TSTP Solution File: SEV119^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV119^5 : TPTP v8.1.2. 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 : n009.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 : Sun May 5 09:41:24 EDT 2024
% Result : Theorem 0.22s 0.55s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 34
% Syntax : Number of formulae : 231 ( 18 unt; 24 typ; 0 def)
% Number of atoms : 2045 ( 206 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 5406 ( 371 ~; 474 |; 221 &;3173 @)
% ( 9 <=>; 499 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 859 ( 859 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 31 usr; 24 con; 0-2 aty)
% ( 659 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 837 ( 752 ^ 84 !; 0 ?; 837 :)
% ( 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 ) > $o ).
thf(func_def_23,type,
sK4: a > a > $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 > a > $o ).
thf(func_def_30,type,
sK11: a > a > $o ).
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 ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a > a > $o ).
thf(func_def_41,type,
sK22: a > a > $o ).
thf(f802,plain,
$false,
inference(avatar_sat_refutation,[],[f29,f36,f65,f106,f203,f207,f298,f382,f500,f558,f801]) ).
thf(f801,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f800]) ).
thf(f800,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f799]) ).
thf(f799,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f790,f681]) ).
thf(f681,plain,
( ( ( sK21 @ sK9 @ sK8 )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f680]) ).
thf(f680,plain,
( ( $false
= ( $true
=> ( sK21 @ sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(backward_demodulation,[],[f674,f679]) ).
thf(f679,plain,
( ( ( ( sK3 @ sK21 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK21 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f674]) ).
thf(f674,plain,
( ( ( ( ( sK3 @ sK21 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK21 @ Y1 @ Y0 ) ) ) ) )
=> ( sK21 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f672]) ).
thf(f672,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) )
@ sK21 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(sigma_clausification,[],[f671]) ).
thf(f671,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f670]) ).
thf(f670,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| $false )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(backward_demodulation,[],[f663,f666]) ).
thf(f666,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f663]) ).
thf(f663,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f653]) ).
thf(f653,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f651]) ).
thf(f651,plain,
( ( $true
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f631,f580]) ).
thf(f580,plain,
( ( ( sK7 @ sK9 @ sK8 )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f579]) ).
thf(f579,plain,
( ( ( $true
=> ( sK7 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f578]) ).
thf(f578,plain,
( ( ( ( $true
| ( sK4 @ sK9 @ sK8 ) )
=> ( sK7 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f577,f105]) ).
thf(f105,plain,
( ( $true
= ( sK2 @ sK9 @ sK8 ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f104,plain,
( spl0_8
<=> ( $true
= ( sK2 @ sK9 @ sK8 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f577,plain,
( ( ( ( ( sK2 @ sK9 @ sK8 )
| ( sK4 @ sK9 @ sK8 ) )
=> ( sK7 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f576]) ).
thf(f576,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK8 )
| ( sK4 @ Y0 @ sK8 ) )
=> ( sK7 @ Y0 @ sK8 ) )
@ sK9 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f563]) ).
thf(f563,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK8 )
| ( sK4 @ Y0 @ sK8 ) )
=> ( sK7 @ Y0 @ sK8 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f562]) ).
thf(f562,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ sK8 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f58]) ).
thf(f58,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f57,plain,
( spl0_5
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f631,plain,
( ! [X2: a,X1: a] :
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X1 @ X2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X1 @ X2 ) ) ) )
=> ( sK7 @ X1 @ X2 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f630]) ).
thf(f630,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) ) )
=> ( sK7 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f627]) ).
thf(f627,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) ) )
=> ( sK7 @ X1 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f626]) ).
thf(f626,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f619]) ).
thf(f619,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f618]) ).
thf(f618,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& $true ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f606,f616]) ).
thf(f616,plain,
( ( ( sK3 @ sK7 )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f606]) ).
thf(f606,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK3 @ sK7 ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f594]) ).
thf(f594,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK3 @ sK7 ) )
=> ( sK7 @ sK5 @ sK6 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f593]) ).
thf(f593,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f32]) ).
thf(f32,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f31,plain,
( spl0_3
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f790,plain,
( ( ( sK21 @ sK9 @ sK8 )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f788]) ).
thf(f788,plain,
( ( $true
= ( $true
=> ( sK21 @ sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f775,f105]) ).
thf(f775,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X2 @ X1 )
=> ( sK21 @ X2 @ X1 ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f774]) ).
thf(f774,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK21 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(pi_clausification,[],[f758]) ).
thf(f758,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK21 @ Y0 @ X1 ) ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f756]) ).
thf(f756,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK21 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(pi_clausification,[],[f682]) ).
thf(f682,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK21 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f679]) ).
thf(f558,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f557]) ).
thf(f557,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f556]) ).
thf(f556,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(boolean_simplification,[],[f555]) ).
thf(f555,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(boolean_simplification,[],[f554]) ).
thf(f554,plain,
( ( $true
= ( ~ ( $true
| ( sK4 @ sK20 @ sK19 ) ) ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(forward_demodulation,[],[f553,f549]) ).
thf(f549,plain,
( ( ( sK2 @ sK20 @ sK19 )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f547]) ).
thf(f547,plain,
( ( ( ( sK2 @ sK20 @ sK19 )
=> ( sK12 @ sK20 @ sK19 ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f546]) ).
thf(f546,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK19 )
=> ( sK12 @ Y0 @ sK19 ) )
@ sK20 )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(sigma_clausification,[],[f543]) ).
thf(f543,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK19 )
=> ( sK12 @ Y0 @ sK19 ) ) ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f541]) ).
thf(f541,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ sK19 )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(sigma_clausification,[],[f528]) ).
thf(f528,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(not_proxy_clausification,[],[f522]) ).
thf(f522,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(boolean_simplification,[],[f521]) ).
thf(f521,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(forward_demodulation,[],[f512,f367]) ).
thf(f367,plain,
( ( ( sK12 @ sK13 @ sK14 )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f366]) ).
thf(f366,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
=> ( sK12 @ sK13 @ sK14 ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f365]) ).
thf(f365,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK13 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK13 @ Y0 ) ) ) )
=> ( sK12 @ sK13 @ Y0 ) )
@ sK14 )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(sigma_clausification,[],[f364]) ).
thf(f364,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK13 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK13 @ Y0 ) ) ) )
=> ( sK12 @ sK13 @ Y0 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f360]) ).
thf(f360,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK12 @ Y0 @ Y1 ) ) )
@ sK13 )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(sigma_clausification,[],[f351]) ).
thf(f351,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f319]) ).
thf(f319,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[],[f316]) ).
thf(f316,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& $true ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(backward_demodulation,[],[f313,f315]) ).
thf(f315,plain,
( ( $true
= ( sK3 @ sK12 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f304]) ).
thf(f304,plain,
( ( $true
= ( ( sK3 @ sK12 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f302]) ).
thf(f302,plain,
( ( ( ( ( sK3 @ sK12 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
=> ( sK12 @ sK5 @ sK6 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f301]) ).
thf(f301,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f35]) ).
thf(f35,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f34,plain,
( spl0_4
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f313,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& ( sK3 @ sK12 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[],[f312]) ).
thf(f312,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& ( sK3 @ sK12 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f310,f303]) ).
thf(f303,plain,
( ( ( sK12 @ sK5 @ sK6 )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f302]) ).
thf(f310,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( sK3 @ X1 ) )
=> ( X1 @ sK5 @ sK6 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f309]) ).
thf(f309,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ X1 )
= $true )
| ~ 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] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ 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] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f512,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
=> ( sK12 @ sK13 @ sK14 ) )
= $true )
| ~ spl0_4
| ~ spl0_12 ),
inference(boolean_simplification,[],[f510]) ).
thf(f510,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
=> ( sK12 @ sK13 @ sK14 ) )
= $true )
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f504,f315]) ).
thf(f504,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( sK3 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK13 @ sK14 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f503]) ).
thf(f503,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) )
@ X1 )
= $true )
| ~ spl0_12 ),
inference(pi_clausification,[],[f381]) ).
thf(f381,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f380]) ).
thf(f380,plain,
( spl0_12
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f553,plain,
( ( ( ~ ( ( sK2 @ sK20 @ sK19 )
| ( sK4 @ sK20 @ sK19 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(boolean_simplification,[],[f552]) ).
thf(f552,plain,
( ( ( ( ( sK2 @ sK20 @ sK19 )
| ( sK4 @ sK20 @ sK19 ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f327,f551]) ).
thf(f551,plain,
( ( ( sK12 @ sK20 @ sK19 )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(boolean_simplification,[],[f550]) ).
thf(f550,plain,
( ( ( $true
=> ( sK12 @ sK20 @ sK19 ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_12 ),
inference(backward_demodulation,[],[f547,f549]) ).
thf(f327,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X2 @ X1 )
| ( sK4 @ X2 @ X1 ) )
=> ( sK12 @ X2 @ X1 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f326]) ).
thf(f326,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK12 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f321]) ).
thf(f321,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK4 @ Y0 @ X1 ) )
=> ( sK12 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f320]) ).
thf(f320,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f318]) ).
thf(f318,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f317]) ).
thf(f317,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f304,f315]) ).
thf(f500,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f499]) ).
thf(f499,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f498]) ).
thf(f498,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[],[f497]) ).
thf(f497,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[],[f496]) ).
thf(f496,plain,
( ( ( ~ ( ( sK2 @ sK17 @ sK18 )
| $true ) )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f495,f491]) ).
thf(f491,plain,
( ( ( sK4 @ sK17 @ sK18 )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f489]) ).
thf(f489,plain,
( ( ( ( sK4 @ sK17 @ sK18 )
=> ( sK12 @ sK17 @ sK18 ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f488]) ).
thf(f488,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ sK17 @ Y0 )
=> ( sK12 @ sK17 @ Y0 ) )
@ sK18 )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(sigma_clausification,[],[f487]) ).
thf(f487,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK17 @ Y0 )
=> ( sK12 @ sK17 @ Y0 ) ) ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f483]) ).
thf(f483,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK12 @ Y0 @ Y1 ) ) )
@ sK17 )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(sigma_clausification,[],[f480]) ).
thf(f480,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(not_proxy_clausification,[],[f402]) ).
thf(f402,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[],[f401]) ).
thf(f401,plain,
( ( ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f400,f315]) ).
thf(f400,plain,
( ( $true
= ( ~ ( ( sK3 @ sK12 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[],[f397]) ).
thf(f397,plain,
( ( ( ( ( sK3 @ sK12 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f389,f367]) ).
thf(f389,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( sK3 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK13 @ sK14 ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f388]) ).
thf(f388,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) )
@ X1 )
= $true )
| ~ spl0_11 ),
inference(pi_clausification,[],[f378]) ).
thf(f378,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f377]) ).
thf(f377,plain,
( spl0_11
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f495,plain,
( ( ( ~ ( ( sK2 @ sK17 @ sK18 )
| ( sK4 @ sK17 @ sK18 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[],[f494]) ).
thf(f494,plain,
( ( $true
= ( ( ( sK2 @ sK17 @ sK18 )
| ( sK4 @ sK17 @ sK18 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f327,f493]) ).
thf(f493,plain,
( ( ( sK12 @ sK17 @ sK18 )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(boolean_simplification,[],[f492]) ).
thf(f492,plain,
( ( ( $true
=> ( sK12 @ sK17 @ sK18 ) )
= $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_11 ),
inference(backward_demodulation,[],[f489,f491]) ).
thf(f382,plain,
( spl0_11
| spl0_12
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f375,f34,f24,f380,f377]) ).
thf(f375,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f368]) ).
thf(f368,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f366]) ).
thf(f298,plain,
( spl0_5
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f297,f31,f27,f57]) ).
thf(f27,plain,
( spl0_2
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f297,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f296,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f264,f222]) ).
thf(f222,plain,
( ( ( sK7 @ sK5 @ sK6 )
= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f221]) ).
thf(f221,plain,
( ( $false
= ( $true
=> ( sK7 @ sK5 @ sK6 ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f218,f220]) ).
thf(f220,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK3 @ sK7 ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f218]) ).
thf(f218,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK3 @ sK7 ) )
=> ( sK7 @ sK5 @ sK6 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f217]) ).
thf(f217,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f32]) ).
thf(f264,plain,
( ( ( sK7 @ sK5 @ sK6 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f262]) ).
thf(f262,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( sK7 @ sK5 @ sK6 )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f211,f231]) ).
thf(f231,plain,
( ( ( sK3 @ sK7 )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f230]) ).
thf(f230,plain,
( ( $true
= ( $true
& ( sK3 @ sK7 ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f220,f229]) ).
thf(f229,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f220]) ).
thf(f211,plain,
( ! [X1: a > a > $o] :
( ( ( ( sK3 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( X1 @ sK5 @ sK6 )
= $true ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f90]) ).
thf(f90,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( sK3 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK5 @ sK6 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f88]) ).
thf(f88,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f28]) ).
thf(f28,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f207,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f206]) ).
thf(f206,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f205,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[],[f28,f35]) ).
thf(f203,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f202]) ).
thf(f202,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f201,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f195,f169]) ).
thf(f169,plain,
( ( ( sK11 @ sK9 @ sK8 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f168]) ).
thf(f168,plain,
( ( ( $true
=> ( sK11 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f161,f167]) ).
thf(f167,plain,
( ( $true
= ( ( sK3 @ sK11 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f161]) ).
thf(f161,plain,
( ( ( ( ( sK3 @ sK11 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
=> ( sK11 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f158]) ).
thf(f158,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) )
@ sK11 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f153]) ).
thf(f153,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f152]) ).
thf(f152,plain,
( ( ( $false
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f139,f149]) ).
thf(f149,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f139]) ).
thf(f139,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(not_proxy_clausification,[],[f117]) ).
thf(f117,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f115]) ).
thf(f115,plain,
( ( $true
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 @ sK8 ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f112,f82]) ).
thf(f82,plain,
( ( ( sK7 @ sK9 @ sK8 )
= $false )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f72]) ).
thf(f72,plain,
( ( ( ( ( sK2 @ sK9 @ sK8 )
| ( sK4 @ sK9 @ sK8 ) )
=> ( sK7 @ sK9 @ sK8 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f71]) ).
thf(f71,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK8 )
| ( sK4 @ Y0 @ sK8 ) )
=> ( sK7 @ Y0 @ sK8 ) )
@ sK9 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f68]) ).
thf(f68,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK8 )
| ( sK4 @ Y0 @ sK8 ) )
=> ( sK7 @ Y0 @ sK8 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f67]) ).
thf(f67,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ sK8 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f58]) ).
thf(f112,plain,
( ! [X2: a,X1: a] :
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X1 @ X2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ X1 @ X2 ) ) ) )
=> ( sK7 @ X1 @ X2 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f111]) ).
thf(f111,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) ) )
=> ( sK7 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f110]) ).
thf(f110,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ X1 @ Y0 ) ) ) )
=> ( sK7 @ X1 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f109]) ).
thf(f109,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f92]) ).
thf(f92,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f45,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK3 @ sK7 ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f43]) ).
thf(f43,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK3 @ sK7 ) )
=> ( sK7 @ sK5 @ sK6 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f42]) ).
thf(f42,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f32]) ).
thf(f195,plain,
( ( ( sK11 @ sK9 @ sK8 )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f194]) ).
thf(f194,plain,
( ( $true
= ( $true
=> ( sK11 @ sK9 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f187,f102]) ).
thf(f102,plain,
( ( ( sK4 @ sK9 @ sK8 )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f101,plain,
( spl0_7
<=> ( ( sK4 @ sK9 @ sK8 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f187,plain,
( ! [X2: a,X1: a] :
( ( ( sK4 @ X1 @ X2 )
=> ( sK11 @ X1 @ X2 ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f186]) ).
thf(f186,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK11 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f182]) ).
thf(f182,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK11 @ X1 @ Y0 ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f181]) ).
thf(f181,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f178]) ).
thf(f178,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f177]) ).
thf(f177,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK11 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f167,f176]) ).
thf(f176,plain,
( ( $true
= ( sK3 @ sK11 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f167]) ).
thf(f106,plain,
( spl0_7
| spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f99,f57,f104,f101]) ).
thf(f99,plain,
( ( $true
= ( sK2 @ sK9 @ sK8 ) )
| ( ( sK4 @ sK9 @ sK8 )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f83]) ).
thf(f83,plain,
( ( ( ( sK2 @ sK9 @ sK8 )
| ( sK4 @ sK9 @ sK8 ) )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f72]) ).
thf(f65,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f64]) ).
thf(f64,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f63,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f25,f32]) ).
thf(f36,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f22,f34,f31]) ).
thf(f22,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f20]) ).
thf(f20,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ),
inference(beta_eta_normalization,[],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( 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] :
( ( ( sK3 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK3 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK4 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK3 @ Y1 ) )
=> ( Y1 @ sK5 @ Y0 ) ) )
@ sK6 ) ),
inference(negative_extensionality,[],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK3 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK3 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK4 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK3 @ Y1 ) )
=> ( Y1 @ sK5 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK3 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK5 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( 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] :
( ( ( sK3 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK3 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK4 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK3 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK3 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK3 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK4 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK3 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK3 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK3 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK4 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK3 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK3 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a > a > $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] :
( ( ( sK3 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK3 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK3 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $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] :
( ( ( sK3 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK3 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK3 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: ( a > a > $o ) > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $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] :
( ( ( Y0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( sK2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( Y0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( Y0 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y0: ( a > a > $o ) > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $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] :
( ( ( Y0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( sK2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( Y0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( Y0 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( Y0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $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] :
( ( ( Y1 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y1 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y2 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( Y1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( Y1 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $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] :
( ( ( Y1 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y1 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y2 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( Y1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( Y1 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $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] :
( ( ( Y1 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y1 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y2 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( Y1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( Y1 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( ( a > a > $o ) > $o )
@ ^ [Y1: ( a > a > $o ) > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $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] :
( ( ( Y1 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y0 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( Y1 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y2 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( Y1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( Y1 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X1 @ X5 )
& ! [X6: a,X7: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X0 @ X10 @ X9 )
=> ( X8 @ X10 @ X9 ) )
& ( X1 @ X8 ) )
=> ( X8 @ X7 @ X6 ) )
| ! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X2 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X1 @ X11 ) )
=> ( X11 @ X7 @ X6 ) ) )
=> ( X5 @ X7 @ X6 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X14: a,X15: a] :
! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ( ( X0 @ X17 @ X18 )
| ( X2 @ X17 @ X18 ) )
=> ( X16 @ X17 @ X18 ) )
& ( X1 @ X16 ) )
=> ( X16 @ X14 @ X15 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > a > $o,X0: ( a > a > $o ) > $o,X1: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X7: a,X6: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X2 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
& ( X0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X2: a > a > $o,X0: ( a > a > $o ) > $o,X1: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ( X0 @ X5 )
& ! [X7: a,X6: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X10: a,X9: a] :
( ( X2 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) )
| ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ( X0 @ X8 ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X2 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
& ( X0 @ X5 ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.cA17ylHlAt/Vampire---4.8_28674',cTHM252_pme) ).
thf(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f21,f27,f24]) ).
thf(f21,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK3 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK6 ) ) )
= $true )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK3 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK3 @ Y0 ) )
=> ( Y0 @ sK5 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEV119^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % 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
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 11:51:25 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.cA17ylHlAt/Vampire---4.8_28674
% 0.15/0.38 % (28892)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38 % (28890)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 Vampire---4 for (2999ds/27Mi)
% 0.15/0.38 % (28888)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.38 % (28891)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38 % (28894)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.38 % (28889)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 Vampire---4 for (2999ds/4Mi)
% 0.15/0.39 % (28893)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.39 % (28892)Instruction limit reached!
% 0.15/0.39 % (28892)------------------------------
% 0.15/0.39 % (28892)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (28895)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.39 % (28892)Termination reason: Unknown
% 0.15/0.39 % (28892)Termination phase: Preprocessing 1
% 0.15/0.39
% 0.15/0.39 % (28892)Memory used [KB]: 1023
% 0.15/0.39 % (28892)Time elapsed: 0.004 s
% 0.15/0.39 % (28892)Instructions burned: 2 (million)
% 0.15/0.39 % (28892)------------------------------
% 0.15/0.39 % (28892)------------------------------
% 0.15/0.39 % (28891)Instruction limit reached!
% 0.15/0.39 % (28891)------------------------------
% 0.15/0.39 % (28891)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (28891)Termination reason: Unknown
% 0.15/0.39 % (28891)Termination phase: Property scanning
% 0.15/0.39
% 0.15/0.39 % (28891)Memory used [KB]: 1023
% 0.15/0.39 % (28891)Time elapsed: 0.004 s
% 0.15/0.39 % (28891)Instructions burned: 3 (million)
% 0.15/0.39 % (28891)------------------------------
% 0.15/0.39 % (28891)------------------------------
% 0.15/0.39 % (28895)Instruction limit reached!
% 0.15/0.39 % (28895)------------------------------
% 0.15/0.39 % (28895)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (28895)Termination reason: Unknown
% 0.15/0.39 % (28895)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (28895)Memory used [KB]: 1023
% 0.15/0.39 % (28895)Time elapsed: 0.004 s
% 0.15/0.39 % (28895)Instructions burned: 3 (million)
% 0.15/0.39 % (28895)------------------------------
% 0.15/0.39 % (28895)------------------------------
% 0.15/0.39 % (28889)Instruction limit reached!
% 0.15/0.39 % (28889)------------------------------
% 0.15/0.39 % (28889)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (28889)Termination reason: Unknown
% 0.15/0.39 % (28889)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (28889)Memory used [KB]: 5500
% 0.15/0.39 % (28889)Time elapsed: 0.005 s
% 0.15/0.39 % (28889)Instructions burned: 4 (million)
% 0.15/0.39 % (28889)------------------------------
% 0.15/0.39 % (28889)------------------------------
% 0.15/0.40 % (28894)Instruction limit reached!
% 0.15/0.40 % (28894)------------------------------
% 0.15/0.40 % (28894)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (28894)Termination reason: Unknown
% 0.15/0.40 % (28894)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (28894)Memory used [KB]: 5500
% 0.15/0.40 % (28894)Time elapsed: 0.018 s
% 0.15/0.40 % (28894)Instructions burned: 19 (million)
% 0.15/0.40 % (28894)------------------------------
% 0.15/0.40 % (28894)------------------------------
% 0.15/0.41 % (28890)Instruction limit reached!
% 0.15/0.41 % (28890)------------------------------
% 0.15/0.41 % (28890)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (28890)Termination reason: Unknown
% 0.15/0.41 % (28890)Termination phase: Saturation
% 0.15/0.41
% 0.15/0.41 % (28890)Memory used [KB]: 5756
% 0.15/0.41 % (28890)Time elapsed: 0.024 s
% 0.15/0.41 % (28890)Instructions burned: 28 (million)
% 0.15/0.41 % (28890)------------------------------
% 0.15/0.41 % (28890)------------------------------
% 0.15/0.41 % (28911)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 Vampire---4 for (2999ds/37Mi)
% 0.15/0.41 % (28914)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 Vampire---4 for (2999ds/15Mi)
% 0.15/0.41 % (28915)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.41 % (28916)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 Vampire---4 for (2999ds/1041Mi)
% 0.15/0.42 % (28915)Instruction limit reached!
% 0.15/0.42 % (28915)------------------------------
% 0.15/0.42 % (28915)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (28915)Termination reason: Unknown
% 0.15/0.42 % (28915)Termination phase: Saturation
% 0.15/0.42
% 0.15/0.42 % (28915)Memory used [KB]: 1023
% 0.15/0.42 % (28915)Time elapsed: 0.005 s
% 0.15/0.42 % (28915)Instructions burned: 3 (million)
% 0.15/0.42 % (28915)------------------------------
% 0.15/0.42 % (28915)------------------------------
% 0.15/0.43 % (28914)Instruction limit reached!
% 0.15/0.43 % (28914)------------------------------
% 0.15/0.43 % (28914)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (28914)Termination reason: Unknown
% 0.15/0.43 % (28914)Termination phase: Saturation
% 0.15/0.43
% 0.15/0.43 % (28914)Memory used [KB]: 5756
% 0.15/0.43 % (28914)Time elapsed: 0.016 s
% 0.15/0.43 % (28914)Instructions burned: 15 (million)
% 0.15/0.43 % (28914)------------------------------
% 0.15/0.43 % (28914)------------------------------
% 0.15/0.43 % (28917)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.43 % (28918)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.22/0.43 % (28917)Instruction limit reached!
% 0.22/0.43 % (28917)------------------------------
% 0.22/0.43 % (28917)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (28917)Termination reason: Unknown
% 0.22/0.43 % (28917)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (28917)Memory used [KB]: 1023
% 0.22/0.43 % (28917)Time elapsed: 0.009 s
% 0.22/0.43 % (28917)Instructions burned: 7 (million)
% 0.22/0.43 % (28917)------------------------------
% 0.22/0.43 % (28917)------------------------------
% 0.22/0.44 % (28911)Instruction limit reached!
% 0.22/0.44 % (28911)------------------------------
% 0.22/0.44 % (28911)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (28911)Termination reason: Unknown
% 0.22/0.44 % (28911)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (28911)Memory used [KB]: 5628
% 0.22/0.44 % (28911)Time elapsed: 0.033 s
% 0.22/0.44 % (28911)Instructions burned: 37 (million)
% 0.22/0.44 % (28911)------------------------------
% 0.22/0.44 % (28911)------------------------------
% 0.22/0.44 % (28919)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 Vampire---4 for (2999ds/3Mi)
% 0.22/0.44 % (28919)Instruction limit reached!
% 0.22/0.44 % (28919)------------------------------
% 0.22/0.44 % (28919)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (28919)Termination reason: Unknown
% 0.22/0.44 % (28919)Termination phase: Preprocessing 3
% 0.22/0.44
% 0.22/0.44 % (28919)Memory used [KB]: 1023
% 0.22/0.44 % (28919)Time elapsed: 0.005 s
% 0.22/0.44 % (28919)Instructions burned: 3 (million)
% 0.22/0.44 % (28919)------------------------------
% 0.22/0.44 % (28919)------------------------------
% 0.22/0.44 % (28918)Instruction limit reached!
% 0.22/0.44 % (28918)------------------------------
% 0.22/0.44 % (28918)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (28918)Termination reason: Unknown
% 0.22/0.44 % (28918)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (28918)Memory used [KB]: 5756
% 0.22/0.44 % (28918)Time elapsed: 0.017 s
% 0.22/0.44 % (28918)Instructions burned: 16 (million)
% 0.22/0.44 % (28918)------------------------------
% 0.22/0.44 % (28918)------------------------------
% 0.22/0.45 % (28920)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 Vampire---4 for (2999ds/3Mi)
% 0.22/0.45 % (28920)Instruction limit reached!
% 0.22/0.45 % (28920)------------------------------
% 0.22/0.45 % (28920)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (28920)Termination reason: Unknown
% 0.22/0.45 % (28920)Termination phase: Preprocessing 3
% 0.22/0.45
% 0.22/0.45 % (28920)Memory used [KB]: 1023
% 0.22/0.45 % (28920)Time elapsed: 0.005 s
% 0.22/0.45 % (28920)Instructions burned: 3 (million)
% 0.22/0.45 % (28920)------------------------------
% 0.22/0.45 % (28920)------------------------------
% 0.22/0.46 % (28921)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.46 % (28922)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.46 % (28922)Instruction limit reached!
% 0.22/0.46 % (28922)------------------------------
% 0.22/0.46 % (28922)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (28922)Termination reason: Unknown
% 0.22/0.46 % (28922)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (28922)Memory used [KB]: 5500
% 0.22/0.46 % (28922)Time elapsed: 0.005 s
% 0.22/0.46 % (28922)Instructions burned: 3 (million)
% 0.22/0.46 % (28922)------------------------------
% 0.22/0.46 % (28922)------------------------------
% 0.22/0.46 % (28921)Instruction limit reached!
% 0.22/0.46 % (28921)------------------------------
% 0.22/0.46 % (28921)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (28921)Termination reason: Unknown
% 0.22/0.46 % (28921)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (28921)Memory used [KB]: 5500
% 0.22/0.46 % (28921)Time elapsed: 0.009 s
% 0.22/0.46 % (28921)Instructions burned: 7 (million)
% 0.22/0.46 % (28921)------------------------------
% 0.22/0.46 % (28921)------------------------------
% 0.22/0.47 % (28924)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.22/0.47 % (28923)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.22/0.47 % (28923)Instruction limit reached!
% 0.22/0.47 % (28923)------------------------------
% 0.22/0.47 % (28923)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (28923)Termination reason: Unknown
% 0.22/0.47 % (28923)Termination phase: Saturation
% 0.22/0.47
% 0.22/0.47 % (28923)Memory used [KB]: 5500
% 0.22/0.47 % (28923)Time elapsed: 0.005 s
% 0.22/0.47 % (28923)Instructions burned: 4 (million)
% 0.22/0.47 % (28923)------------------------------
% 0.22/0.47 % (28923)------------------------------
% 0.22/0.47 % (28925)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.22/0.48 % (28924)Instruction limit reached!
% 0.22/0.48 % (28924)------------------------------
% 0.22/0.48 % (28924)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (28924)Termination reason: Unknown
% 0.22/0.48 % (28924)Termination phase: Saturation
% 0.22/0.48
% 0.22/0.48 % (28924)Memory used [KB]: 5500
% 0.22/0.48 % (28924)Time elapsed: 0.015 s
% 0.22/0.48 % (28924)Instructions burned: 19 (million)
% 0.22/0.48 % (28924)------------------------------
% 0.22/0.48 % (28924)------------------------------
% 0.22/0.48 % (28926)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.49 % (28926)Instruction limit reached!
% 0.22/0.49 % (28926)------------------------------
% 0.22/0.49 % (28926)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (28926)Termination reason: Unknown
% 0.22/0.49 % (28926)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (28926)Memory used [KB]: 5500
% 0.22/0.49 % (28926)Time elapsed: 0.006 s
% 0.22/0.49 % (28926)Instructions burned: 7 (million)
% 0.22/0.49 % (28926)------------------------------
% 0.22/0.49 % (28926)------------------------------
% 0.22/0.49 % (28928)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 Vampire---4 for (2999ds/21Mi)
% 0.22/0.49 % (28927)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 Vampire---4 for (2999ds/902Mi)
% 0.22/0.50 % (28929)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2998ds/5Mi)
% 0.22/0.50 % (28929)Instruction limit reached!
% 0.22/0.50 % (28929)------------------------------
% 0.22/0.50 % (28929)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50 % (28929)Termination reason: Unknown
% 0.22/0.50 % (28929)Termination phase: Saturation
% 0.22/0.50
% 0.22/0.50 % (28929)Memory used [KB]: 5500
% 0.22/0.50 % (28929)Time elapsed: 0.005 s
% 0.22/0.50 % (28929)Instructions burned: 6 (million)
% 0.22/0.50 % (28929)------------------------------
% 0.22/0.50 % (28929)------------------------------
% 0.22/0.50 % (28928)Instruction limit reached!
% 0.22/0.50 % (28928)------------------------------
% 0.22/0.50 % (28928)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50 % (28928)Termination reason: Unknown
% 0.22/0.50 % (28928)Termination phase: Saturation
% 0.22/0.50
% 0.22/0.50 % (28928)Memory used [KB]: 5628
% 0.22/0.50 % (28928)Time elapsed: 0.015 s
% 0.22/0.50 % (28928)Instructions burned: 21 (million)
% 0.22/0.50 % (28928)------------------------------
% 0.22/0.50 % (28928)------------------------------
% 0.22/0.50 % (28930)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 Vampire---4 for (2998ds/6Mi)
% 0.22/0.51 % (28930)Instruction limit reached!
% 0.22/0.51 % (28930)------------------------------
% 0.22/0.51 % (28930)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (28930)Termination reason: Unknown
% 0.22/0.51 % (28930)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (28930)Memory used [KB]: 5500
% 0.22/0.51 % (28930)Time elapsed: 0.005 s
% 0.22/0.51 % (28930)Instructions burned: 7 (million)
% 0.22/0.51 % (28930)------------------------------
% 0.22/0.51 % (28930)------------------------------
% 0.22/0.51 % (28888)Instruction limit reached!
% 0.22/0.51 % (28888)------------------------------
% 0.22/0.51 % (28888)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (28888)Termination reason: Unknown
% 0.22/0.51 % (28888)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (28888)Memory used [KB]: 7675
% 0.22/0.51 % (28888)Time elapsed: 0.125 s
% 0.22/0.51 % (28888)Instructions burned: 184 (million)
% 0.22/0.51 % (28888)------------------------------
% 0.22/0.51 % (28888)------------------------------
% 0.22/0.51 % (28931)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2998ds/377Mi)
% 0.22/0.52 % (28932)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 Vampire---4 for (2998ds/779Mi)
% 0.22/0.52 % (28933)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 Vampire---4 for (2998ds/19Mi)
% 0.22/0.52 % (28934)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2998ds/879Mi)
% 0.22/0.53 % (28933)Instruction limit reached!
% 0.22/0.53 % (28933)------------------------------
% 0.22/0.53 % (28933)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53 % (28933)Termination reason: Unknown
% 0.22/0.53 % (28933)Termination phase: Saturation
% 0.22/0.53
% 0.22/0.53 % (28933)Memory used [KB]: 5500
% 0.22/0.53 % (28933)Time elapsed: 0.010 s
% 0.22/0.53 % (28933)Instructions burned: 19 (million)
% 0.22/0.53 % (28933)------------------------------
% 0.22/0.53 % (28933)------------------------------
% 0.22/0.54 % (28916)First to succeed.
% 0.22/0.54 % (28935)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.22/0.55 % (28935)Instruction limit reached!
% 0.22/0.55 % (28935)------------------------------
% 0.22/0.55 % (28935)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (28935)Termination reason: Unknown
% 0.22/0.55 % (28935)Termination phase: Saturation
% 0.22/0.55
% 0.22/0.55 % (28935)Memory used [KB]: 5756
% 0.22/0.55 % (28935)Time elapsed: 0.010 s
% 0.22/0.55 % (28935)Instructions burned: 19 (million)
% 0.22/0.55 % (28935)------------------------------
% 0.22/0.55 % (28935)------------------------------
% 0.22/0.55 % (28916)Refutation found. Thanks to Tanya!
% 0.22/0.55 % SZS status Theorem for Vampire---4
% 0.22/0.55 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.55 % (28916)------------------------------
% 0.22/0.55 % (28916)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (28916)Termination reason: Refutation
% 0.22/0.55
% 0.22/0.55 % (28916)Memory used [KB]: 6140
% 0.22/0.55 % (28916)Time elapsed: 0.138 s
% 0.22/0.55 % (28916)Instructions burned: 165 (million)
% 0.22/0.55 % (28916)------------------------------
% 0.22/0.55 % (28916)------------------------------
% 0.22/0.55 % (28885)Success in time 0.168 s
% 0.22/0.55 % Vampire---4.8 exiting
%------------------------------------------------------------------------------