TSTP Solution File: SEV119^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV119^5 : 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 : n024.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 04:12:02 EDT 2024
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 40
% Syntax : Number of formulae : 232 ( 18 unt; 31 typ; 0 def)
% Number of atoms : 1897 ( 199 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 5102 ( 284 ~; 375 |; 215 &;3091 @)
% ( 8 <=>; 490 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 841 ( 841 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 37 usr; 30 con; 0-2 aty)
% ( 639 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 818 ( 732 ^ 85 !; 0 ?; 818 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a > a > $o ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: ( a > a > $o ) > $o ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a ).
thf(func_def_26,type,
sK7: a > a > $o ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a > a > $o ).
thf(func_def_32,type,
sK13: a ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a > a > $o ).
thf(func_def_35,type,
sK16: a > a > $o ).
thf(func_def_36,type,
sK17: a > a > $o ).
thf(func_def_37,type,
sK18: a > a > $o ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(f757,plain,
$false,
inference(avatar_sat_refutation,[],[f29,f36,f40,f98,f175,f247,f421,f573,f756]) ).
thf(f756,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f755]) ).
thf(f755,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f754]) ).
thf(f754,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f753]) ).
thf(f753,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f752]) ).
thf(f752,plain,
( ( $true
= ( ~ ( $true
| ( sK2 @ sK28 @ sK27 ) ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f751,f747]) ).
thf(f747,plain,
( ( $true
= ( sK3 @ sK28 @ sK27 ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f743]) ).
thf(f743,plain,
( ( $false
= ( ( sK3 @ sK28 @ sK27 )
=> ( sK7 @ sK28 @ sK27 ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f742]) ).
thf(f742,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ sK27 )
=> ( sK7 @ Y0 @ sK27 ) )
@ sK28 ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[],[f734]) ).
thf(f734,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ sK27 )
=> ( sK7 @ Y0 @ sK27 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f730]) ).
thf(f730,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ sK27 )
= $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[],[f724]) ).
thf(f724,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(not_proxy_clausification,[],[f674]) ).
thf(f674,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f673]) ).
thf(f673,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[],[f642,f672]) ).
thf(f672,plain,
( ( ( sK7 @ sK9 @ sK8 )
= $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f671]) ).
thf(f671,plain,
( ( $false
= ( $true
=> ( sK7 @ sK9 @ sK8 ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f670]) ).
thf(f670,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| $true )
=> ( sK7 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f669,f97]) ).
thf(f97,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f96]) ).
thf(f96,plain,
( spl0_6
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f669,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
=> ( sK7 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f668]) ).
thf(f668,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK8 ) ) ) )
=> ( sK7 @ Y0 @ sK8 ) )
@ sK9 ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(sigma_clausification,[],[f665]) ).
thf(f665,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK8 ) ) ) )
=> ( sK7 @ Y0 @ sK8 ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f661]) ).
thf(f661,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ sK8 ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(sigma_clausification,[],[f655]) ).
thf(f655,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f608]) ).
thf(f608,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f607]) ).
thf(f607,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& $true ) )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(backward_demodulation,[],[f600,f606]) ).
thf(f606,plain,
( ( $true
= ( sK4 @ sK7 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f605]) ).
thf(f605,plain,
( ( ( ( sK4 @ sK7 )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f589,f603]) ).
thf(f603,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f589]) ).
thf(f589,plain,
( ( $true
= ( ( sK4 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f587]) ).
thf(f587,plain,
( ( $false
= ( ( ( sK4 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
=> ( sK7 @ sK5 @ sK6 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f586]) ).
thf(f586,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f32]) ).
thf(f32,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f31,plain,
( spl0_3
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f600,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f599]) ).
thf(f599,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f595,f588]) ).
thf(f588,plain,
( ( ( sK7 @ sK5 @ sK6 )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f587]) ).
thf(f595,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ X1 ) )
=> ( X1 @ sK5 @ sK6 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f594]) ).
thf(f594,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f25]) ).
thf(f25,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f24,plain,
( spl0_1
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f642,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f641]) ).
thf(f641,plain,
( ( $true
= ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
=> ( sK7 @ sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f637,f606]) ).
thf(f637,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( sK4 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK9 @ sK8 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f636]) ).
thf(f636,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) )
@ X1 ) )
| ~ spl0_6 ),
inference(pi_clausification,[],[f97]) ).
thf(f751,plain,
( ( $true
= ( ~ ( ( sK3 @ sK28 @ sK27 )
| ( sK2 @ sK28 @ sK27 ) ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f750]) ).
thf(f750,plain,
( ( $true
= ( ( ( sK3 @ sK28 @ sK27 )
| ( sK2 @ sK28 @ sK27 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f620,f749]) ).
thf(f749,plain,
( ( ( sK7 @ sK28 @ sK27 )
= $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f748]) ).
thf(f748,plain,
( ( ( $true
=> ( sK7 @ sK28 @ sK27 ) )
= $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[],[f743,f747]) ).
thf(f620,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK3 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
=> ( sK7 @ X1 @ X2 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f619]) ).
thf(f619,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK7 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f614]) ).
thf(f614,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK7 @ X1 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f613]) ).
thf(f613,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f603]) ).
thf(f573,plain,
( ~ spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f572]) ).
thf(f572,plain,
( $false
| ~ spl0_4
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f571]) ).
thf(f571,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f565,f396]) ).
thf(f396,plain,
( ( ( sK18 @ sK13 @ sK14 )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f395]) ).
thf(f395,plain,
( ( ( $true
=> ( sK18 @ sK13 @ sK14 ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f388,f394]) ).
thf(f394,plain,
( ( $true
= ( ( sK4 @ sK18 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK18 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f388]) ).
thf(f388,plain,
( ( ( ( ( sK4 @ sK18 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK18 @ Y1 @ Y0 ) ) ) ) )
=> ( sK18 @ sK13 @ sK14 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f385]) ).
thf(f385,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) )
@ sK18 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f333]) ).
thf(f333,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f324]) ).
thf(f324,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK13 @ sK14 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f239,plain,
( ( $true
= ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK13 @ sK14 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f238]) ).
thf(f238,plain,
( ( $true
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK13 @ sK14 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[],[f220,f237]) ).
thf(f237,plain,
( ( ( sK12 @ sK13 @ sK14 )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f236]) ).
thf(f236,plain,
( ( $false
= ( $true
=> ( sK12 @ sK13 @ sK14 ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f233,f235]) ).
thf(f235,plain,
( ( $true
= ( ( sK3 @ sK13 @ sK14 )
| ( sK2 @ sK13 @ sK14 ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f233]) ).
thf(f233,plain,
( ( ( ( ( sK3 @ sK13 @ sK14 )
| ( sK2 @ sK13 @ sK14 ) )
=> ( sK12 @ sK13 @ sK14 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f232]) ).
thf(f232,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ sK13 @ Y0 )
| ( sK2 @ sK13 @ Y0 ) )
=> ( sK12 @ sK13 @ Y0 ) )
@ sK14 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f231]) ).
thf(f231,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK13 @ Y0 )
| ( sK2 @ sK13 @ Y0 ) )
=> ( sK12 @ sK13 @ Y0 ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f227]) ).
thf(f227,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) )
@ sK13 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f221]) ).
thf(f221,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f202,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f199]) ).
thf(f199,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f196,f197]) ).
thf(f197,plain,
( ( $true
= ( sK4 @ sK12 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f190]) ).
thf(f190,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK12 ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f188]) ).
thf(f188,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK12 ) )
=> ( sK12 @ sK5 @ sK6 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f187]) ).
thf(f187,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f35]) ).
thf(f35,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f34,plain,
( spl0_4
<=> ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f196,plain,
( ( $true
= ( ~ ( ( sK4 @ sK12 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f195]) ).
thf(f195,plain,
( ( ( ( ( sK4 @ sK12 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_4 ),
inference(superposition,[],[f182,f189]) ).
thf(f189,plain,
( ( ( sK12 @ sK5 @ sK6 )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f188]) ).
thf(f182,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( sK4 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK5 @ sK6 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f181]) ).
thf(f181,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f180]) ).
thf(f180,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
!= $false )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f20,f35]) ).
thf(f20,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ),
inference(beta_eta_normalization,[],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK5 @ Y0 ) ) )
@ sK6 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( sK4 @ Y4 ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK4 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ sK5 @ Y0 ) ) )
@ sK6 ) ),
inference(negative_extensionality,[],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK5 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( sK4 @ Y4 ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK4 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ sK5 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK5 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( sK4 @ Y5 ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK4 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( sK4 @ Y5 ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK4 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f15]) ).
thf(f15,plain,
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( sK4 @ Y5 ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK4 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: ( a > a > $o ) > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( Y0 @ Y6 ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( Y0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( Y0 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y0: ( a > a > $o ) > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( Y0 @ Y6 ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( Y0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( Y0 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( Y0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( sK2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( Y1 @ Y7 ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( Y1 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( Y1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y1 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( sK2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( Y1 @ Y7 ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( Y1 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( Y1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y1 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y2: ( a > a > $o ) > $o] :
( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) )
& ( Y2 @ Y8 ) )
=> ( Y8 @ Y7 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y1 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y7 @ Y6 ) ) ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( Y2 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y2: ( a > a > $o ) > $o] :
( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) )
& ( Y2 @ Y8 ) )
=> ( Y8 @ Y7 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y1 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y7 @ Y6 ) ) ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( Y2 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y2: ( a > a > $o ) > $o] :
( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) )
& ( Y2 @ Y8 ) )
=> ( Y8 @ Y7 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y1 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y7 @ Y6 ) ) ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( Y2 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y2: ( a > a > $o ) > $o] :
( ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) )
& ( Y2 @ Y8 ) )
=> ( Y8 @ Y7 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y2 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y1 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y7 @ Y6 ) ) ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( Y2 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( Y2 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a > a > $o,X2: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X11: a > a > $o] :
( ( ( X0 @ X11 )
& ! [X12: a,X13: a] :
( ( X2 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) ) )
=> ( X11 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X14: a,X15: a] :
! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ( ( X2 @ X18 @ X17 )
| ( X1 @ X18 @ X17 ) )
=> ( X16 @ X18 @ X17 ) )
& ( X0 @ X16 ) )
=> ( X16 @ X14 @ X15 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > $o ) > $o,X2: a > a > $o,X1: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ( X0 @ X8 )
& ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X1 @ X6 @ X7 )
| ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
& ( X0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > a > $o ) > $o,X2: a > a > $o,X1: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ( X0 @ X8 )
& ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X1 @ X6 @ X7 )
| ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
& ( X0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM252_pme) ).
thf(f220,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ X2 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X2 @ X1 ) ) ) )
=> ( sK12 @ X2 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f219]) ).
thf(f219,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK12 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f210]) ).
thf(f210,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK12 @ Y0 @ X1 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f209]) ).
thf(f209,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f201]) ).
thf(f201,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f200]) ).
thf(f200,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
& $true )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f190,f197]) ).
thf(f565,plain,
( ( $true
= ( sK18 @ sK13 @ sK14 ) )
| ~ spl0_4
| ~ spl0_9 ),
inference(boolean_simplification,[],[f557]) ).
thf(f557,plain,
( ( $true
= ( $true
=> ( sK18 @ sK13 @ sK14 ) ) )
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[],[f551,f243]) ).
thf(f243,plain,
( ( $true
= ( sK3 @ sK13 @ sK14 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f242,plain,
( spl0_9
<=> ( $true
= ( sK3 @ sK13 @ sK14 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f551,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X2 @ X1 )
=> ( sK18 @ X2 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f550]) ).
thf(f550,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK18 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f547]) ).
thf(f547,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK18 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f546]) ).
thf(f546,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK18 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f431]) ).
thf(f431,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK18 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f394]) ).
thf(f421,plain,
( ~ spl0_4
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f420]) ).
thf(f420,plain,
( $false
| ~ spl0_4
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f419]) ).
thf(f419,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_10 ),
inference(boolean_simplification,[],[f418]) ).
thf(f418,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f412,f246]) ).
thf(f246,plain,
( ( $true
= ( sK2 @ sK13 @ sK14 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f245,plain,
( spl0_10
<=> ( $true
= ( sK2 @ sK13 @ sK14 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f412,plain,
( ( ( ~ ( sK2 @ sK13 @ sK14 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f409]) ).
thf(f409,plain,
( ( $true
= ( ( sK2 @ sK13 @ sK14 )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[],[f407,f360]) ).
thf(f360,plain,
( ( ( sK17 @ sK13 @ sK14 )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f359]) ).
thf(f359,plain,
( ( ( $true
=> ( sK17 @ sK13 @ sK14 ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f352,f358]) ).
thf(f358,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK17 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK17 ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f352]) ).
thf(f352,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK17 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK17 ) )
=> ( sK17 @ sK13 @ sK14 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f349]) ).
thf(f349,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK13 @ sK14 ) )
@ sK17 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f338]) ).
thf(f338,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK13 @ sK14 ) ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f337]) ).
thf(f337,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK13 @ sK14 ) ) )
| $false )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f324,f333]) ).
thf(f407,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X2 @ X1 )
=> ( sK17 @ X2 @ X1 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f406]) ).
thf(f406,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK17 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f405]) ).
thf(f405,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK17 @ Y0 @ X1 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f404]) ).
thf(f404,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK17 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f369]) ).
thf(f369,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK17 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f358]) ).
thf(f247,plain,
( spl0_9
| spl0_10
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f240,f34,f245,f242]) ).
thf(f240,plain,
( ( $true
= ( sK2 @ sK13 @ sK14 ) )
| ( $true
= ( sK3 @ sK13 @ sK14 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f235]) ).
thf(f175,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f174]) ).
thf(f174,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f173]) ).
thf(f173,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f172]) ).
thf(f172,plain,
( ( $true = ~ $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f171]) ).
thf(f171,plain,
( ( $true
= ( ~ ( ( sK3 @ sK11 @ sK10 )
| $true ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f170,f166]) ).
thf(f166,plain,
( ( $true
= ( sK2 @ sK11 @ sK10 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f164]) ).
thf(f164,plain,
( ( ( ( sK2 @ sK11 @ sK10 )
=> ( sK7 @ sK11 @ sK10 ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f163]) ).
thf(f163,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK10 )
=> ( sK7 @ Y0 @ sK10 ) )
@ sK11 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f160]) ).
thf(f160,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK10 )
=> ( sK7 @ Y0 @ sK10 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f158]) ).
thf(f158,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ sK10 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f149]) ).
thf(f149,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(not_proxy_clausification,[],[f118]) ).
thf(f118,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f117]) ).
thf(f117,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f116,f83]) ).
thf(f83,plain,
( ( ( sK7 @ sK9 @ sK8 )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f79]) ).
thf(f79,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
=> ( sK7 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f78]) ).
thf(f78,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK8 ) ) ) )
=> ( sK7 @ Y0 @ sK8 ) )
@ sK9 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f73]) ).
thf(f73,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( sK4 @ Y1 ) )
=> ( Y1 @ Y0 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK4 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK8 ) ) ) )
=> ( sK7 @ Y0 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f71]) ).
thf(f71,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f66]) ).
thf(f66,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f58]) ).
thf(f58,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f57]) ).
thf(f57,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& $true ) )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f52,f56]) ).
thf(f56,plain,
( ( $true
= ( sK4 @ sK7 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f55]) ).
thf(f55,plain,
( ( ( ( sK4 @ sK7 )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f48,f53]) ).
thf(f53,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f48]) ).
thf(f48,plain,
( ( $true
= ( ( sK4 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f45,plain,
( ( $false
= ( ( ( sK4 @ sK7 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
=> ( sK7 @ sK5 @ sK6 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f32]) ).
thf(f52,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f51]) ).
thf(f51,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ sK7 ) )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[],[f43,f50]) ).
thf(f50,plain,
( ( ( sK7 @ sK5 @ sK6 )
= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f49]) ).
thf(f49,plain,
( ( $false
= ( $true
=> ( sK7 @ sK5 @ sK6 ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f45,f48]) ).
thf(f43,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( sK4 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK4 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ X1 ) )
=> ( X1 @ sK5 @ sK6 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f42]) ).
thf(f42,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f41]) ).
thf(f41,plain,
( ( $false
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f20,f32]) ).
thf(f116,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
=> ( sK7 @ sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f114]) ).
thf(f114,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
& $true )
=> ( sK7 @ sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f105,f56]) ).
thf(f105,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( sK4 @ X1 ) )
=> ( X1 @ sK9 @ sK8 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f104]) ).
thf(f104,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK9 @ sK8 ) )
@ X1 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[],[f94]) ).
thf(f94,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f93,plain,
( spl0_5
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f170,plain,
( ( $true
= ( ~ ( ( sK3 @ sK11 @ sK10 )
| ( sK2 @ sK11 @ sK10 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f169]) ).
thf(f169,plain,
( ( $true
= ( ( ( sK3 @ sK11 @ sK10 )
| ( sK2 @ sK11 @ sK10 ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f77,f168]) ).
thf(f168,plain,
( ( ( sK7 @ sK11 @ sK10 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f167]) ).
thf(f167,plain,
( ( ( $true
=> ( sK7 @ sK11 @ sK10 ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f164,f166]) ).
thf(f77,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK3 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
=> ( sK7 @ X1 @ X2 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f76]) ).
thf(f76,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK7 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f70]) ).
thf(f70,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK7 @ X1 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f69]) ).
thf(f69,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f53]) ).
thf(f98,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f91,f31,f96,f93]) ).
thf(f91,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f84]) ).
thf(f84,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f79]) ).
thf(f40,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f39]) ).
thf(f39,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f38]) ).
thf(f38,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[],[f28,f32]) ).
thf(f28,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f27,plain,
( spl0_2
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f36,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f22,f34,f31]) ).
thf(f22,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f20]) ).
thf(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f21,f27,f24]) ).
thf(f21,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( sK4 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK4 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( sK4 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK4 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV119^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 18:42:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % (13393)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)
% 0.14/0.37 % (13386)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.37 % (13393)Instruction limit reached!
% 0.14/0.37 % (13393)------------------------------
% 0.14/0.37 % (13393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (13393)Termination reason: Unknown
% 0.14/0.37 % (13388)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)
% 0.14/0.37 % (13393)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (13393)Memory used [KB]: 1023
% 0.14/0.37 % (13393)Time elapsed: 0.003 s
% 0.14/0.37 % (13393)Instructions burned: 3 (million)
% 0.14/0.37 % (13389)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.37 % (13393)------------------------------
% 0.14/0.37 % (13393)------------------------------
% 0.14/0.37 % (13387)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)
% 0.14/0.37 % (13391)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)
% 0.14/0.37 % (13390)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)
% 0.14/0.37 % (13389)Instruction limit reached!
% 0.14/0.37 % (13389)------------------------------
% 0.14/0.37 % (13389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (13389)Termination reason: Unknown
% 0.14/0.37 % (13389)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (13389)Memory used [KB]: 895
% 0.14/0.37 % (13389)Time elapsed: 0.003 s
% 0.14/0.37 % (13389)Instructions burned: 2 (million)
% 0.14/0.37 % (13389)------------------------------
% 0.14/0.37 % (13389)------------------------------
% 0.14/0.37 % (13390)Instruction limit reached!
% 0.14/0.37 % (13390)------------------------------
% 0.14/0.37 % (13390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (13390)Termination reason: Unknown
% 0.14/0.37 % (13390)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (13390)Memory used [KB]: 1023
% 0.14/0.37 % (13390)Time elapsed: 0.003 s
% 0.14/0.37 % (13390)Instructions burned: 3 (million)
% 0.14/0.37 % (13390)------------------------------
% 0.14/0.37 % (13390)------------------------------
% 0.14/0.37 % (13387)Instruction limit reached!
% 0.14/0.37 % (13387)------------------------------
% 0.14/0.37 % (13387)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (13387)Termination reason: Unknown
% 0.14/0.37 % (13387)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (13387)Memory used [KB]: 5500
% 0.14/0.37 % (13387)Time elapsed: 0.004 s
% 0.14/0.37 % (13387)Instructions burned: 4 (million)
% 0.14/0.37 % (13387)------------------------------
% 0.14/0.37 % (13387)------------------------------
% 0.14/0.37 % (13392)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.14/0.38 % (13395)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.38 % (13388)Instruction limit reached!
% 0.14/0.38 % (13388)------------------------------
% 0.14/0.38 % (13388)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (13388)Termination reason: Unknown
% 0.14/0.38 % (13388)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (13388)Memory used [KB]: 5756
% 0.14/0.38 % (13388)Time elapsed: 0.018 s
% 0.14/0.38 % (13388)Instructions burned: 28 (million)
% 0.14/0.38 % (13388)------------------------------
% 0.14/0.38 % (13388)------------------------------
% 0.14/0.38 % (13392)Instruction limit reached!
% 0.14/0.38 % (13392)------------------------------
% 0.14/0.38 % (13392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (13392)Termination reason: Unknown
% 0.14/0.38 % (13392)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (13392)Memory used [KB]: 5500
% 0.14/0.38 % (13392)Time elapsed: 0.012 s
% 0.14/0.38 % (13392)Instructions burned: 18 (million)
% 0.14/0.38 % (13392)------------------------------
% 0.14/0.38 % (13392)------------------------------
% 0.14/0.38 % (13396)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.14/0.38 % (13398)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.39 % (13398)Instruction limit reached!
% 0.14/0.39 % (13398)------------------------------
% 0.14/0.39 % (13398)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (13398)Termination reason: Unknown
% 0.14/0.39 % (13398)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (13398)Memory used [KB]: 5500
% 0.14/0.39 % (13398)Time elapsed: 0.004 s
% 0.14/0.39 % (13398)Instructions burned: 3 (million)
% 0.14/0.39 % (13398)------------------------------
% 0.14/0.39 % (13398)------------------------------
% 0.14/0.39 % (13399)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.14/0.39 % (13396)Instruction limit reached!
% 0.14/0.39 % (13396)------------------------------
% 0.14/0.39 % (13396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (13396)Termination reason: Unknown
% 0.14/0.39 % (13396)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (13396)Memory used [KB]: 5756
% 0.14/0.39 % (13396)Time elapsed: 0.011 s
% 0.14/0.39 % (13396)Instructions burned: 16 (million)
% 0.14/0.39 % (13396)------------------------------
% 0.14/0.39 % (13396)------------------------------
% 0.14/0.40 % (13405)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.40 % (13406)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.40 % (13395)Instruction limit reached!
% 0.14/0.40 % (13395)------------------------------
% 0.14/0.40 % (13395)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (13395)Termination reason: Unknown
% 0.14/0.40 % (13395)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (13395)Memory used [KB]: 5628
% 0.14/0.40 % (13395)Time elapsed: 0.021 s
% 0.14/0.40 % (13395)Instructions burned: 37 (million)
% 0.14/0.40 % (13395)------------------------------
% 0.14/0.40 % (13395)------------------------------
% 0.14/0.40 % (13408)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)
% 0.14/0.40 % (13405)Instruction limit reached!
% 0.14/0.40 % (13405)------------------------------
% 0.14/0.40 % (13405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (13405)Termination reason: Unknown
% 0.14/0.40 % (13405)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (13405)Memory used [KB]: 1023
% 0.14/0.40 % (13405)Time elapsed: 0.006 s
% 0.14/0.40 % (13405)Instructions burned: 7 (million)
% 0.14/0.40 % (13405)------------------------------
% 0.14/0.40 % (13405)------------------------------
% 0.14/0.40 % (13408)Instruction limit reached!
% 0.14/0.40 % (13408)------------------------------
% 0.14/0.40 % (13408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (13408)Termination reason: Unknown
% 0.14/0.40 % (13408)Termination phase: Preprocessing 3
% 0.14/0.40
% 0.14/0.40 % (13408)Memory used [KB]: 1023
% 0.14/0.40 % (13408)Time elapsed: 0.003 s
% 0.14/0.40 % (13408)Instructions burned: 3 (million)
% 0.14/0.40 % (13408)------------------------------
% 0.14/0.40 % (13408)------------------------------
% 0.14/0.41 % (13412)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)
% 0.14/0.41 % (13406)Instruction limit reached!
% 0.14/0.41 % (13406)------------------------------
% 0.14/0.41 % (13406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (13406)Termination reason: Unknown
% 0.14/0.41 % (13406)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.41 % (13406)Memory used [KB]: 5756
% 0.14/0.41 % (13406)Time elapsed: 0.013 s
% 0.14/0.41 % (13406)Instructions burned: 17 (million)
% 0.14/0.41 % (13406)------------------------------
% 0.14/0.41 % (13406)------------------------------
% 0.14/0.41 % (13412)Instruction limit reached!
% 0.14/0.41 % (13412)------------------------------
% 0.14/0.41 % (13412)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (13412)Termination reason: Unknown
% 0.14/0.41 % (13412)Termination phase: Property scanning
% 0.14/0.41
% 0.14/0.41 % (13412)Memory used [KB]: 1023
% 0.14/0.41 % (13412)Time elapsed: 0.004 s
% 0.14/0.41 % (13412)Instructions burned: 3 (million)
% 0.14/0.41 % (13412)------------------------------
% 0.14/0.41 % (13412)------------------------------
% 0.14/0.41 % (13413)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)
% 0.14/0.42 % (13414)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)
% 0.14/0.42 % (13415)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.42 % (13413)Instruction limit reached!
% 0.14/0.42 % (13413)------------------------------
% 0.14/0.42 % (13413)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (13413)Termination reason: Unknown
% 0.14/0.42 % (13413)Termination phase: Saturation
% 0.14/0.42
% 0.14/0.42 % (13413)Memory used [KB]: 5500
% 0.14/0.42 % (13413)Time elapsed: 0.006 s
% 0.14/0.42 % (13413)Instructions burned: 8 (million)
% 0.14/0.42 % (13413)------------------------------
% 0.14/0.42 % (13413)------------------------------
% 0.20/0.42 % (13414)Instruction limit reached!
% 0.20/0.42 % (13414)------------------------------
% 0.20/0.42 % (13414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (13414)Termination reason: Unknown
% 0.20/0.42 % (13414)Termination phase: Saturation
% 0.20/0.42
% 0.20/0.42 % (13414)Memory used [KB]: 5500
% 0.20/0.42 % (13414)Time elapsed: 0.004 s
% 0.20/0.42 % (13414)Instructions burned: 4 (million)
% 0.20/0.42 % (13414)------------------------------
% 0.20/0.42 % (13414)------------------------------
% 0.20/0.42 % (13415)Instruction limit reached!
% 0.20/0.42 % (13415)------------------------------
% 0.20/0.42 % (13415)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (13415)Termination reason: Unknown
% 0.20/0.42 % (13415)Termination phase: Saturation
% 0.20/0.42
% 0.20/0.42 % (13415)Memory used [KB]: 5500
% 0.20/0.42 % (13415)Time elapsed: 0.005 s
% 0.20/0.42 % (13415)Instructions burned: 4 (million)
% 0.20/0.42 % (13415)------------------------------
% 0.20/0.42 % (13415)------------------------------
% 0.20/0.42 % (13416)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.42 % (13417)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.43 % (13418)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.43 % (13416)Instruction limit reached!
% 0.20/0.43 % (13416)------------------------------
% 0.20/0.43 % (13416)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (13418)Instruction limit reached!
% 0.20/0.43 % (13418)------------------------------
% 0.20/0.43 % (13418)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (13418)Termination reason: Unknown
% 0.20/0.43 % (13418)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (13418)Memory used [KB]: 5500
% 0.20/0.43 % (13418)Time elapsed: 0.005 s
% 0.20/0.43 % (13418)Instructions burned: 6 (million)
% 0.20/0.43 % (13418)------------------------------
% 0.20/0.43 % (13418)------------------------------
% 0.20/0.43 % (13416)Termination reason: Unknown
% 0.20/0.43 % (13416)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (13416)Memory used [KB]: 5500
% 0.20/0.43 % (13416)Time elapsed: 0.011 s
% 0.20/0.43 % (13416)Instructions burned: 18 (million)
% 0.20/0.43 % (13416)------------------------------
% 0.20/0.43 % (13416)------------------------------
% 0.20/0.43 % (13419)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.20/0.43 % (13420)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.20/0.44 % (13421)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.45 % (13422)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.45 % (13421)Instruction limit reached!
% 0.20/0.45 % (13421)------------------------------
% 0.20/0.45 % (13421)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (13421)Termination reason: Unknown
% 0.20/0.45 % (13421)Termination phase: Saturation
% 0.20/0.45
% 0.20/0.45 % (13421)Memory used [KB]: 5500
% 0.20/0.45 % (13421)Time elapsed: 0.005 s
% 0.20/0.45 % (13421)Instructions burned: 6 (million)
% 0.20/0.45 % (13421)------------------------------
% 0.20/0.45 % (13421)------------------------------
% 0.20/0.45 % (13420)Instruction limit reached!
% 0.20/0.45 % (13420)------------------------------
% 0.20/0.45 % (13420)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (13420)Termination reason: Unknown
% 0.20/0.45 % (13420)Termination phase: Saturation
% 0.20/0.45
% 0.20/0.45 % (13420)Memory used [KB]: 5628
% 0.20/0.45 % (13420)Time elapsed: 0.016 s
% 0.20/0.45 % (13420)Instructions burned: 22 (million)
% 0.20/0.45 % (13420)------------------------------
% 0.20/0.45 % (13420)------------------------------
% 0.20/0.45 % (13422)Instruction limit reached!
% 0.20/0.45 % (13422)------------------------------
% 0.20/0.45 % (13422)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (13422)Termination reason: Unknown
% 0.20/0.45 % (13422)Termination phase: Saturation
% 0.20/0.45
% 0.20/0.45 % (13422)Memory used [KB]: 5500
% 0.20/0.45 % (13422)Time elapsed: 0.005 s
% 0.20/0.45 % (13422)Instructions burned: 6 (million)
% 0.20/0.45 % (13422)------------------------------
% 0.20/0.45 % (13422)------------------------------
% 0.20/0.46 % (13424)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.20/0.46 % (13386)Instruction limit reached!
% 0.20/0.46 % (13386)------------------------------
% 0.20/0.46 % (13386)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (13386)Termination reason: Unknown
% 0.20/0.46 % (13386)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (13386)Memory used [KB]: 7675
% 0.20/0.46 % (13386)Time elapsed: 0.096 s
% 0.20/0.46 % (13386)Instructions burned: 183 (million)
% 0.20/0.46 % (13386)------------------------------
% 0.20/0.46 % (13386)------------------------------
% 0.20/0.46 % (13423)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.20/0.46 % (13425)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.20/0.47 % (13425)Instruction limit reached!
% 0.20/0.47 % (13425)------------------------------
% 0.20/0.47 % (13425)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47 % (13425)Termination reason: Unknown
% 0.20/0.47 % (13425)Termination phase: Saturation
% 0.20/0.47
% 0.20/0.47 % (13425)Memory used [KB]: 5628
% 0.20/0.47 % (13425)Time elapsed: 0.009 s
% 0.20/0.47 % (13425)Instructions burned: 19 (million)
% 0.20/0.47 % (13425)------------------------------
% 0.20/0.47 % (13425)------------------------------
% 0.20/0.47 % (13428)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)
% 0.20/0.48 % (13432)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.20/0.48 % (13399)First to succeed.
% 0.20/0.48 % (13432)Instruction limit reached!
% 0.20/0.48 % (13432)------------------------------
% 0.20/0.48 % (13432)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.48 % (13432)Termination reason: Unknown
% 0.20/0.48 % (13432)Termination phase: Saturation
% 0.20/0.48
% 0.20/0.48 % (13432)Memory used [KB]: 5756
% 0.20/0.48 % (13432)Time elapsed: 0.007 s
% 0.20/0.48 % (13432)Instructions burned: 19 (million)
% 0.20/0.48 % (13432)------------------------------
% 0.20/0.48 % (13432)------------------------------
% 0.20/0.49 % (13399)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (13399)------------------------------
% 0.20/0.49 % (13399)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.49 % (13399)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (13399)Memory used [KB]: 6140
% 0.20/0.49 % (13399)Time elapsed: 0.100 s
% 0.20/0.49 % (13399)Instructions burned: 144 (million)
% 0.20/0.49 % (13399)------------------------------
% 0.20/0.49 % (13399)------------------------------
% 0.20/0.49 % (13383)Success in time 0.121 s
% 0.20/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------