0.17/0.52 % (858)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.52 % (858)Termination reason: Unknown
% 0.17/0.52 % (858)Termination phase: Saturation
% 0.17/0.52
% 0.17/0.52 % (858)Memory used [KB]: 5884
% 0.17/0.52 % (858)Time elapsed: 0.013 s
% 0.17/0.52 % (858)Instructions burned: 39 (million)
% 0.17/0.52 % (858)------------------------------
% 0.17/0.52 % (858)------------------------------
% 0.17/0.53 % (855)Instruction limit reached!
% 0.17/0.53 % (855)------------------------------
% 0.17/0.53 % (855)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.53 % (855)Termination reason: Unknown
% 0.17/0.53 % (855)Termination phase: Saturation
% 0.17/0.53
% 0.17/0.53 % (855)Memory used [KB]: 5884
% 0.17/0.53 % (855)Time elapsed: 0.026 s
% 0.17/0.53 % (855)Instructions burned: 86 (million)
% 0.17/0.53 % (855)------------------------------
% 0.17/0.53 % (855)------------------------------
% 0.17/0.53 % (865)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)
% 1.82/0.54 % (856)Instruction limit reached!
% 1.82/0.54 % (856)------------------------------
% 1.82/0.54 % (856)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.82/0.54 % (856)Termination reason: Unknown
% 1.82/0.54 % (856)Termination phase: Saturation
% 1.82/0.54
% 1.82/0.54 % (856)Memory used [KB]: 5884
% 1.82/0.54 % (856)Time elapsed: 0.033 s
% 1.82/0.54 % (856)Instructions burned: 107 (million)
% 1.82/0.54 % (856)------------------------------
% 1.82/0.54 % (856)------------------------------
% 1.82/0.54 % (869)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)
% 1.92/0.55 % (875)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)
% 1.92/0.56 % (869)Instruction limit reached!
% 1.92/0.56 % (869)------------------------------
% 1.92/0.56 % (869)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.92/0.56 % (869)Termination reason: Unknown
% 1.92/0.56 % (869)Termination phase: Saturation
% 1.92/0.56
% 1.92/0.56 % (869)Memory used [KB]: 5756
% 1.92/0.56 % (869)Time elapsed: 0.018 s
% 1.92/0.56 % (869)Instructions burned: 47 (million)
% 1.92/0.56 % (869)------------------------------
% 1.92/0.56 % (869)------------------------------
% 1.92/0.56 % (880)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)
% 1.92/0.58 % (875)Instruction limit reached!
% 1.92/0.58 % (875)------------------------------
% 1.92/0.58 % (875)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.92/0.58 % (875)Termination reason: Unknown
% 1.92/0.58 % (875)Termination phase: Saturation
% 1.92/0.58
% 1.92/0.58 % (875)Memory used [KB]: 1279
% 1.92/0.58 % (875)Time elapsed: 0.034 s
% 1.92/0.58 % (875)Instructions burned: 100 (million)
% 1.92/0.58 % (875)------------------------------
% 1.92/0.58 % (875)------------------------------
% 1.92/0.59 % (891)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 (2997ds/149Mi)
% 1.92/0.59 % (813)Instruction limit reached!
% 1.92/0.59 % (813)------------------------------
% 1.92/0.59 % (813)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.92/0.59 % (813)Termination reason: Unknown
% 1.92/0.59 % (813)Termination phase: Saturation
% 1.92/0.59
% 1.92/0.59 % (813)Memory used [KB]: 8955
% 1.92/0.59 % (813)Time elapsed: 0.235 s
% 1.92/0.59 % (813)Instructions burned: 711 (million)
% 1.92/0.59 % (813)------------------------------
% 1.92/0.59 % (813)------------------------------
% 1.92/0.60 % (896)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 1.92/0.61 % (896)Instruction limit reached!
% 1.92/0.61 % (896)------------------------------
% 1.92/0.61 % (896)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.92/0.61 % (896)Termination reason: Unknown
% 1.92/0.61 % (896)Termination phase: Saturation
% 1.92/0.61
% 1.92/0.61 % (896)Memory used [KB]: 5756
% 1.92/0.61 % (896)Time elapsed: 0.013 s
% 1.92/0.61 % (896)Instructions burned: 40 (million)
% 1.92/0.61 % (896)------------------------------
% 1.92/0.61 % (896)------------------------------
% 2.36/0.62 % (913)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 (2997ds/6Mi)
% 2.36/0.62 % (913)Instruction limit reached!
% 2.36/0.62 % (913)------------------------------
% 2.36/0.62 % (913)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.36/0.62 % (913)Termination reason: Unknown
% 2.36/0.62 % (913)Termination phase: Saturation
% 2.36/0.62
% 2.36/0.62 % (913)Memory used [KB]: 9978
% 2.36/0.62 % (913)Time elapsed: 0.004 s
% 2.36/0.62 % (913)Instructions burned: 7 (million)
% 2.36/0.62 % (913)------------------------------
% 2.36/0.62 % (913)------------------------------
% 2.36/0.63 % (921)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)
% 2.36/0.63 % (891)Instruction limit reached!
% 2.36/0.63 % (891)------------------------------
% 2.36/0.63 % (891)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.36/0.63 % (891)Termination reason: Unknown
% 2.36/0.63 % (891)Termination phase: Saturation
% 2.36/0.63
% 2.36/0.63 % (891)Memory used [KB]: 5756
% 2.36/0.63 % (891)Time elapsed: 0.047 s
% 2.36/0.63 % (891)Instructions burned: 151 (million)
% 2.36/0.63 % (891)------------------------------
% 2.36/0.63 % (891)------------------------------
% 2.36/0.64 % (820)Instruction limit reached!
% 2.36/0.64 % (820)------------------------------
% 2.36/0.64 % (820)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.36/0.64 % (820)Termination reason: Unknown
% 2.36/0.64 % (820)Termination phase: Saturation
% 2.36/0.64
% 2.36/0.64 % (820)Memory used [KB]: 6652
% 2.36/0.64 % (820)Time elapsed: 0.262 s
% 2.36/0.64 % (820)Instructions burned: 780 (million)
% 2.36/0.64 % (820)------------------------------
% 2.36/0.64 % (820)------------------------------
% 2.36/0.64 % (929)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2996ds/47Mi)
% 2.36/0.65 % (934)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)
% 2.36/0.66 % (929)Instruction limit reached!
% 2.36/0.66 % (929)------------------------------
% 2.36/0.66 % (929)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.36/0.66 % (929)Termination reason: Unknown
% 2.36/0.66 % (929)Termination phase: Saturation
% 2.36/0.66
% 2.36/0.66 % (929)Memory used [KB]: 5628
% 2.36/0.66 % (929)Time elapsed: 0.016 s
% 2.36/0.66 % (929)Instructions burned: 48 (million)
% 2.36/0.66 % (929)------------------------------
% 2.36/0.66 % (929)------------------------------
% 2.36/0.66 % (934)Instruction limit reached!
% 2.36/0.66 % (934)------------------------------
% 2.36/0.66 % (934)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.36/0.66 % (934)Termination reason: Unknown
% 2.36/0.66 % (934)Termination phase: Saturation
% 2.36/0.66
% 2.36/0.66 % (934)Memory used [KB]: 1151
% 2.36/0.66 % (934)Time elapsed: 0.014 s
% 2.36/0.66 % (934)Instructions burned: 45 (million)
% 2.36/0.66 % (934)------------------------------
% 2.36/0.66 % (934)------------------------------
% 2.36/0.67 % (951)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 (2996ds/432Mi)
% 2.36/0.67 % (953)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2996ds/62Mi)
% 2.64/0.68 % (815)Instruction limit reached!
% 2.64/0.68 % (815)------------------------------
% 2.64/0.68 % (815)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.68 % (815)Termination reason: Unknown
% 2.64/0.68 % (815)Termination phase: Saturation
% 2.64/0.68
% 2.64/0.68 % (815)Memory used [KB]: 10106
% 2.64/0.68 % (815)Time elapsed: 0.315 s
% 2.64/0.68 % (815)Instructions burned: 903 (million)
% 2.64/0.68 % (815)------------------------------
% 2.64/0.68 % (815)------------------------------
% 2.64/0.69 % (822)Instruction limit reached!
% 2.64/0.69 % (822)------------------------------
% 2.64/0.69 % (822)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.69 % (822)Termination reason: Unknown
% 2.64/0.69 % (822)Termination phase: Saturation
% 2.64/0.69
% 2.64/0.69 % (953)Instruction limit reached!
% 2.64/0.69 % (953)------------------------------
% 2.64/0.69 % (953)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.69 % (953)Termination reason: Unknown
% 2.64/0.69 % (953)Termination phase: Saturation
% 2.64/0.69
% 2.64/0.69 % (953)Memory used [KB]: 5884
% 2.64/0.69 % (953)Time elapsed: 0.021 s
% 2.64/0.69 % (953)Instructions burned: 63 (million)
% 2.64/0.69 % (953)------------------------------
% 2.64/0.69 % (953)------------------------------
% 2.64/0.69 % (822)Memory used [KB]: 9978
% 2.64/0.69 % (822)Time elapsed: 0.295 s
% 2.64/0.69 % (822)Instructions burned: 879 (million)
% 2.64/0.69 % (822)------------------------------
% 2.64/0.69 % (822)------------------------------
% 2.64/0.69 % (979)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 (2996ds/31Mi)
% 2.64/0.70 % (980)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2996ds/96Mi)
% 2.64/0.70 % (981)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 (2996ds/453Mi)
% 2.64/0.70 % (979)Instruction limit reached!
% 2.64/0.70 % (979)------------------------------
% 2.64/0.70 % (979)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.70 % (979)Termination reason: Unknown
% 2.64/0.70 % (979)Termination phase: Saturation
% 2.64/0.70
% 2.64/0.70 % (979)Memory used [KB]: 5628
% 2.64/0.70 % (979)Time elapsed: 0.011 s
% 2.64/0.70 % (979)Instructions burned: 33 (million)
% 2.64/0.70 % (979)------------------------------
% 2.64/0.70 % (979)------------------------------
% 2.64/0.71 % (989)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 (2996ds/71Mi)
% 2.64/0.71 % (865)Instruction limit reached!
% 2.64/0.71 % (865)------------------------------
% 2.64/0.71 % (865)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.71 % (865)Termination reason: Unknown
% 2.64/0.71 % (865)Termination phase: Saturation
% 2.64/0.71
% 2.64/0.71 % (865)Memory used [KB]: 6652
% 2.64/0.71 % (865)Time elapsed: 0.175 s
% 2.64/0.71 % (865)Instructions burned: 449 (million)
% 2.64/0.71 % (865)------------------------------
% 2.64/0.71 % (865)------------------------------
% 2.64/0.72 % (996)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on theBenchmark for (2996ds/83Mi)
% 2.64/0.72 % (980)Instruction limit reached!
% 2.64/0.72 % (980)------------------------------
% 2.64/0.72 % (980)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.72 % (980)Termination reason: Unknown
% 2.64/0.72 % (980)Termination phase: Saturation
% 2.64/0.72
% 2.64/0.72 % (980)Memory used [KB]: 6012
% 2.64/0.72 % (980)Time elapsed: 0.030 s
% 2.64/0.72 % (980)Instructions burned: 96 (million)
% 2.64/0.72 % (980)------------------------------
% 2.64/0.72 % (980)------------------------------
% 2.64/0.73 % (989)Instruction limit reached!
% 2.64/0.73 % (989)------------------------------
% 2.64/0.73 % (989)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.73 % (989)Termination reason: Unknown
% 2.64/0.73 % (989)Termination phase: Saturation
% 2.64/0.73
% 2.64/0.73 % (989)Memory used [KB]: 5628
% 2.64/0.73 % (989)Time elapsed: 0.027 s
% 2.64/0.73 % (989)Instructions burned: 72 (million)
% 2.64/0.73 % (989)------------------------------
% 2.64/0.73 % (989)------------------------------
% 2.64/0.73 % (880)Instruction limit reached!
% 2.64/0.73 % (880)------------------------------
% 2.64/0.73 % (880)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.73 % (880)Termination reason: Unknown
% 2.64/0.73 % (880)Termination phase: Saturation
% 2.64/0.73
% 2.64/0.73 % (880)Memory used [KB]: 6268
% 2.64/0.73 % (880)Time elapsed: 0.169 s
% 2.64/0.73 % (880)Instructions burned: 509 (million)
% 2.64/0.73 % (880)------------------------------
% 2.64/0.73 % (880)------------------------------
% 2.64/0.73 % (1003)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2995ds/11Mi)
% 2.64/0.74 % (1003)Instruction limit reached!
% 2.64/0.74 % (1003)------------------------------
% 2.64/0.74 % (1003)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.74 % (1003)Termination reason: Unknown
% 2.64/0.74 % (1003)Termination phase: Saturation
% 2.64/0.74
% 2.64/0.74 % (1003)Memory used [KB]: 5500
% 2.64/0.74 % (1003)Time elapsed: 0.005 s
% 2.64/0.74 % (1003)Instructions burned: 13 (million)
% 2.64/0.74 % (1003)------------------------------
% 2.64/0.74 % (1003)------------------------------
% 2.64/0.74 % (804)Instruction limit reached!
% 2.64/0.74 % (804)------------------------------
% 2.64/0.74 % (804)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.74 % (804)Termination reason: Unknown
% 2.64/0.74 % (804)Termination phase: Saturation
% 2.64/0.74
% 2.64/0.74 % (804)Memory used [KB]: 8443
% 2.64/0.74 % (804)Time elapsed: 0.398 s
% 2.64/0.74 % (804)Instructions burned: 1042 (million)
% 2.64/0.74 % (804)------------------------------
% 2.64/0.74 % (804)------------------------------
% 2.64/0.74 % (1007)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on theBenchmark for (2995ds/41Mi)
% 2.64/0.74 % (1008)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2995ds/6Mi)
% 2.64/0.74 % (996)Instruction limit reached!
% 2.64/0.74 % (996)------------------------------
% 2.64/0.74 % (996)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.74 % (996)Termination reason: Unknown
% 2.64/0.74 % (996)Termination phase: Saturation
% 2.64/0.74
% 2.64/0.74 % (996)Memory used [KB]: 5884
% 2.64/0.74 % (996)Time elapsed: 0.028 s
% 2.64/0.74 % (996)Instructions burned: 84 (million)
% 2.64/0.74 % (996)------------------------------
% 2.64/0.74 % (996)------------------------------
% 2.64/0.74 % (1008)Instruction limit reached!
% 2.64/0.74 % (1008)------------------------------
% 2.64/0.74 % (1008)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.74 % (1008)Termination reason: Unknown
% 2.64/0.74 % (1008)Termination phase: Saturation
% 2.64/0.74
% 2.64/0.74 % (1008)Memory used [KB]: 5500
% 2.64/0.74 % (1008)Time elapsed: 0.003 s
% 2.64/0.74 % (1008)Instructions burned: 6 (million)
% 2.64/0.74 % (1008)------------------------------
% 2.64/0.74 % (1008)------------------------------
% 2.64/0.74 % (1007)Refutation not found, incomplete strategy
% 2.64/0.74 % (1007)------------------------------
% 2.64/0.74 % (1007)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.64/0.74 % (1007)Termination reason: Refutation not found, incomplete strategy
% 2.64/0.74
% 2.64/0.74
% 2.64/0.74 % (1007)Memory used [KB]: 5500
% 2.64/0.74 % (1007)Time elapsed: 0.005 s
% 2.64/0.74 % (1007)Instructions burned: 13 (million)
% 2.64/0.74 % (1007)------------------------------
% 2.64/0.74 % (1007)------------------------------
% 3.30/0.75 % (1014)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on theBenchmark for (2995ds/150Mi)
% 3.30/0.75 % (1015)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on theBenchmark for (2995ds/343Mi)
% 3.30/0.75 % (1018)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on theBenchmark for (2995ds/109Mi)
% 3.30/0.75 % (1020)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on theBenchmark for (2995ds/253Mi)
% 3.30/0.75 % (1014)Refutation not found, incomplete strategy
% 3.30/0.75 % (1014)------------------------------
% 3.30/0.75 % (1014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.30/0.75 % (1014)Termination reason: Refutation not found, incomplete strategy
% 3.30/0.75
% 3.30/0.75
% 3.30/0.75 % (1014)Memory used [KB]: 5628
% 3.30/0.75 % (1014)Time elapsed: 0.006 s
% 3.30/0.75 % (1014)Instructions burned: 16 (million)
% 3.30/0.75 % (1014)------------------------------
% 3.30/0.75 % (1014)------------------------------
% 3.30/0.75 % (1022)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2995ds/140Mi)
% 3.30/0.76 % (1022)Refutation not found, incomplete strategy
% 3.30/0.76 % (1022)------------------------------
% 3.30/0.76 % (1022)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.30/0.76 % (1022)Termination reason: Refutation not found, incomplete strategy
% 3.30/0.76
% 3.30/0.76
% 3.30/0.76 % (1022)Memory used [KB]: 5500
% 3.30/0.76 % (1022)Time elapsed: 0.003 s
% 3.30/0.76 % (1022)Instructions burned: 6 (million)
% 3.30/0.76 % (1022)------------------------------
% 3.30/0.76 % (1022)------------------------------
% 3.30/0.76 % (1026)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on theBenchmark for (2995ds/614Mi)
% 3.30/0.76 % (1029)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on theBenchmark for (2995ds/202Mi)
% 3.35/0.78 % (1018)Instruction limit reached!
% 3.35/0.78 % (1018)------------------------------
% 3.35/0.78 % (1018)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.78 % (1018)Termination reason: Unknown
% 3.35/0.78 % (1018)Termination phase: Saturation
% 3.35/0.78
% 3.35/0.78 % (1018)Memory used [KB]: 6012
% 3.35/0.78 % (1018)Time elapsed: 0.034 s
% 3.35/0.78 % (1018)Instructions burned: 109 (million)
% 3.35/0.78 % (1018)------------------------------
% 3.35/0.78 % (1018)------------------------------
% 3.35/0.79 % (1044)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on theBenchmark for (2995ds/339Mi)
% 3.35/0.79 % (951)Instruction limit reached!
% 3.35/0.79 % (951)------------------------------
% 3.35/0.79 % (951)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.79 % (951)Termination reason: Unknown
% 3.35/0.79 % (951)Termination phase: Saturation
% 3.35/0.79
% 3.35/0.79 % (951)Memory used [KB]: 3709
% 3.35/0.79 % (951)Time elapsed: 0.127 s
% 3.35/0.79 % (951)Instructions burned: 435 (million)
% 3.35/0.79 % (951)------------------------------
% 3.35/0.79 % (951)------------------------------
% 3.35/0.79 % (1044)Refutation not found, incomplete strategy
% 3.35/0.79 % (1044)------------------------------
% 3.35/0.79 % (1044)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.79 % (1044)Termination reason: Refutation not found, incomplete strategy
% 3.35/0.79
% 3.35/0.79
% 3.35/0.79 % (1044)Memory used [KB]: 5500
% 3.35/0.79 % (1044)Time elapsed: 0.003 s
% 3.35/0.79 % (1044)Instructions burned: 7 (million)
% 3.35/0.79 % (1044)------------------------------
% 3.35/0.79 % (1044)------------------------------
% 3.35/0.80 % (1045)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=283:si=on:rtra=on_0 on theBenchmark for (2995ds/283Mi)
% 3.35/0.80 % (1046)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on theBenchmark for (2995ds/134Mi)
% 3.54/0.83 % (1029)Instruction limit reached!
% 3.54/0.83 % (1029)------------------------------
% 3.54/0.83 % (1029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.54/0.83 % (1029)Termination reason: Unknown
% 3.54/0.83 % (1029)Termination phase: Saturation
% 3.54/0.83
% 3.54/0.83 % (1029)Memory used [KB]: 6524
% 3.54/0.83 % (1029)Time elapsed: 0.063 s
% 3.54/0.83 % (1029)Instructions burned: 203 (million)
% 3.54/0.83 % (1029)------------------------------
% 3.54/0.83 % (1029)------------------------------
% 3.54/0.83 % (1020)Instruction limit reached!
% 3.54/0.83 % (1020)------------------------------
% 3.54/0.83 % (1020)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.54/0.83 % (1020)Termination reason: Unknown
% 3.54/0.83 % (1020)Termination phase: Saturation
% 3.54/0.83
% 3.54/0.83 % (1020)Memory used [KB]: 6652
% 3.54/0.83 % (1020)Time elapsed: 0.077 s
% 3.54/0.83 % (1020)Instructions burned: 254 (million)
% 3.54/0.83 % (1020)------------------------------
% 3.54/0.83 % (1020)------------------------------
% 3.54/0.83 % (1057)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on theBenchmark for (2995ds/298Mi)
% 3.54/0.83 % (1058)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on theBenchmark for (2995ds/192Mi)
% 3.54/0.85 % (981)Instruction limit reached!
% 3.54/0.85 % (981)------------------------------
% 3.54/0.85 % (981)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.54/0.85 % (981)Termination reason: Unknown
% 3.54/0.85 % (981)Termination phase: Saturation
% 3.54/0.85
% 3.54/0.85 % (981)Memory used [KB]: 6652
% 3.54/0.85 % (981)Time elapsed: 0.150 s
% 3.54/0.85 % (981)Instructions burned: 453 (million)
% 3.54/0.85 % (981)------------------------------
% 3.54/0.85 % (981)------------------------------
% 3.84/0.85 % (1046)Instruction limit reached!
% 3.84/0.85 % (1046)------------------------------
% 3.84/0.85 % (1046)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.84/0.85 % (1046)Termination reason: Unknown
% 3.84/0.85 % (1046)Termination phase: Saturation
% 3.84/0.85
% 3.84/0.85 % (1046)Memory used [KB]: 6012
% 3.84/0.85 % (1046)Time elapsed: 0.045 s
% 3.84/0.85 % (1046)Instructions burned: 135 (million)
% 3.84/0.85 % (1046)------------------------------
% 3.84/0.85 % (1046)------------------------------
% 3.84/0.85 % (1015)Instruction limit reached!
% 3.84/0.85 % (1015)------------------------------
% 3.84/0.85 % (1015)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.84/0.85 % (1015)Termination reason: Unknown
% 3.84/0.85 % (1015)Termination phase: Saturation
% 3.84/0.85
% 3.84/0.85 % (1015)Memory used [KB]: 6908
% 3.84/0.85 % (1015)Time elapsed: 0.106 s
% 3.84/0.85 % (1015)Instructions burned: 345 (million)
% 3.84/0.85 % (1015)------------------------------
% 3.84/0.85 % (1015)------------------------------
% 3.84/0.85 % (1063)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on theBenchmark for (2994ds/258Mi)
% 3.84/0.86 % (1064)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on theBenchmark for (2994ds/90Mi)
% 3.84/0.86 % (1067)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on theBenchmark for (2994ds/231Mi)
% 3.84/0.88 % (1045)Instruction limit reached!
% 3.84/0.88 % (1045)------------------------------
% 3.84/0.88 % (1045)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.84/0.88 % (1045)Termination reason: Unknown
% 3.84/0.88 % (1045)Termination phase: Saturation
% 3.84/0.88
% 3.84/0.88 % (1045)Memory used [KB]: 7547
% 3.84/0.88 % (1045)Time elapsed: 0.079 s
% 3.84/0.88 % (1045)Instructions burned: 283 (million)
% 3.84/0.88 % (1045)------------------------------
% 3.84/0.88 % (1045)------------------------------
% 3.84/0.88 % (1064)Instruction limit reached!
% 3.84/0.88 % (1064)------------------------------
% 3.84/0.88 % (1064)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.84/0.88 % (1064)Termination reason: Unknown
% 3.84/0.88 % (1064)Termination phase: Saturation
% 3.84/0.88
% 3.84/0.88 % (1064)Memory used [KB]: 6012
% 3.84/0.88 % (1064)Time elapsed: 0.030 s
% 3.84/0.88 % (1064)Instructions burned: 91 (million)
% 3.84/0.88 % (1064)------------------------------
% 3.84/0.88 % (1064)------------------------------
% 3.84/0.89 % (1073)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on theBenchmark for (2994ds/458Mi)
% 3.84/0.89 % (1058)Instruction limit reached!
% 3.84/0.89 % (1058)------------------------------
% 3.84/0.89 % (1058)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.84/0.89 % (1058)Termination reason: Unknown
% 3.84/0.89 % (1058)Termination phase: Saturation
% 3.84/0.89
% 3.84/0.89 % (1058)Memory used [KB]: 6268
% 3.84/0.89 % (1058)Time elapsed: 0.056 s
% 3.84/0.89 % (1058)Instructions burned: 194 (million)
% 3.84/0.89 % (1058)------------------------------
% 3.84/0.89 % (1058)------------------------------
% 3.84/0.89 % (1076)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 (2994ds/31Mi)
% 3.84/0.90 % (1077)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on theBenchmark for (2994ds/297Mi)
% 3.84/0.90 % (1076)Instruction limit reached!
% 3.84/0.90 % (1076)------------------------------
% 3.84/0.90 % (1076)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.84/0.90 % (1076)Termination reason: Unknown
% 3.84/0.90 % (1076)Termination phase: Saturation
% 3.84/0.90
% 3.84/0.90 % (1076)Memory used [KB]: 5628
% 3.84/0.90 % (1076)Time elapsed: 0.010 s
% 3.84/0.90 % (1076)Instructions burned: 32 (million)
% 3.84/0.90 % (1076)------------------------------
% 3.84/0.90 % (1076)------------------------------
% 3.84/0.91 % (1080)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on theBenchmark for (2994ds/987Mi)
% 4.20/0.92 % (1067)Instruction limit reached!
% 4.20/0.92 % (1067)------------------------------
% 4.20/0.92 % (1067)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.20/0.92 % (1067)Termination reason: Unknown
% 4.20/0.92 % (1067)Termination phase: Saturation
% 4.20/0.92
% 4.20/0.92 % (1067)Memory used [KB]: 6268
% 4.20/0.92 % (1067)Time elapsed: 0.063 s
% 4.20/0.92 % (1067)Instructions burned: 231 (million)
% 4.20/0.92 % (1067)------------------------------
% 4.20/0.92 % (1067)------------------------------
% 4.20/0.92 % (1026)Instruction limit reached!
% 4.20/0.92 % (1026)------------------------------
% 4.20/0.92 % (1026)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.20/0.92 % (1026)Termination reason: Unknown
% 4.20/0.92 % (1026)Termination phase: Saturation
% 4.20/0.92
% 4.20/0.92 % (1026)Memory used [KB]: 7547
% 4.20/0.92 % (1026)Time elapsed: 0.165 s
% 4.20/0.92 % (1026)Instructions burned: 615 (million)
% 4.20/0.92 % (1026)------------------------------
% 4.20/0.92 % (1026)------------------------------
% 4.20/0.93 % (1057)Instruction limit reached!
% 4.20/0.93 % (1057)------------------------------
% 4.20/0.93 % (1057)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.20/0.93 % (1057)Termination reason: Unknown
% 4.20/0.93 % (1057)Termination phase: Saturation
% 4.20/0.93
% 4.20/0.93 % (1057)Memory used [KB]: 6268
% 4.20/0.93 % (1057)Time elapsed: 0.092 s
% 4.20/0.93 % (1057)Instructions burned: 299 (million)
% 4.20/0.93 % (1057)------------------------------
% 4.20/0.93 % (1057)------------------------------
% 4.20/0.93 % (1063)Instruction limit reached!
% 4.20/0.93 % (1063)------------------------------
% 4.20/0.93 % (1063)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.20/0.93 % (1063)Termination reason: Unknown
% 4.20/0.93 % (1063)Termination phase: Saturation
% 4.20/0.93
% 4.20/0.93 % (1063)Memory used [KB]: 6780
% 4.20/0.93 % (1063)Time elapsed: 0.075 s
% 4.20/0.93 % (1063)Instructions burned: 258 (million)
% 4.20/0.93 % (1063)------------------------------
% 4.20/0.93 % (1063)------------------------------
% 4.20/0.93 % (1081)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on theBenchmark for (2994ds/182Mi)
% 4.20/0.93 % (1082)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on theBenchmark for (2994ds/182Mi)
% 4.20/0.93 % (1083)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on theBenchmark for (2994ds/154Mi)
% 4.20/0.94 % (1084)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on theBenchmark for (2994ds/79Mi)
% 4.20/0.96 % (1084)Instruction limit reached!
% 4.20/0.96 % (1084)------------------------------
% 4.20/0.96 % (1084)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.20/0.96 % (1084)Termination reason: Unknown
% 4.20/0.96 % (1084)Termination phase: Saturation
% 4.20/0.96
% 4.20/0.96 % (1084)Memory used [KB]: 5884
% 4.20/0.96 % (1084)Time elapsed: 0.023 s
% 4.20/0.96 % (1084)Instructions burned: 80 (million)
% 4.20/0.96 % (1084)------------------------------
% 4.20/0.96 % (1084)------------------------------
% 4.20/0.97 % (1089)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on theBenchmark for (2993ds/216Mi)
% 4.66/0.97 % (921)Instruction limit reached!
% 4.66/0.97 % (921)------------------------------
% 4.66/0.97 % (921)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/0.97 % (921)Termination reason: Unknown
% 4.66/0.97 % (921)Termination phase: Saturation
% 4.66/0.97
% 4.66/0.97 % (921)Memory used [KB]: 10618
% 4.66/0.97 % (921)Time elapsed: 0.339 s
% 4.66/0.97 % (921)Instructions burned: 1090 (million)
% 4.66/0.97 % (921)------------------------------
% 4.66/0.97 % (921)------------------------------
% 4.66/0.98 % (1090)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on theBenchmark for (2993ds/114Mi)
% 4.66/0.98 % (1083)Instruction limit reached!
% 4.66/0.98 % (1083)------------------------------
% 4.66/0.98 % (1083)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/0.98 % (1083)Termination reason: Unknown
% 4.66/0.98 % (1083)Termination phase: Saturation
% 4.66/0.98
% 4.66/0.98 % (1083)Memory used [KB]: 6268
% 4.66/0.98 % (1083)Time elapsed: 0.071 s
% 4.66/0.98 % (1083)Instructions burned: 156 (million)
% 4.66/0.98 % (1083)------------------------------
% 4.66/0.98 % (1083)------------------------------
% 4.66/0.98 % (1090)Refutation not found, incomplete strategy
% 4.66/0.98 % (1090)------------------------------
% 4.66/0.98 % (1090)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/0.98 % (1090)Termination reason: Refutation not found, incomplete strategy
% 4.66/0.98
% 4.66/0.98
% 4.66/0.98 % (1090)Memory used [KB]: 5500
% 4.66/0.98 % (1090)Time elapsed: 0.003 s
% 4.66/0.98 % (1090)Instructions burned: 6 (million)
% 4.66/0.98 % (1090)------------------------------
% 4.66/0.98 % (1090)------------------------------
% 4.66/0.98 % (1077)Instruction limit reached!
% 4.66/0.98 % (1077)------------------------------
% 4.66/0.98 % (1077)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/0.98 % (1077)Termination reason: Unknown
% 4.66/0.98 % (1077)Termination phase: Saturation
% 4.66/0.98
% 4.66/0.98 % (1077)Memory used [KB]: 6396
% 4.66/0.98 % (1077)Time elapsed: 0.107 s
% 4.66/0.98 % (1077)Instructions burned: 300 (million)
% 4.66/0.98 % (1077)------------------------------
% 4.66/0.98 % (1077)------------------------------
% 4.66/0.98 % (1081)Instruction limit reached!
% 4.66/0.98 % (1081)------------------------------
% 4.66/0.98 % (1081)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/0.98 % (1081)Termination reason: Unknown
% 4.66/0.98 % (1081)Termination phase: Saturation
% 4.66/0.98
% 4.66/0.98 % (1081)Memory used [KB]: 6524
% 4.66/0.98 % (1081)Time elapsed: 0.074 s
% 4.66/0.98 % (1081)Instructions burned: 183 (million)
% 4.66/0.98 % (1081)------------------------------
% 4.66/0.98 % (1081)------------------------------
% 4.66/0.98 % (1082)Instruction limit reached!
% 4.66/0.98 % (1082)------------------------------
% 4.66/0.98 % (1082)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/0.98 % (1082)Termination reason: Unknown
% 4.66/0.98 % (1082)Termination phase: Saturation
% 4.66/0.98
% 4.66/0.98 % (1082)Memory used [KB]: 6268
% 4.66/0.98 % (1082)Time elapsed: 0.074 s
% 4.66/0.98 % (1082)Instructions burned: 185 (million)
% 4.66/0.98 % (1082)------------------------------
% 4.66/0.98 % (1082)------------------------------
% 4.66/0.99 % (1092)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on theBenchmark for (2993ds/922Mi)
% 4.66/0.99 % (1093)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on theBenchmark for (2993ds/182Mi)
% 4.66/0.99 % (1094)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on theBenchmark for (2993ds/164Mi)
% 4.66/0.99 % (1095)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on theBenchmark for (2993ds/50Mi)
% 4.66/0.99 % (1096)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on theBenchmark for (2993ds/368Mi)
% 4.66/0.99 % (1093)Refutation not found, incomplete strategy
% 4.66/0.99 % (1093)------------------------------
% 4.66/0.99 % (1093)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/0.99 % (1093)Termination reason: Refutation not found, incomplete strategy
% 4.66/0.99
% 4.66/0.99
% 4.66/0.99 % (1093)Memory used [KB]: 5500
% 4.66/0.99 % (1093)Time elapsed: 0.031 s
% 4.66/0.99 % (1093)Instructions burned: 10 (million)
% 4.66/0.99 % (1093)------------------------------
% 4.66/0.99 % (1093)------------------------------
% 4.66/1.00 % (1100)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on theBenchmark for (2993ds/1021Mi)
% 4.66/1.00 % (1089)Refutation not found, incomplete strategy
% 4.66/1.00 % (1089)------------------------------
% 4.66/1.00 % (1089)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/1.00 % (1089)Termination reason: Refutation not found, incomplete strategy
% 4.66/1.00
% 4.66/1.00
% 4.66/1.00 % (1089)Memory used [KB]: 5756
% 4.66/1.00 % (1089)Time elapsed: 0.059 s
% 4.66/1.00 % (1089)Instructions burned: 127 (million)
% 4.66/1.00 % (1089)------------------------------
% 4.66/1.00 % (1089)------------------------------
% 4.66/1.01 % (1095)Instruction limit reached!
% 4.66/1.01 % (1095)------------------------------
% 4.66/1.01 % (1095)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/1.01 % (1095)Termination reason: Unknown
% 4.66/1.01 % (1095)Termination phase: Saturation
% 4.66/1.01
% 4.66/1.01 % (1095)Memory used [KB]: 10618
% 4.66/1.01 % (1095)Time elapsed: 0.016 s
% 4.66/1.01 % (1095)Instructions burned: 53 (million)
% 4.66/1.01 % (1095)------------------------------
% 4.66/1.01 % (1095)------------------------------
% 4.66/1.01 % (1105)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on theBenchmark for (2993ds/267Mi)
% 4.66/1.01 % (1106)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on theBenchmark for (2993ds/204Mi)
% 4.66/1.02 % (1073)Instruction limit reached!
% 4.66/1.02 % (1073)------------------------------
% 4.66/1.02 % (1073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/1.02 % (1073)Termination reason: Unknown
% 4.66/1.02 % (1073)Termination phase: Saturation
% 4.66/1.02
% 4.66/1.02 % (1073)Memory used [KB]: 7419
% 4.66/1.02 % (1073)Time elapsed: 0.134 s
% 4.66/1.02 % (1073)Instructions burned: 460 (million)
% 4.66/1.02 % (1073)------------------------------
% 4.66/1.02 % (1073)------------------------------
% 4.66/1.03 % (1107)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2992ds/26Mi)
% 4.66/1.03 % (1094)Instruction limit reached!
% 4.66/1.03 % (1094)------------------------------
% 4.66/1.03 % (1094)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/1.03 % (1094)Termination reason: Unknown
% 4.66/1.03 % (1094)Termination phase: Saturation
% 4.66/1.03
% 4.66/1.03 % (1094)Memory used [KB]: 1279
% 4.66/1.03 % (1094)Time elapsed: 0.042 s
% 4.66/1.03 % (1094)Instructions burned: 168 (million)
% 4.66/1.03 % (1094)------------------------------
% 4.66/1.03 % (1094)------------------------------
% 4.66/1.03 % (1107)Refutation not found, incomplete strategy
% 4.66/1.03 % (1107)------------------------------
% 4.66/1.03 % (1107)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.66/1.03 % (1107)Termination reason: Refutation not found, incomplete strategy
% 4.66/1.03
% 4.66/1.03
% 4.66/1.03 % (1107)Memory used [KB]: 5500
% 4.66/1.03 % (1107)Time elapsed: 0.005 s
% 4.66/1.03 % (1107)Instructions burned: 13 (million)
% 4.66/1.03 % (1107)------------------------------
% 4.66/1.03 % (1107)------------------------------
% 4.66/1.04 % (1108)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on theBenchmark for (2992ds/53Mi)
% 4.66/1.04 % (1109)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on theBenchmark for (2992ds/4436Mi)
% 5.56/1.05 % (1108)Instruction limit reached!
% 5.56/1.05 % (1108)------------------------------
% 5.56/1.05 % (1108)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.56/1.05 % (1108)Termination reason: Unknown
% 5.56/1.05 % (1108)Termination phase: Saturation
% 5.56/1.05
% 5.56/1.05 % (1108)Memory used [KB]: 5628
% 5.56/1.05 % (1108)Time elapsed: 0.016 s
% 5.56/1.05 % (1108)Instructions burned: 55 (million)
% 5.56/1.05 % (1108)------------------------------
% 5.56/1.05 % (1108)------------------------------
% 5.56/1.06 % (1110)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on theBenchmark for (2992ds/1539Mi)
% 6.20/1.08 % (1106)Instruction limit reached!
% 6.20/1.08 % (1106)------------------------------
% 6.20/1.08 % (1106)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.20/1.08 % (1106)Termination reason: Unknown
% 6.20/1.08 % (1106)Termination phase: Saturation
% 6.20/1.08
% 6.20/1.08 % (1106)Memory used [KB]: 6524
% 6.20/1.08 % (1106)Time elapsed: 0.059 s
% 6.20/1.08 % (1106)Instructions burned: 204 (million)
% 6.20/1.08 % (1106)------------------------------
% 6.20/1.08 % (1106)------------------------------
% 6.20/1.09 % (1111)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on theBenchmark for (2992ds/408Mi)
% 6.20/1.09 % (1105)Instruction limit reached!
% 6.20/1.09 % (1105)------------------------------
% 6.20/1.09 % (1105)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.20/1.09 % (1105)Termination reason: Unknown
% 6.20/1.09 % (1105)Termination phase: Saturation
% 6.20/1.09
% 6.20/1.09 % (1105)Memory used [KB]: 6396
% 6.20/1.09 % (1105)Time elapsed: 0.084 s
% 6.20/1.09 % (1105)Instructions burned: 269 (million)
% 6.20/1.09 % (1105)------------------------------
% 6.20/1.09 % (1105)------------------------------
% 6.20/1.10 % (1096)Instruction limit reached!
% 6.20/1.10 % (1096)------------------------------
% 6.20/1.10 % (1096)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.20/1.10 % (1096)Termination reason: Unknown
% 6.20/1.10 % (1096)Termination phase: Saturation
% 6.20/1.10
% 6.20/1.10 % (1096)Memory used [KB]: 7547
% 6.20/1.10 % (1096)Time elapsed: 0.108 s
% 6.20/1.10 % (1096)Instructions burned: 368 (million)
% 6.20/1.10 % (1096)------------------------------
% 6.20/1.10 % (1096)------------------------------
% 6.20/1.10 % (1112)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on theBenchmark for (2992ds/5205Mi)
% 6.20/1.11 % (1113)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on theBenchmark for (2992ds/1913Mi)
% 6.65/1.21 % (1111)Instruction limit reached!
% 6.65/1.21 % (1111)------------------------------
% 6.65/1.21 % (1111)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.65/1.21 % (1111)Termination reason: Unknown
% 6.65/1.21 % (1111)Termination phase: Saturation
% 6.65/1.21
% 6.65/1.21 % (1111)Memory used [KB]: 7547
% 6.65/1.21 % (1111)Time elapsed: 0.120 s
% 6.65/1.21 % (1111)Instructions burned: 408 (million)
% 6.65/1.21 % (1111)------------------------------
% 6.65/1.21 % (1111)------------------------------
% 6.65/1.22 % (1114)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on theBenchmark for (2991ds/4350Mi)
% 6.65/1.22 % (1080)Instruction limit reached!
% 6.65/1.22 % (1080)------------------------------
% 6.65/1.22 % (1080)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.65/1.22 % (1080)Termination reason: Unknown
% 6.65/1.22 % (1080)Termination phase: Saturation
% 6.65/1.22
% 6.65/1.22 % (1080)Memory used [KB]: 8571
% 6.65/1.22 % (1080)Time elapsed: 0.335 s
% 6.65/1.22 % (1080)Instructions burned: 987 (million)
% 6.65/1.22 % (1080)------------------------------
% 6.65/1.22 % (1080)------------------------------
% 7.07/1.23 % (1115)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on theBenchmark for (2990ds/68Mi)
% 7.07/1.25 % (1115)Instruction limit reached!
% 7.07/1.25 % (1115)------------------------------
% 7.07/1.25 % (1115)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.07/1.25 % (1115)Termination reason: Unknown
% 7.07/1.25 % (1115)Termination phase: Saturation
% 7.07/1.25
% 7.07/1.25 % (1115)Memory used [KB]: 5884
% 7.07/1.25 % (1115)Time elapsed: 0.020 s
% 7.07/1.25 % (1115)Instructions burned: 69 (million)
% 7.07/1.25 % (1115)------------------------------
% 7.07/1.25 % (1115)------------------------------
% 7.07/1.25 % (1092)Instruction limit reached!
% 7.07/1.25 % (1092)------------------------------
% 7.07/1.25 % (1092)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.07/1.25 % (1092)Termination reason: Unknown
% 7.07/1.25 % (1092)Termination phase: Saturation
% 7.07/1.25
% 7.07/1.25 % (1092)Memory used [KB]: 10490
% 7.07/1.25 % (1092)Time elapsed: 0.268 s
% 7.07/1.25 % (1092)Instructions burned: 922 (million)
% 7.07/1.25 % (1092)------------------------------
% 7.07/1.25 % (1092)------------------------------
% 7.07/1.25 % (1116)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on theBenchmark for (2990ds/358Mi)
% 7.28/1.26 % (1117)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 (2990ds/31Mi)
% 7.28/1.27 % (1117)Instruction limit reached!
% 7.28/1.27 % (1117)------------------------------
% 7.28/1.27 % (1117)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.28/1.27 % (1117)Termination reason: Unknown
% 7.28/1.27 % (1117)Termination phase: Saturation
% 7.28/1.27
% 7.28/1.27 % (1117)Memory used [KB]: 5628
% 7.28/1.27 % (1117)Time elapsed: 0.010 s
% 7.28/1.27 % (1117)Instructions burned: 32 (million)
% 7.28/1.27 % (1117)------------------------------
% 7.28/1.27 % (1117)------------------------------
% 7.28/1.28 % (1118)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on theBenchmark for (2990ds/279Mi)
% 7.28/1.30 % (1100)Instruction limit reached!
% 7.28/1.30 % (1100)------------------------------
% 7.28/1.30 % (1100)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.28/1.30 % (1100)Termination reason: Unknown
% 7.28/1.30 % (1100)Termination phase: Saturation
% 7.28/1.30
% 7.28/1.30 % (1100)Memory used [KB]: 10490
% 7.28/1.30 % (1100)Time elapsed: 0.301 s
% 7.28/1.30 % (1100)Instructions burned: 1022 (million)
% 7.28/1.30 % (1100)------------------------------
% 7.28/1.30 % (1100)------------------------------
% 7.28/1.31 % (1119)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on theBenchmark for (2990ds/258Mi)
% 7.48/1.36 % (1116)Instruction limit reached!
% 7.48/1.36 % (1116)------------------------------
% 7.48/1.36 % (1116)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.48/1.36 % (1116)Termination reason: Unknown
% 7.48/1.36 % (1116)Termination phase: Saturation
% 7.48/1.36
% 7.48/1.36 % (1116)Memory used [KB]: 7164
% 7.48/1.36 % (1116)Time elapsed: 0.106 s
% 7.48/1.36 % (1116)Instructions burned: 360 (million)
% 7.48/1.36 % (1116)------------------------------
% 7.48/1.36 % (1116)------------------------------
% 7.48/1.37 % (1124)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2989ds/26Mi)
% 7.48/1.37 % (1118)Instruction limit reached!
% 7.48/1.37 % (1118)------------------------------
% 7.48/1.37 % (1118)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.48/1.37 % (1118)Termination reason: Unknown
% 7.48/1.37 % (1118)Termination phase: Saturation
% 7.48/1.37
% 7.48/1.37 % (1118)Memory used [KB]: 6140
% 7.48/1.37 % (1118)Time elapsed: 0.092 s
% 7.48/1.37 % (1118)Instructions burned: 280 (million)
% 7.48/1.37 % (1118)------------------------------
% 7.48/1.37 % (1118)------------------------------
% 7.77/1.37 % (1124)Refutation not found, incomplete strategy
% 7.77/1.37 % (1124)------------------------------
% 7.77/1.37 % (1124)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.77/1.37 % (1124)Termination reason: Refutation not found, incomplete strategy
% 7.77/1.37
% 7.77/1.37
% 7.77/1.37 % (1124)Memory used [KB]: 5500
% 7.77/1.37 % (1124)Time elapsed: 0.005 s
% 7.77/1.37 % (1124)Instructions burned: 10 (million)
% 7.77/1.37 % (1124)------------------------------
% 7.77/1.37 % (1124)------------------------------
% 7.77/1.38 % (1127)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on theBenchmark for (2989ds/995Mi)
% 7.77/1.38 % (1128)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on theBenchmark for (2989ds/373Mi)
% 7.77/1.38 % (1119)Instruction limit reached!
% 7.77/1.38 % (1119)------------------------------
% 7.77/1.38 % (1119)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.77/1.38 % (1119)Termination reason: Unknown
% 7.77/1.38 % (1119)Termination phase: Saturation
% 7.77/1.38
% 7.77/1.38 % (1119)Memory used [KB]: 6780
% 7.77/1.38 % (1119)Time elapsed: 0.077 s
% 7.77/1.38 % (1119)Instructions burned: 260 (million)
% 7.77/1.38 % (1119)------------------------------
% 7.77/1.38 % (1119)------------------------------
% 7.77/1.39 % (1133)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on theBenchmark for (2989ds/253Mi)
% 8.04/1.46 % (1133)Instruction limit reached!
% 8.04/1.46 % (1133)------------------------------
% 8.04/1.46 % (1133)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.04/1.46 % (1133)Termination reason: Unknown
% 8.04/1.46 % (1133)Termination phase: Saturation
% 8.04/1.46
% 8.04/1.46 % (1133)Memory used [KB]: 6140
% 8.04/1.46 % (1133)Time elapsed: 0.074 s
% 8.04/1.46 % (1133)Instructions burned: 254 (million)
% 8.04/1.46 % (1133)------------------------------
% 8.04/1.46 % (1133)------------------------------
% 8.04/1.47 % (1195)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on theBenchmark for (2988ds/832Mi)
% 8.04/1.49 % (1128)Instruction limit reached!
% 8.04/1.49 % (1128)------------------------------
% 8.04/1.49 % (1128)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.04/1.49 % (1128)Termination reason: Unknown
% 8.04/1.49 % (1128)Termination phase: Saturation
% 8.04/1.49
% 8.04/1.49 % (1128)Memory used [KB]: 7164
% 8.04/1.49 % (1128)Time elapsed: 0.110 s
% 8.04/1.49 % (1128)Instructions burned: 374 (million)
% 8.04/1.49 % (1128)------------------------------
% 8.04/1.49 % (1128)------------------------------
% 8.04/1.50 % (1200)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on theBenchmark for (2988ds/668Mi)
% 8.04/1.51 % (1110)Instruction limit reached!
% 8.04/1.51 % (1110)------------------------------
% 8.04/1.51 % (1110)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.04/1.51 % (1110)Termination reason: Unknown
% 8.04/1.51 % (1110)Termination phase: Saturation
% 8.04/1.51
% 8.04/1.51 % (1110)Memory used [KB]: 13432
% 8.04/1.51 % (1110)Time elapsed: 0.456 s
% 8.04/1.51 % (1110)Instructions burned: 1540 (million)
% 8.04/1.51 % (1110)------------------------------
% 8.04/1.51 % (1110)------------------------------
% 8.37/1.52 % (1201)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=40:si=on:rtra=on_0 on theBenchmark for (2988ds/40Mi)
% 8.37/1.53 % (1201)Instruction limit reached!
% 8.37/1.53 % (1201)------------------------------
% 8.37/1.53 % (1201)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.37/1.53 % (1201)Termination reason: Unknown
% 8.37/1.53 % (1201)Termination phase: Saturation
% 8.37/1.53
% 8.37/1.53 % (1201)Memory used [KB]: 5884
% 8.37/1.53 % (1201)Time elapsed: 0.013 s
% 8.37/1.53 % (1201)Instructions burned: 42 (million)
% 8.37/1.53 % (1201)------------------------------
% 8.37/1.53 % (1201)------------------------------
% 8.37/1.54 % (1202)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on theBenchmark for (2987ds/294Mi)
% 8.43/1.63 % (1202)Instruction limit reached!
% 8.43/1.63 % (1202)------------------------------
% 8.43/1.63 % (1202)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.43/1.63 % (1202)Termination reason: Unknown
% 8.43/1.63 % (1202)Termination phase: Saturation
% 8.43/1.63
% 8.43/1.63 % (1202)Memory used [KB]: 6140
% 8.43/1.63 % (1202)Time elapsed: 0.087 s
% 8.43/1.63 % (1202)Instructions burned: 296 (million)
% 8.43/1.63 % (1202)------------------------------
% 8.43/1.63 % (1202)------------------------------
% 8.43/1.64 % (1112)First to succeed.
% 8.43/1.64 % (1203)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on theBenchmark for (2986ds/187Mi)
% 10.69/1.65 % (1112)Refutation found. Thanks to Tanya!
% 10.69/1.65 % SZS status Theorem for theBenchmark
% 10.69/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 10.69/1.66 % (1112)------------------------------
% 10.69/1.66 % (1112)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.69/1.66 % (1112)Termination reason: Refutation
% 10.69/1.66
% 10.69/1.66 % (1112)Memory used [KB]: 11001
% 10.69/1.66 % (1112)Time elapsed: 0.550 s
% 10.69/1.66 % (1112)Instructions burned: 1594 (million)
% 10.69/1.66 % (1112)------------------------------
% 10.69/1.66 % (1112)------------------------------
% 10.69/1.66 % (792)Success in time 1.33 s
% 10.69/1.66 % Vampire---4.8 exiting
%------------------------------------------------------------------------------