TSTP Solution File: SEV154^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV154^5 : 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 : n016.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 04:12:10 EDT 2024
% Result : Theorem 1.99s 0.63s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 53
% Syntax : Number of formulae : 422 ( 28 unt; 31 typ; 0 def)
% Number of atoms : 4307 ( 365 equ; 0 cnn)
% Maximal formula atoms : 5 ( 11 avg)
% Number of connectives : 12450 ( 577 ~;1191 |; 826 &;7221 @)
% ( 21 <=>;1210 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 631 ( 631 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 50 usr; 47 con; 0-2 aty)
% (1404 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1635 (1463 ^ 171 !; 0 ?;1635 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_21,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK2: a > a > $o ).
thf(func_def_23,type,
sK3: a ).
thf(func_def_24,type,
sK4: a ).
thf(func_def_25,type,
sK5: a > a > $o ).
thf(func_def_26,type,
sK6: a > $o ).
thf(func_def_27,type,
sK7: a ).
thf(func_def_28,type,
sK8: a ).
thf(func_def_29,type,
sK9: a ).
thf(func_def_30,type,
sK10: a > $o ).
thf(func_def_31,type,
sK11: a ).
thf(func_def_32,type,
sK12: a ).
thf(func_def_33,type,
sK13: a > $o ).
thf(func_def_34,type,
sK14: a ).
thf(func_def_35,type,
sK15: a ).
thf(func_def_36,type,
sK16: a ).
thf(func_def_37,type,
sK17: a ).
thf(func_def_38,type,
sK18: a ).
thf(func_def_39,type,
sK19: a ).
thf(func_def_40,type,
sK20: a ).
thf(func_def_41,type,
sK21: a ).
thf(func_def_42,type,
sK22: a ).
thf(func_def_43,type,
sK23: a ).
thf(func_def_44,type,
sK24: a ).
thf(func_def_45,type,
sK25: a ).
thf(func_def_46,type,
sK26: a ).
thf(func_def_47,type,
sK27: a ).
thf(func_def_48,type,
sK28: a ).
thf(func_def_49,type,
sK29: a ).
thf(f2953,plain,
$false,
inference(avatar_sat_refutation,[],[f50,f66,f226,f282,f397,f508,f518,f580,f668,f974,f1044,f1050,f1058,f1109,f1135,f1139,f1528,f1887,f1934,f2060,f2575,f2900]) ).
thf(f2900,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f2899]) ).
thf(f2899,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f2898]) ).
thf(f2898,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f2897,f2726]) ).
thf(f2726,plain,
( ( $false
= ( sK10 @ sK16 ) )
| ~ spl0_5
| ~ spl0_18 ),
inference(boolean_simplification,[],[f2725]) ).
thf(f2725,plain,
( ( ( $true
=> ( sK10 @ sK16 ) )
= $false )
| ~ spl0_5
| ~ spl0_18 ),
inference(backward_demodulation,[],[f2708,f2724]) ).
thf(f2724,plain,
( ( $true
= ( sK10 @ sK17 ) )
| ~ spl0_5
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f2708]) ).
thf(f2708,plain,
( ( ( ( sK10 @ sK17 )
=> ( sK10 @ sK16 ) )
= $false )
| ~ spl0_5
| ~ spl0_18 ),
inference(boolean_simplification,[],[f2707]) ).
thf(f2707,plain,
( ( ( ( ( sK10 @ sK17 )
& $true )
=> ( sK10 @ sK16 ) )
= $false )
| ~ spl0_5
| ~ spl0_18 ),
inference(boolean_simplification,[],[f2706]) ).
thf(f2706,plain,
( ( ( ( ( sK10 @ sK17 )
& ( ( sK5 @ sK17 @ sK16 )
| $true ) )
=> ( sK10 @ sK16 ) )
= $false )
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f2705,f579]) ).
thf(f579,plain,
( ( ( sK2 @ sK17 @ sK16 )
= $true )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f578]) ).
thf(f578,plain,
( spl0_18
<=> ( ( sK2 @ sK17 @ sK16 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f2705,plain,
( ( ( ( ( sK10 @ sK17 )
& ( ( sK5 @ sK17 @ sK16 )
| ( sK2 @ sK17 @ sK16 ) ) )
=> ( sK10 @ sK16 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f2704]) ).
thf(f2704,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ sK16 )
| ( sK2 @ Y0 @ sK16 ) ) )
=> ( sK10 @ sK16 ) )
@ sK17 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f2687]) ).
thf(f2687,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ sK16 )
| ( sK2 @ Y0 @ sK16 ) ) )
=> ( sK10 @ sK16 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f2685]) ).
thf(f2685,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) )
@ sK16 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f222]) ).
thf(f222,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f221]) ).
thf(f221,plain,
( spl0_5
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f2897,plain,
( ( $true
= ( sK10 @ sK16 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(boolean_simplification,[],[f2896]) ).
thf(f2896,plain,
( ( ( $true
=> ( sK10 @ sK16 ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f2859,f2724]) ).
thf(f2859,plain,
( ( ( ( sK10 @ sK17 )
=> ( sK10 @ sK16 ) )
= $true )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[],[f2858]) ).
thf(f2858,plain,
( ( ( ( ( sK10 @ sK17 )
& $true )
=> ( sK10 @ sK16 ) )
= $true )
| ~ spl0_3
| ~ spl0_18 ),
inference(boolean_simplification,[],[f2800]) ).
thf(f2800,plain,
( ( $true
= ( ( ( sK10 @ sK17 )
& ( ( sK5 @ sK17 @ sK16 )
| $true ) )
=> ( sK10 @ sK16 ) ) )
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f2773,f579]) ).
thf(f2773,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK10 @ X1 )
& ( ( sK5 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) ) )
=> ( sK10 @ X2 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f2772]) ).
thf(f2772,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK5 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f2758]) ).
thf(f2758,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK5 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f2757]) ).
thf(f2757,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f2740]) ).
thf(f2740,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f2739]) ).
thf(f2739,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f2634,f2737]) ).
thf(f2737,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f2634]) ).
thf(f2634,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f2621]) ).
thf(f2621,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> ( sK10 @ sK9 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f2620]) ).
thf(f2620,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f2611]) ).
thf(f2611,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f2607]) ).
thf(f2607,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK5 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f2606]) ).
thf(f2606,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK7 @ Y2 )
| ( sK5 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK5 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f2597]) ).
thf(f2597,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK7 @ Y2 )
| ( sK5 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK5 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f2596]) ).
thf(f2596,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK7 @ Y3 )
| ( sK5 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK5 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f2587]) ).
thf(f2587,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK7 @ Y3 )
| ( sK5 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK5 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f2586]) ).
thf(f2586,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f62]) ).
thf(f62,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f61,plain,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f2575,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f2574]) ).
thf(f2574,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f2573]) ).
thf(f2573,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f2572]) ).
thf(f2572,plain,
( ( ~ $true = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f2571]) ).
thf(f2571,plain,
( ( ( ~ ( ( sK2 @ sK11 @ sK28 )
| $true ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f2561,f2428]) ).
thf(f2428,plain,
( ( ( sK5 @ sK11 @ sK28 )
= $true )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f2406]) ).
thf(f2406,plain,
( ( ( ( sK5 @ sK11 @ sK28 )
=> ( sK13 @ sK28 ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f2404]) ).
thf(f2404,plain,
( ( ( ^ [Y0: a] :
( ( sK5 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) )
@ sK28 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f396]) ).
thf(f396,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f395]) ).
thf(f395,plain,
( spl0_10
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f2561,plain,
( ( $true
= ( ~ ( ( sK2 @ sK11 @ sK28 )
| ( sK5 @ sK11 @ sK28 ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f2558]) ).
thf(f2558,plain,
( ( $true
= ( ( ( sK2 @ sK11 @ sK28 )
| ( sK5 @ sK11 @ sK28 ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f2541,f2430]) ).
thf(f2430,plain,
( ( ( sK13 @ sK28 )
= $false )
| ~ spl0_10 ),
inference(boolean_simplification,[],[f2429]) ).
thf(f2429,plain,
( ( ( $true
=> ( sK13 @ sK28 ) )
= $false )
| ~ spl0_10 ),
inference(backward_demodulation,[],[f2406,f2428]) ).
thf(f2541,plain,
( ! [X1: a] :
( ( ( ( sK2 @ sK11 @ X1 )
| ( sK5 @ sK11 @ X1 ) )
=> ( sK13 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f2540]) ).
thf(f2540,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f2109]) ).
thf(f2109,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f2070]) ).
thf(f2070,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f2065]) ).
thf(f2065,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f2064]) ).
thf(f2064,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[],[f2063]) ).
thf(f2063,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f2062]) ).
thf(f2062,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f2061]) ).
thf(f2061,plain,
( ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1169,f278]) ).
thf(f278,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f277,plain,
( spl0_7
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f1169,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1168]) ).
thf(f1168,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f1158]) ).
thf(f1158,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1157]) ).
thf(f1157,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f65]) ).
thf(f65,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f64,plain,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f2060,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_46 ),
inference(avatar_contradiction_clause,[],[f2059]) ).
thf(f2059,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_46 ),
inference(trivial_inequality_removal,[],[f2058]) ).
thf(f2058,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_46 ),
inference(forward_demodulation,[],[f2057,f1976]) ).
thf(f1976,plain,
( ( ( sK13 @ sK25 )
= $false )
| ~ spl0_46 ),
inference(boolean_simplification,[],[f1975]) ).
thf(f1975,plain,
( ( ( $true
=> ( sK13 @ sK25 ) )
= $false )
| ~ spl0_46 ),
inference(backward_demodulation,[],[f1955,f1974]) ).
thf(f1974,plain,
( ( $true
= ( ( sK2 @ sK24 @ sK25 )
& ( sK13 @ sK24 ) ) )
| ~ spl0_46 ),
inference(binary_proxy_clausification,[],[f1955]) ).
thf(f1955,plain,
( ( ( ( ( sK2 @ sK24 @ sK25 )
& ( sK13 @ sK24 ) )
=> ( sK13 @ sK25 ) )
= $false )
| ~ spl0_46 ),
inference(beta_eta_normalization,[],[f1954]) ).
thf(f1954,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK24 @ Y0 )
& ( sK13 @ sK24 ) )
=> ( sK13 @ Y0 ) )
@ sK25 )
= $false )
| ~ spl0_46 ),
inference(sigma_clausification,[],[f1941]) ).
thf(f1941,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK24 @ Y0 )
& ( sK13 @ sK24 ) )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_46 ),
inference(beta_eta_normalization,[],[f1937]) ).
thf(f1937,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) )
@ sK24 ) )
| ~ spl0_46 ),
inference(sigma_clausification,[],[f1886]) ).
thf(f1886,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f1885]) ).
thf(f1885,plain,
( spl0_46
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
thf(f2057,plain,
( ( ( sK13 @ sK25 )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_46 ),
inference(boolean_simplification,[],[f2056]) ).
thf(f2056,plain,
( ( $true
= ( $true
=> ( sK13 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_46 ),
inference(forward_demodulation,[],[f2055,f2018]) ).
thf(f2018,plain,
( ( ( sK13 @ sK24 )
= $true )
| ~ spl0_46 ),
inference(boolean_simplification,[],[f2017]) ).
thf(f2017,plain,
( ( ( $true
& ( sK13 @ sK24 ) )
= $true )
| ~ spl0_46 ),
inference(backward_demodulation,[],[f1974,f2016]) ).
thf(f2016,plain,
( ( ( sK2 @ sK24 @ sK25 )
= $true )
| ~ spl0_46 ),
inference(binary_proxy_clausification,[],[f1974]) ).
thf(f2055,plain,
( ( $true
= ( ( sK13 @ sK24 )
=> ( sK13 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_46 ),
inference(boolean_simplification,[],[f2054]) ).
thf(f2054,plain,
( ( $true
= ( ( ( sK13 @ sK24 )
& $true )
=> ( sK13 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_46 ),
inference(boolean_simplification,[],[f2050]) ).
thf(f2050,plain,
( ( $true
= ( ( ( sK13 @ sK24 )
& ( $true
| ( sK5 @ sK24 @ sK25 ) ) )
=> ( sK13 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_46 ),
inference(superposition,[],[f1596,f2016]) ).
thf(f1596,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK13 @ X1 )
& ( ( sK2 @ X1 @ X2 )
| ( sK5 @ X1 @ X2 ) ) )
=> ( sK13 @ X2 ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1595]) ).
thf(f1595,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK13 @ X1 )
& ( ( sK2 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) ) )
=> ( sK13 @ Y0 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1585]) ).
thf(f1585,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ X1 )
& ( ( sK2 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1584]) ).
thf(f1584,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1578]) ).
thf(f1578,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1577]) ).
thf(f1577,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[],[f1555,f1576]) ).
thf(f1576,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1555]) ).
thf(f1555,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1543]) ).
thf(f1543,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1542]) ).
thf(f1542,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(sigma_clausification,[],[f1531]) ).
thf(f1531,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1530]) ).
thf(f1530,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1529]) ).
thf(f1529,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| $true )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[],[f1169,f281]) ).
thf(f281,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f280,plain,
( spl0_8
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f1934,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_45 ),
inference(avatar_contradiction_clause,[],[f1933]) ).
thf(f1933,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_45 ),
inference(trivial_inequality_removal,[],[f1932]) ).
thf(f1932,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_45 ),
inference(boolean_simplification,[],[f1931]) ).
thf(f1931,plain,
( ( ~ $true = $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_45 ),
inference(boolean_simplification,[],[f1930]) ).
thf(f1930,plain,
( ( ( ~ ( $true
| ( sK5 @ sK11 @ sK23 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1928,f1913]) ).
thf(f1913,plain,
( ( ( sK2 @ sK11 @ sK23 )
= $true )
| ~ spl0_45 ),
inference(binary_proxy_clausification,[],[f1911]) ).
thf(f1911,plain,
( ( ( ( sK2 @ sK11 @ sK23 )
=> ( sK13 @ sK23 ) )
= $false )
| ~ spl0_45 ),
inference(beta_eta_normalization,[],[f1907]) ).
thf(f1907,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) )
@ sK23 )
= $false )
| ~ spl0_45 ),
inference(sigma_clausification,[],[f1883]) ).
thf(f1883,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1882]) ).
thf(f1882,plain,
( spl0_45
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
thf(f1928,plain,
( ( $true
= ( ~ ( ( sK2 @ sK11 @ sK23 )
| ( sK5 @ sK11 @ sK23 ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_45 ),
inference(boolean_simplification,[],[f1921]) ).
thf(f1921,plain,
( ( ( ( ( sK2 @ sK11 @ sK23 )
| ( sK5 @ sK11 @ sK23 ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_45 ),
inference(superposition,[],[f1821,f1912]) ).
thf(f1912,plain,
( ( ( sK13 @ sK23 )
= $false )
| ~ spl0_45 ),
inference(binary_proxy_clausification,[],[f1911]) ).
thf(f1821,plain,
( ! [X1: a] :
( ( ( ( sK2 @ sK11 @ X1 )
| ( sK5 @ sK11 @ X1 ) )
=> ( sK13 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1820]) ).
thf(f1820,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1576]) ).
thf(f1887,plain,
( spl0_45
| spl0_46
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1878,f280,f64,f1885,f1882]) ).
thf(f1878,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1858]) ).
thf(f1858,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f1572]) ).
thf(f1572,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1570]) ).
thf(f1570,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f1561,f1554]) ).
thf(f1554,plain,
( ( ( sK13 @ sK12 )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1543]) ).
thf(f1561,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK12 ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1560]) ).
thf(f1560,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[],[f281]) ).
thf(f1528,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1527]) ).
thf(f1527,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f1526]) ).
thf(f1526,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1525,f1448]) ).
thf(f1448,plain,
( ( ( sK13 @ sK20 )
= $false )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f1439]) ).
thf(f1439,plain,
( ( ( ( ( sK5 @ sK21 @ sK20 )
& ( sK13 @ sK21 ) )
=> ( sK13 @ sK20 ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f1438]) ).
thf(f1438,plain,
( ( ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK20 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ sK20 ) )
@ sK21 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f1423]) ).
thf(f1423,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK20 )
& ( sK13 @ Y0 ) )
=> ( sK13 @ sK20 ) ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f1421]) ).
thf(f1421,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) )
@ sK20 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f393]) ).
thf(f393,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f392,plain,
( spl0_9
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f1525,plain,
( ( $true
= ( sK13 @ sK20 ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1524]) ).
thf(f1524,plain,
( ( $true
= ( $true
=> ( sK13 @ sK20 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1521,f1506]) ).
thf(f1506,plain,
( ( ( sK13 @ sK22 )
= $true )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f1494]) ).
thf(f1494,plain,
( ( $true
= ( ( sK5 @ sK22 @ sK20 )
& ( sK13 @ sK22 ) ) )
| ~ spl0_9 ),
inference(not_proxy_clausification,[],[f1483]) ).
thf(f1483,plain,
( ( ( ~ ( ( sK5 @ sK22 @ sK20 )
& ( sK13 @ sK22 ) ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f1482]) ).
thf(f1482,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK5 @ Y0 @ sK20 )
& ( sK13 @ Y0 ) )
@ sK22 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f1453]) ).
thf(f1453,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK5 @ Y0 @ sK20 )
& ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1451]) ).
thf(f1451,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK20 )
& ( sK13 @ Y0 ) )
=> $false ) )
= $false )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f1423,f1448]) ).
thf(f1521,plain,
( ( $true
= ( ( sK13 @ sK22 )
=> ( sK13 @ sK20 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1520]) ).
thf(f1520,plain,
( ( $true
= ( ( ( sK13 @ sK22 )
& $true )
=> ( sK13 @ sK20 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1518]) ).
thf(f1518,plain,
( ( $true
= ( ( ( sK13 @ sK22 )
& ( ( sK2 @ sK22 @ sK20 )
| $true ) )
=> ( sK13 @ sK20 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f1261,f1509]) ).
thf(f1509,plain,
( ( $true
= ( sK5 @ sK22 @ sK20 ) )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1508]) ).
thf(f1508,plain,
( ( $true
= ( ( sK5 @ sK22 @ sK20 )
& $true ) )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f1494,f1506]) ).
thf(f1261,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK13 @ X1 )
& ( ( sK2 @ X1 @ X2 )
| ( sK5 @ X1 @ X2 ) ) )
=> ( sK13 @ X2 ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1260]) ).
thf(f1260,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK13 @ X1 )
& ( ( sK2 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) ) )
=> ( sK13 @ Y0 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1250]) ).
thf(f1250,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ X1 )
& ( ( sK2 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1249]) ).
thf(f1249,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1238]) ).
thf(f1238,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1237]) ).
thf(f1237,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[],[f1196,f1236]) ).
thf(f1236,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1196]) ).
thf(f1196,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1184]) ).
thf(f1184,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1183]) ).
thf(f1183,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[],[f1172]) ).
thf(f1172,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1171]) ).
thf(f1171,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1170]) ).
thf(f1170,plain,
( ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1169,f278]) ).
thf(f1139,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f1138]) ).
thf(f1138,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f1137]) ).
thf(f1137,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16 ),
inference(boolean_simplification,[],[f1136]) ).
thf(f1136,plain,
( ( ( $false
=> ( sK6 @ sK15 ) )
= $false )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1131,f531]) ).
thf(f531,plain,
( ( ( sK6 @ sK14 )
= $false )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f530]) ).
thf(f530,plain,
( spl0_16
<=> ( ( sK6 @ sK14 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f1131,plain,
( ( ( ( sK6 @ sK14 )
=> ( sK6 @ sK15 ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1130]) ).
thf(f1130,plain,
( ( ( ( $true
& ( sK6 @ sK14 ) )
=> ( sK6 @ sK15 ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1129]) ).
thf(f1129,plain,
( ( ( ( ( ( sK5 @ sK14 @ sK15 )
| $true )
& ( sK6 @ sK14 ) )
=> ( sK6 @ sK15 ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1128,f507]) ).
thf(f507,plain,
( ( ( sK2 @ sK14 @ sK15 )
= $true )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f506]) ).
thf(f506,plain,
( spl0_14
<=> ( ( sK2 @ sK14 @ sK15 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f1128,plain,
( ( ( ( ( ( sK5 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) )
& ( sK6 @ sK14 ) )
=> ( sK6 @ sK15 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1127]) ).
thf(f1127,plain,
( ( ( ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK2 @ sK14 @ Y0 ) )
& ( sK6 @ sK14 ) )
=> ( sK6 @ Y0 ) )
@ sK15 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1114]) ).
thf(f1114,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK2 @ sK14 @ Y0 ) )
& ( sK6 @ sK14 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1112]) ).
thf(f1112,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1105]) ).
thf(f1105,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f1094]) ).
thf(f1094,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f1093]) ).
thf(f1093,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1089,f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK3 @ Y0 )
| ( sK5 @ sK3 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ),
inference(boolean_simplification,[],[f30]) ).
thf(f30,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK3 @ Y0 )
| ( sK5 @ sK3 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[],[f25,f29]) ).
thf(f29,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK3 @ Y0 )
| ( sK5 @ sK3 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK3 @ Y0 )
| ( sK5 @ sK3 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK4 ) )
= $false ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f21]) ).
thf(f21,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) ) )
= $false ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( ( $false
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
= $false ),
inference(backward_demodulation,[],[f17,f19]) ).
thf(f19,plain,
( ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a > a > $o] :
( ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( Y0 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y1 @ Y5 )
| ( Y0 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( sK2 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y0 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( sK2 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK3 @ Y2 )
| ( Y0 @ sK3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( Y0 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK2 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK3 @ Y2 )
| ( Y0 @ sK3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK4 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y1 @ Y4 )
| ( Y0 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y1 @ Y5 )
| ( Y0 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( sK2 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y0 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y2 @ Y5 )
| ( sK2 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK3 @ Y2 )
| ( Y0 @ sK3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( Y0 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK2 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK3 @ Y2 )
| ( Y0 @ sK3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK4 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y2 @ Y6 )
| ( Y1 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y1 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y1 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y3 @ Y6 )
| ( sK2 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( Y1 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y3 @ Y6 )
| ( sK2 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK3 @ Y3 )
| ( Y1 @ sK3 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( Y1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK2 @ Y4 @ Y3 )
| ( Y1 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK3 @ Y3 )
| ( Y1 @ sK3 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y2 @ Y5 )
| ( Y1 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y2 @ Y6 )
| ( Y1 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y1 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y1 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y3 @ Y6 )
| ( sK2 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( Y1 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y3 @ Y6 )
| ( sK2 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK3 @ Y3 )
| ( Y1 @ sK3 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( Y1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK2 @ Y4 @ Y3 )
| ( Y1 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK3 @ Y3 )
| ( Y1 @ sK3 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y3 @ Y6 )
| ( Y2 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y3 @ Y7 )
| ( Y2 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y2 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y2 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( sK2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y2 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( sK2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( Y2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( Y2 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK2 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( Y2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y7 @ Y6 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y3 @ Y6 )
| ( Y2 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y3 @ Y7 )
| ( Y2 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y2 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y2 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( sK2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y2 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y4 @ Y7 )
| ( sK2 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( Y2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( Y2 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK2 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( Y2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y3 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y3 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y4 @ Y8 )
| ( Y3 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y3 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y3 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y3 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( Y3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( Y3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ ( 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] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y3 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y3 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y4 @ Y8 )
| ( Y3 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y3 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y3 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y3 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( Y3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( Y3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,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] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y3 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y3 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y4 @ Y8 )
| ( Y3 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y3 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y3 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y3 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( Y3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( Y3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,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] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y8 @ Y7 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y3 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y3 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y4 @ Y8 )
| ( Y3 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y3 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y3 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y3 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( Y3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( Y3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a,X2: a,X3: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X3 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X3 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X1 ) )
| ~ ( ( ! [X8: a,X9: a,X10: a] :
( ( ! [X11: a > $o] :
( ( ! [X12: a] :
( ( ( X3 @ X9 @ X12 )
| ( X0 @ X9 @ X12 ) )
=> ( X11 @ X12 ) )
& ! [X13: a,X14: a] :
( ( ( ( X3 @ X13 @ X14 )
| ( X0 @ X13 @ X14 ) )
& ( X11 @ X13 ) )
=> ( X11 @ X14 ) ) )
=> ( X11 @ X10 ) )
& ! [X15: a > $o] :
( ( ! [X16: a,X17: a] :
( ( ( ( X3 @ X16 @ X17 )
| ( X0 @ X16 @ X17 ) )
& ( X15 @ X16 ) )
=> ( X15 @ X17 ) )
& ! [X18: a] :
( ( ( X0 @ X10 @ X18 )
| ( X3 @ X10 @ X18 ) )
=> ( X15 @ X18 ) ) )
=> ( X15 @ X8 ) ) )
=> ! [X19: a > $o] :
( ( ! [X20: a] :
( ( ( X3 @ X9 @ X20 )
| ( X0 @ X9 @ X20 ) )
=> ( X19 @ X20 ) )
& ! [X21: a,X22: a] :
( ( ( ( X3 @ X22 @ X21 )
| ( X0 @ X22 @ X21 ) )
& ( X19 @ X22 ) )
=> ( X19 @ X21 ) ) )
=> ( X19 @ X8 ) ) )
& ! [X23: a,X24: a] :
( ( ! [X25: a > $o] :
( ( ! [X26: a,X27: a] :
( ( ( X25 @ X27 )
& ( X3 @ X27 @ X26 ) )
=> ( X25 @ X26 ) )
& ! [X28: a] :
( ( X3 @ X24 @ X28 )
=> ( X25 @ X28 ) ) )
=> ( X25 @ X23 ) )
| ! [X29: a > $o] :
( ( ! [X30: a] :
( ( X0 @ X24 @ X30 )
=> ( X29 @ X30 ) )
& ! [X31: a,X32: a] :
( ( ( X29 @ X31 )
& ( X0 @ X31 @ X32 ) )
=> ( X29 @ X32 ) ) )
=> ( X29 @ X23 ) ) )
=> ! [X33: a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( ( X0 @ X35 @ X34 )
| ( X3 @ X35 @ X34 ) )
& ( X33 @ X35 ) )
=> ( X33 @ X34 ) )
& ! [X36: a] :
( ( ( X0 @ X24 @ X36 )
| ( X3 @ X24 @ X36 ) )
=> ( X33 @ X36 ) ) )
=> ( X33 @ X23 ) ) ) )
=> ! [X37: a > $o] :
( ( ! [X38: a,X39: a] :
( ( ( X37 @ X39 )
& ( ( X3 @ X39 @ X38 )
| ( X0 @ X39 @ X38 ) ) )
=> ( X37 @ X38 ) )
& ! [X40: a] :
( ( ( X0 @ X2 @ X40 )
| ( X3 @ X2 @ X40 ) )
=> ( X37 @ X40 ) ) )
=> ( X37 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > $o,X3: a,X2: a,X0: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) )
| ~ ( ( ! [X10: a,X8: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X8 @ X5 )
| ( X1 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
& ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X9 @ X5 )
| ( X0 @ X9 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X10 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X8 @ X5 )
| ( X1 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X1 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) ) )
=> ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: a > a > $o,X3: a,X2: a,X0: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) )
| ~ ( ( ! [X10: a,X8: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X8 @ X5 )
| ( X1 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
& ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X9 @ X5 )
| ( X0 @ X9 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X10 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X0 @ X8 @ X5 )
| ( X1 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( X1 @ X6 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) ) )
=> ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM251G_pme) ).
thf(f1089,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK3 @ Y0 )
| ( sK5 @ sK3 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f1080]) ).
thf(f1080,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK3 @ Y0 )
| ( sK5 @ sK3 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f1074,f27]) ).
thf(f27,plain,
( ( sK6 @ sK4 )
= $false ),
inference(boolean_simplification,[],[f26]) ).
thf(f26,plain,
( ( $true
=> ( sK6 @ sK4 ) )
= $false ),
inference(backward_demodulation,[],[f23,f25]) ).
thf(f1074,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK3 @ Y0 )
| ( sK5 @ sK3 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK4 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1073]) ).
thf(f1073,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f46]) ).
thf(f46,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f45,plain,
( spl0_1
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f1135,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f1134]) ).
thf(f1134,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f1133]) ).
thf(f1133,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(boolean_simplification,[],[f1132]) ).
thf(f1132,plain,
( ( ( ( sK6 @ sK14 )
=> $true )
= $false )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1131,f528]) ).
thf(f528,plain,
( ( $true
= ( sK6 @ sK15 ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f527]) ).
thf(f527,plain,
( spl0_15
<=> ( $true
= ( sK6 @ sK15 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f1109,plain,
( spl0_16
| spl0_15
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f1108,f506,f527,f530]) ).
thf(f1108,plain,
( ( ( sK6 @ sK14 )
= $false )
| ( $true
= ( sK6 @ sK15 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f1077]) ).
thf(f1077,plain,
( ( ( ( sK6 @ sK14 )
=> ( sK6 @ sK15 ) )
= $true )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1076]) ).
thf(f1076,plain,
( ( ( ( ( sK6 @ sK14 )
& $true )
=> ( sK6 @ sK15 ) )
= $true )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1075]) ).
thf(f1075,plain,
( ( $true
= ( ( ( sK6 @ sK14 )
& ( $true
| ( sK5 @ sK14 @ sK15 ) ) )
=> ( sK6 @ sK15 ) ) )
| ~ spl0_14 ),
inference(superposition,[],[f86,f507]) ).
thf(f86,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 )
& ( ( sK2 @ X2 @ X1 )
| ( sK5 @ X2 @ X1 ) ) )
=> ( sK6 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f85]) ).
thf(f85,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f82]) ).
thf(f82,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ X1 )
| ( sK5 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f81]) ).
thf(f81,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f29]) ).
thf(f1058,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_32 ),
inference(avatar_contradiction_clause,[],[f1057]) ).
thf(f1057,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_32 ),
inference(trivial_inequality_removal,[],[f1056]) ).
thf(f1056,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_32 ),
inference(boolean_simplification,[],[f1055]) ).
thf(f1055,plain,
( ( ~ $true = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_32 ),
inference(boolean_simplification,[],[f1054]) ).
thf(f1054,plain,
( ( ( ~ ( ( sK5 @ sK7 @ sK19 )
| $true ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1025,f1040]) ).
thf(f1040,plain,
( ( ( sK2 @ sK7 @ sK19 )
= $true )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1039]) ).
thf(f1039,plain,
( spl0_32
<=> ( ( sK2 @ sK7 @ sK19 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
thf(f1025,plain,
( ( ( ~ ( ( sK5 @ sK7 @ sK19 )
| ( sK2 @ sK7 @ sK19 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31 ),
inference(boolean_simplification,[],[f1022]) ).
thf(f1022,plain,
( ( ( ( ( sK5 @ sK7 @ sK19 )
| ( sK2 @ sK7 @ sK19 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31 ),
inference(superposition,[],[f683,f1019]) ).
thf(f1019,plain,
( ( ( sK10 @ sK19 )
= $false )
| ~ spl0_31 ),
inference(boolean_simplification,[],[f1018]) ).
thf(f1018,plain,
( ( ( $true
=> ( sK10 @ sK19 ) )
= $false )
| ~ spl0_31 ),
inference(backward_demodulation,[],[f996,f1017]) ).
thf(f1017,plain,
( ( ( ( sK2 @ sK7 @ sK19 )
| ( sK5 @ sK7 @ sK19 ) )
= $true )
| ~ spl0_31 ),
inference(binary_proxy_clausification,[],[f996]) ).
thf(f996,plain,
( ( ( ( ( sK2 @ sK7 @ sK19 )
| ( sK5 @ sK7 @ sK19 ) )
=> ( sK10 @ sK19 ) )
= $false )
| ~ spl0_31 ),
inference(beta_eta_normalization,[],[f994]) ).
thf(f994,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK5 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) )
@ sK19 )
= $false )
| ~ spl0_31 ),
inference(sigma_clausification,[],[f973]) ).
thf(f973,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK5 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f972]) ).
thf(f972,plain,
( spl0_31
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK5 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
thf(f683,plain,
( ! [X0: a] :
( ( ( ( sK5 @ sK7 @ X0 )
| ( sK2 @ sK7 @ X0 ) )
=> ( sK10 @ X0 ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f680]) ).
thf(f680,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( ( sK5 @ sK7 @ X0 )
| ( sK2 @ sK7 @ X0 ) ) )
=> ( sK10 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f631,f225]) ).
thf(f225,plain,
( ( $true
= ( sK10 @ sK7 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f224,plain,
( spl0_6
<=> ( $true
= ( sK10 @ sK7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f631,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK10 @ X1 )
& ( ( sK5 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) ) )
=> ( sK10 @ X2 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f630]) ).
thf(f630,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK5 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f619]) ).
thf(f619,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK5 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f618]) ).
thf(f618,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f608]) ).
thf(f608,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f607]) ).
thf(f607,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f556,f605]) ).
thf(f605,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f556]) ).
thf(f556,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f554]) ).
thf(f554,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> ( sK10 @ sK9 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f553]) ).
thf(f553,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f541]) ).
thf(f541,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f538]) ).
thf(f538,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK5 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f537]) ).
thf(f537,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK7 @ Y2 )
| ( sK5 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK5 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f534]) ).
thf(f534,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK7 @ Y2 )
| ( sK5 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK5 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f533]) ).
thf(f533,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK7 @ Y3 )
| ( sK5 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK5 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f524]) ).
thf(f524,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK7 @ Y3 )
| ( sK5 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK5 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f523]) ).
thf(f523,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f62]) ).
thf(f1050,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_33 ),
inference(avatar_contradiction_clause,[],[f1049]) ).
thf(f1049,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f1048]) ).
thf(f1048,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_33 ),
inference(boolean_simplification,[],[f1047]) ).
thf(f1047,plain,
( ( ~ $true = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_33 ),
inference(boolean_simplification,[],[f1045]) ).
thf(f1045,plain,
( ( $true
= ( ~ ( $true
| ( sK2 @ sK7 @ sK19 ) ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_31
| ~ spl0_33 ),
inference(backward_demodulation,[],[f1025,f1043]) ).
thf(f1043,plain,
( ( $true
= ( sK5 @ sK7 @ sK19 ) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1042]) ).
thf(f1042,plain,
( spl0_33
<=> ( $true
= ( sK5 @ sK7 @ sK19 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
thf(f1044,plain,
( spl0_32
| spl0_33
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1031,f972,f1042,f1039]) ).
thf(f1031,plain,
( ( $true
= ( sK5 @ sK7 @ sK19 ) )
| ( ( sK2 @ sK7 @ sK19 )
= $true )
| ~ spl0_31 ),
inference(binary_proxy_clausification,[],[f1017]) ).
thf(f974,plain,
( spl0_31
| spl0_5
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f968,f61,f221,f972]) ).
thf(f968,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK5 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f956]) ).
thf(f956,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK5 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f697]) ).
thf(f697,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK5 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f696]) ).
thf(f696,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK5 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[],[f687,f558]) ).
thf(f558,plain,
( ( ( sK10 @ sK9 )
= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f557]) ).
thf(f557,plain,
( ( ( $true
=> ( sK10 @ sK9 ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f554,f556]) ).
thf(f687,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK7 @ Y0 )
| ( sK5 @ sK7 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK9 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f686]) ).
thf(f686,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK5 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f560]) ).
thf(f560,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK5 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f542]) ).
thf(f542,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK5 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f538]) ).
thf(f668,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f667]) ).
thf(f667,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f666]) ).
thf(f666,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f665,f550]) ).
thf(f550,plain,
( ( $false
= ( sK10 @ sK16 ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f549]) ).
thf(f549,plain,
( ( ( $true
=> ( sK10 @ sK16 ) )
= $false )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f540,f548]) ).
thf(f548,plain,
( ( $true
= ( ( sK10 @ sK17 )
& ( ( sK5 @ sK17 @ sK16 )
| ( sK2 @ sK17 @ sK16 ) ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f540]) ).
thf(f540,plain,
( ( ( ( ( sK10 @ sK17 )
& ( ( sK5 @ sK17 @ sK16 )
| ( sK2 @ sK17 @ sK16 ) ) )
=> ( sK10 @ sK16 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f539]) ).
thf(f539,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ sK16 )
| ( sK2 @ Y0 @ sK16 ) ) )
=> ( sK10 @ sK16 ) )
@ sK17 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f536]) ).
thf(f536,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ sK16 )
| ( sK2 @ Y0 @ sK16 ) ) )
=> ( sK10 @ sK16 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f535]) ).
thf(f535,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) )
@ sK16 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f222]) ).
thf(f665,plain,
( ( $true
= ( sK10 @ sK16 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(boolean_simplification,[],[f664]) ).
thf(f664,plain,
( ( ( $true
=> ( sK10 @ sK16 ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f661,f566]) ).
thf(f566,plain,
( ( $true
= ( sK10 @ sK17 ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f565]) ).
thf(f565,plain,
( ( $true
= ( ( sK10 @ sK17 )
& $true ) )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f548,f563]) ).
thf(f563,plain,
( ( $true
= ( ( sK5 @ sK17 @ sK16 )
| ( sK2 @ sK17 @ sK16 ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f548]) ).
thf(f661,plain,
( ( ( ( sK10 @ sK17 )
=> ( sK10 @ sK16 ) )
= $true )
| ~ spl0_3
| ~ spl0_17 ),
inference(boolean_simplification,[],[f660]) ).
thf(f660,plain,
( ( ( ( ( sK10 @ sK17 )
& $true )
=> ( sK10 @ sK16 ) )
= $true )
| ~ spl0_3
| ~ spl0_17 ),
inference(boolean_simplification,[],[f643]) ).
thf(f643,plain,
( ( $true
= ( ( ( sK10 @ sK17 )
& ( $true
| ( sK2 @ sK17 @ sK16 ) ) )
=> ( sK10 @ sK16 ) ) )
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f631,f576]) ).
thf(f576,plain,
( ( $true
= ( sK5 @ sK17 @ sK16 ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f575]) ).
thf(f575,plain,
( spl0_17
<=> ( $true
= ( sK5 @ sK17 @ sK16 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f580,plain,
( spl0_17
| spl0_18
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f573,f221,f578,f575]) ).
thf(f573,plain,
( ( $true
= ( sK5 @ sK17 @ sK16 ) )
| ( ( sK2 @ sK17 @ sK16 )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f563]) ).
thf(f518,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f517]) ).
thf(f517,plain,
( $false
| ~ spl0_1
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f516]) ).
thf(f516,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_13 ),
inference(forward_demodulation,[],[f515,f454]) ).
thf(f454,plain,
( ( ( sK6 @ sK15 )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f453]) ).
thf(f453,plain,
( ( ( $true
=> ( sK6 @ sK15 ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f450,f452]) ).
thf(f452,plain,
( ( ( ( ( sK5 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) )
& ( sK6 @ sK14 ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f450]) ).
thf(f450,plain,
( ( ( ( ( ( sK5 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) )
& ( sK6 @ sK14 ) )
=> ( sK6 @ sK15 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f449]) ).
thf(f449,plain,
( ( ( ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK2 @ sK14 @ Y0 ) )
& ( sK6 @ sK14 ) )
=> ( sK6 @ Y0 ) )
@ sK15 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f446]) ).
thf(f446,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK5 @ sK14 @ Y0 )
| ( sK2 @ sK14 @ Y0 ) )
& ( sK6 @ sK14 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f444]) ).
thf(f444,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f441]) ).
thf(f441,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f438]) ).
thf(f438,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f437]) ).
thf(f437,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
=> $false )
= $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f435,f27]) ).
thf(f435,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
=> ( sK6 @ sK4 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f432]) ).
thf(f432,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> ( sK6 @ sK4 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f427,f31]) ).
thf(f427,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK3 @ Y0 )
| ( sK5 @ sK3 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK4 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f426]) ).
thf(f426,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f46]) ).
thf(f515,plain,
( ( $true
= ( sK6 @ sK15 ) )
| ~ spl0_1
| ~ spl0_13 ),
inference(boolean_simplification,[],[f514]) ).
thf(f514,plain,
( ( $true
= ( $true
=> ( sK6 @ sK15 ) ) )
| ~ spl0_1
| ~ spl0_13 ),
inference(forward_demodulation,[],[f513,f489]) ).
thf(f489,plain,
( ( $true
= ( sK6 @ sK14 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f452]) ).
thf(f513,plain,
( ( ( ( sK6 @ sK14 )
=> ( sK6 @ sK15 ) )
= $true )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f512]) ).
thf(f512,plain,
( ( ( ( ( sK6 @ sK14 )
& $true )
=> ( sK6 @ sK15 ) )
= $true )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f511]) ).
thf(f511,plain,
( ( $true
= ( ( ( sK6 @ sK14 )
& ( ( sK2 @ sK14 @ sK15 )
| $true ) )
=> ( sK6 @ sK15 ) ) )
| ~ spl0_13 ),
inference(superposition,[],[f86,f504]) ).
thf(f504,plain,
( ( ( sK5 @ sK14 @ sK15 )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f503]) ).
thf(f503,plain,
( spl0_13
<=> ( ( sK5 @ sK14 @ sK15 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f508,plain,
( spl0_13
| spl0_14
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f501,f45,f506,f503]) ).
thf(f501,plain,
( ( ( sK5 @ sK14 @ sK15 )
= $true )
| ( ( sK2 @ sK14 @ sK15 )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f492]) ).
thf(f492,plain,
( ( ( ( sK5 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f491]) ).
thf(f491,plain,
( ( ( ( ( sK5 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) )
& $true )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f452,f489]) ).
thf(f397,plain,
( spl0_9
| spl0_10
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f388,f277,f64,f395,f392]) ).
thf(f388,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f382]) ).
thf(f382,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(not_proxy_clausification,[],[f317]) ).
thf(f317,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f314]) ).
thf(f314,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f298,f242]) ).
thf(f242,plain,
( ( ( sK13 @ sK12 )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f241]) ).
thf(f241,plain,
( ( ( $true
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f238,f240]) ).
thf(f240,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f238]) ).
thf(f238,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK11 @ Y0 )
| ( sK5 @ sK11 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) ) )
=> ( sK13 @ Y1 ) ) ) ) )
=> ( sK13 @ sK12 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f237]) ).
thf(f237,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f236]) ).
thf(f236,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f235]) ).
thf(f235,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f232,f234]) ).
thf(f234,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f232]) ).
thf(f232,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK11 @ Y1 )
| ( sK5 @ sK11 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f231]) ).
thf(f231,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f230]) ).
thf(f230,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK11 @ Y2 )
| ( sK5 @ sK11 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f229]) ).
thf(f229,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f65]) ).
thf(f298,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK11 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK12 ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f297]) ).
thf(f297,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[],[f278]) ).
thf(f282,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f275,f64,f280,f277]) ).
thf(f275,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK12 ) ) ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f234]) ).
thf(f226,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f219,f61,f224,f221]) ).
thf(f219,plain,
( ( $true
= ( sK10 @ sK7 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f170]) ).
thf(f170,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
=> ( sK10 @ sK7 ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f169]) ).
thf(f169,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
& $true )
=> ( sK10 @ sK7 ) ) )
| ~ spl0_3 ),
inference(superposition,[],[f161,f134]) ).
thf(f134,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f133]) ).
thf(f133,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f126,f132]) ).
thf(f132,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f126]) ).
thf(f126,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f108]) ).
thf(f108,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> ( sK10 @ sK9 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f107]) ).
thf(f107,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f90]) ).
thf(f90,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f89]) ).
thf(f89,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f84,f88]) ).
thf(f88,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK5 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f84]) ).
thf(f84,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK5 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f83]) ).
thf(f83,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK7 @ Y2 )
| ( sK5 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK5 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f80]) ).
thf(f80,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ sK7 @ Y2 )
| ( sK5 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK5 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK8 @ Y2 )
| ( sK2 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f79]) ).
thf(f79,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK7 @ Y3 )
| ( sK5 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK5 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f74]) ).
thf(f74,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ sK7 @ Y3 )
| ( sK5 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK5 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f73]) ).
thf(f73,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f62]) ).
thf(f161,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK8 @ Y0 )
| ( sK2 @ sK8 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK7 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f160]) ).
thf(f160,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f156]) ).
thf(f156,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f155]) ).
thf(f155,plain,
( ( $true
= ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK8 @ Y1 )
| ( sK2 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f88,f154]) ).
thf(f154,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK7 @ Y1 )
| ( sK5 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f88]) ).
thf(f66,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f59,f48,f64,f61]) ).
thf(f48,plain,
( spl0_2
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f59,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f49]) ).
thf(f49,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f50,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f43,f48,f45]) ).
thf(f43,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
= $true )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f37]) ).
thf(f37,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y0 @ Y3 )
| ( sK5 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y0 @ Y4 )
| ( sK5 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK5 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK3 @ Y1 )
| ( sK5 @ sK3 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEV154^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.15 % 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
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 19:07:38 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a TH0_THM_NEQ_NAR problem
% 0.15/0.37 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
% 0.22/0.39 % (22185)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (22181)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.39 % (22186)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.22/0.39 % (22185)Instruction limit reached!
% 0.22/0.39 % (22185)------------------------------
% 0.22/0.39 % (22185)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (22185)Termination reason: Unknown
% 0.22/0.39 % (22185)Termination phase: shuffling
% 0.22/0.39
% 0.22/0.39 % (22185)Memory used [KB]: 1023
% 0.22/0.39 % (22185)Time elapsed: 0.003 s
% 0.22/0.39 % (22185)Instructions burned: 2 (million)
% 0.22/0.39 % (22185)------------------------------
% 0.22/0.39 % (22185)------------------------------
% 0.22/0.39 % (22182)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.39 % (22184)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (22182)Instruction limit reached!
% 0.22/0.39 % (22182)------------------------------
% 0.22/0.39 % (22182)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (22184)Instruction limit reached!
% 0.22/0.39 % (22184)------------------------------
% 0.22/0.39 % (22184)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (22184)Termination reason: Unknown
% 0.22/0.39 % (22184)Termination phase: shuffling
% 0.22/0.39
% 0.22/0.39 % (22184)Memory used [KB]: 1023
% 0.22/0.39 % (22184)Time elapsed: 0.005 s
% 0.22/0.39 % (22184)Instructions burned: 2 (million)
% 0.22/0.39 % (22184)------------------------------
% 0.22/0.39 % (22184)------------------------------
% 0.22/0.39 % (22188)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40 % (22188)Instruction limit reached!
% 0.22/0.40 % (22188)------------------------------
% 0.22/0.40 % (22188)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (22188)Termination reason: Unknown
% 0.22/0.40 % (22188)Termination phase: Preprocessing 3
% 0.22/0.40
% 0.22/0.40 % (22188)Memory used [KB]: 1023
% 0.22/0.40 % (22188)Time elapsed: 0.005 s
% 0.22/0.40 % (22188)Instructions burned: 4 (million)
% 0.22/0.40 % (22188)------------------------------
% 0.22/0.40 % (22188)------------------------------
% 0.22/0.40 % (22182)Termination reason: Unknown
% 0.22/0.40 % (22182)Termination phase: Preprocessing 3
% 0.22/0.40
% 0.22/0.40 % (22182)Memory used [KB]: 1023
% 0.22/0.40 % (22182)Time elapsed: 0.006 s
% 0.22/0.40 % (22182)Instructions burned: 4 (million)
% 0.22/0.40 % (22182)------------------------------
% 0.22/0.40 % (22182)------------------------------
% 0.22/0.40 % (22183)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.22/0.40 % (22187)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.41 % (22189)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)
% 0.22/0.41 % (22191)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)
% 0.22/0.41 % (22192)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)
% 0.22/0.41 % (22191)Instruction limit reached!
% 0.22/0.41 % (22191)------------------------------
% 0.22/0.41 % (22191)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (22191)Termination reason: Unknown
% 0.22/0.41 % (22191)Termination phase: Naming
% 0.22/0.41
% 0.22/0.41 % (22191)Memory used [KB]: 1023
% 0.22/0.41 % (22191)Time elapsed: 0.004 s
% 0.22/0.41 % (22191)Instructions burned: 3 (million)
% 0.22/0.41 % (22191)------------------------------
% 0.22/0.41 % (22191)------------------------------
% 0.22/0.41 % (22187)Instruction limit reached!
% 0.22/0.41 % (22187)------------------------------
% 0.22/0.41 % (22187)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (22187)Termination reason: Unknown
% 0.22/0.41 % (22187)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (22187)Memory used [KB]: 5628
% 0.22/0.41 % (22187)Time elapsed: 0.013 s
% 0.22/0.41 % (22187)Instructions burned: 19 (million)
% 0.22/0.41 % (22187)------------------------------
% 0.22/0.41 % (22187)------------------------------
% 0.22/0.42 % (22183)Instruction limit reached!
% 0.22/0.42 % (22183)------------------------------
% 0.22/0.42 % (22183)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (22183)Termination reason: Unknown
% 0.22/0.42 % (22183)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (22183)Memory used [KB]: 5756
% 0.22/0.42 % (22183)Time elapsed: 0.018 s
% 0.22/0.42 % (22183)Instructions burned: 28 (million)
% 0.22/0.42 % (22183)------------------------------
% 0.22/0.42 % (22183)------------------------------
% 0.22/0.42 % (22189)Instruction limit reached!
% 0.22/0.42 % (22189)------------------------------
% 0.22/0.42 % (22189)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (22189)Termination reason: Unknown
% 0.22/0.42 % (22189)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (22189)Memory used [KB]: 5628
% 0.22/0.42 % (22189)Time elapsed: 0.018 s
% 0.22/0.42 % (22189)Instructions burned: 38 (million)
% 0.22/0.42 % (22189)------------------------------
% 0.22/0.42 % (22189)------------------------------
% 0.22/0.43 % (22190)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)
% 0.22/0.43 % (22193)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.43 % (22194)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.43 % (22193)Instruction limit reached!
% 0.22/0.43 % (22193)------------------------------
% 0.22/0.43 % (22193)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (22193)Termination reason: Unknown
% 0.22/0.43 % (22193)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (22193)Memory used [KB]: 1151
% 0.22/0.43 % (22193)Time elapsed: 0.006 s
% 0.22/0.43 % (22193)Instructions burned: 7 (million)
% 0.22/0.43 % (22193)------------------------------
% 0.22/0.43 % (22193)------------------------------
% 0.22/0.43 % (22195)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)
% 0.22/0.43 % (22195)Instruction limit reached!
% 0.22/0.43 % (22195)------------------------------
% 0.22/0.43 % (22195)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (22195)Termination reason: Unknown
% 0.22/0.43 % (22195)Termination phase: Preprocessing 3
% 0.22/0.43
% 0.22/0.43 % (22195)Memory used [KB]: 1023
% 0.22/0.43 % (22195)Time elapsed: 0.004 s
% 0.22/0.43 % (22195)Instructions burned: 4 (million)
% 0.22/0.43 % (22195)------------------------------
% 0.22/0.43 % (22195)------------------------------
% 0.22/0.44 % (22194)Instruction limit reached!
% 0.22/0.44 % (22194)------------------------------
% 0.22/0.44 % (22194)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (22194)Termination reason: Unknown
% 0.22/0.44 % (22194)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (22194)Memory used [KB]: 1151
% 0.22/0.44 % (22194)Time elapsed: 0.006 s
% 0.22/0.44 % (22194)Instructions burned: 17 (million)
% 0.22/0.44 % (22194)------------------------------
% 0.22/0.44 % (22194)------------------------------
% 0.22/0.44 % (22190)Instruction limit reached!
% 0.22/0.44 % (22190)------------------------------
% 0.22/0.44 % (22190)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (22190)Termination reason: Unknown
% 0.22/0.44 % (22190)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (22190)Memory used [KB]: 5756
% 0.22/0.44 % (22190)Time elapsed: 0.011 s
% 0.22/0.44 % (22190)Instructions burned: 15 (million)
% 0.22/0.44 % (22190)------------------------------
% 0.22/0.44 % (22190)------------------------------
% 0.22/0.44 % (22196)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)
% 0.22/0.44 % (22196)Instruction limit reached!
% 0.22/0.44 % (22196)------------------------------
% 0.22/0.44 % (22196)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (22196)Termination reason: Unknown
% 0.22/0.44 % (22196)Termination phase: Preprocessing 3
% 0.22/0.44
% 0.22/0.44 % (22196)Memory used [KB]: 1023
% 0.22/0.44 % (22196)Time elapsed: 0.003 s
% 0.22/0.44 % (22196)Instructions burned: 5 (million)
% 0.22/0.44 % (22196)------------------------------
% 0.22/0.44 % (22196)------------------------------
% 0.22/0.45 % (22197)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)
% 0.22/0.45 % (22199)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.45 % (22198)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)
% 0.22/0.45 % (22199)Instruction limit reached!
% 0.22/0.45 % (22199)------------------------------
% 0.22/0.45 % (22199)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (22199)Termination reason: Unknown
% 0.22/0.45 % (22199)Termination phase: Preprocessing 3
% 0.22/0.45
% 0.22/0.45 % (22199)Memory used [KB]: 1023
% 0.22/0.45 % (22197)Instruction limit reached!
% 0.22/0.45 % (22197)------------------------------
% 0.22/0.45 % (22197)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (22197)Termination reason: Unknown
% 0.22/0.45 % (22197)Termination phase: Property scanning
% 0.22/0.45
% 0.22/0.45 % (22197)Memory used [KB]: 1151
% 0.22/0.45 % (22197)Time elapsed: 0.006 s
% 0.22/0.45 % (22197)Instructions burned: 7 (million)
% 0.22/0.45 % (22197)------------------------------
% 0.22/0.45 % (22197)------------------------------
% 0.22/0.45 % (22199)Time elapsed: 0.004 s
% 0.22/0.45 % (22199)Instructions burned: 5 (million)
% 0.22/0.45 % (22199)------------------------------
% 0.22/0.45 % (22199)------------------------------
% 0.22/0.45 % (22200)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)
% 0.22/0.45 % (22198)Instruction limit reached!
% 0.22/0.45 % (22198)------------------------------
% 0.22/0.45 % (22198)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (22198)Termination reason: Unknown
% 0.22/0.45 % (22198)Termination phase: Property scanning
% 0.22/0.45
% 0.22/0.45 % (22198)Memory used [KB]: 1023
% 0.22/0.45 % (22198)Time elapsed: 0.004 s
% 0.22/0.45 % (22198)Instructions burned: 4 (million)
% 0.22/0.45 % (22198)------------------------------
% 0.22/0.45 % (22198)------------------------------
% 0.22/0.45 % (22201)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.46 % (22200)Instruction limit reached!
% 0.22/0.46 % (22200)------------------------------
% 0.22/0.46 % (22200)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (22200)Termination reason: Unknown
% 0.22/0.46 % (22200)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (22200)Memory used [KB]: 5756
% 0.22/0.46 % (22200)Time elapsed: 0.013 s
% 0.22/0.46 % (22200)Instructions burned: 19 (million)
% 0.22/0.46 % (22200)------------------------------
% 0.22/0.46 % (22200)------------------------------
% 0.22/0.47 % (22202)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.47 % (22204)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)
% 0.22/0.47 % (22202)Instruction limit reached!
% 0.22/0.47 % (22202)------------------------------
% 0.22/0.47 % (22202)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (22202)Termination reason: Unknown
% 0.22/0.47 % (22202)Termination phase: Property scanning
% 0.22/0.47
% 0.22/0.47 % (22202)Memory used [KB]: 1151
% 0.22/0.47 % (22202)Time elapsed: 0.006 s
% 0.22/0.47 % (22202)Instructions burned: 7 (million)
% 0.22/0.47 % (22202)------------------------------
% 0.22/0.47 % (22202)------------------------------
% 0.22/0.47 % (22205)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.47 % (22205)Instruction limit reached!
% 0.22/0.47 % (22205)------------------------------
% 0.22/0.47 % (22205)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (22205)Termination reason: Unknown
% 0.22/0.47 % (22205)Termination phase: Property scanning
% 0.22/0.47
% 0.22/0.47 % (22205)Memory used [KB]: 1023
% 0.22/0.47 % (22205)Time elapsed: 0.003 s
% 0.22/0.47 % (22205)Instructions burned: 7 (million)
% 0.22/0.47 % (22205)------------------------------
% 0.22/0.47 % (22205)------------------------------
% 0.22/0.48 % (22204)Instruction limit reached!
% 0.22/0.48 % (22204)------------------------------
% 0.22/0.48 % (22204)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (22204)Termination reason: Unknown
% 0.22/0.48 % (22204)Termination phase: Saturation
% 0.22/0.48
% 0.22/0.48 % (22204)Memory used [KB]: 5756
% 0.22/0.48 % (22204)Time elapsed: 0.013 s
% 0.22/0.48 % (22204)Instructions burned: 21 (million)
% 0.22/0.48 % (22204)------------------------------
% 0.22/0.48 % (22204)------------------------------
% 0.22/0.48 % (22203)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)
% 0.22/0.48 % (22206)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)
% 0.22/0.48 % (22206)Instruction limit reached!
% 0.22/0.48 % (22206)------------------------------
% 0.22/0.48 % (22206)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (22206)Termination reason: Unknown
% 0.22/0.48 % (22206)Termination phase: Property scanning
% 0.22/0.48
% 0.22/0.48 % (22206)Memory used [KB]: 1023
% 0.22/0.48 % (22206)Time elapsed: 0.003 s
% 0.22/0.48 % (22206)Instructions burned: 7 (million)
% 0.22/0.48 % (22206)------------------------------
% 0.22/0.48 % (22206)------------------------------
% 0.22/0.48 % (22207)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.22/0.49 % (22208)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 (2998ds/779Mi)
% 0.22/0.49 % (22209)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 (2998ds/19Mi)
% 0.22/0.49 % (22181)Instruction limit reached!
% 0.22/0.49 % (22181)------------------------------
% 0.22/0.49 % (22181)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (22181)Termination reason: Unknown
% 0.22/0.49 % (22181)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (22181)Memory used [KB]: 6780
% 0.22/0.49 % (22181)Time elapsed: 0.107 s
% 0.22/0.49 % (22181)Instructions burned: 184 (million)
% 0.22/0.49 % (22181)------------------------------
% 0.22/0.49 % (22181)------------------------------
% 0.22/0.50 % (22209)Instruction limit reached!
% 0.22/0.50 % (22209)------------------------------
% 0.22/0.50 % (22209)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50 % (22209)Termination reason: Unknown
% 0.22/0.50 % (22209)Termination phase: Saturation
% 0.22/0.50
% 0.22/0.50 % (22209)Memory used [KB]: 5500
% 0.22/0.50 % (22209)Time elapsed: 0.007 s
% 0.22/0.50 % (22209)Instructions burned: 20 (million)
% 0.22/0.50 % (22209)------------------------------
% 0.22/0.50 % (22209)------------------------------
% 0.22/0.50 % (22210)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.22/0.51 % (22211)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.22/0.51 % (22211)Instruction limit reached!
% 0.22/0.51 % (22211)------------------------------
% 0.22/0.51 % (22211)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (22211)Termination reason: Unknown
% 0.22/0.51 % (22211)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (22211)Memory used [KB]: 5756
% 0.22/0.51 % (22211)Time elapsed: 0.007 s
% 0.22/0.51 % (22211)Instructions burned: 17 (million)
% 0.22/0.51 % (22211)------------------------------
% 0.22/0.51 % (22211)------------------------------
% 0.22/0.52 % (22212)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.52 % (22212)Instruction limit reached!
% 0.22/0.52 % (22212)------------------------------
% 0.22/0.52 % (22212)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (22212)Termination reason: Unknown
% 0.22/0.52 % (22212)Termination phase: Preprocessing 3
% 0.22/0.52
% 0.22/0.52 % (22212)Memory used [KB]: 1023
% 0.22/0.52 % (22212)Time elapsed: 0.003 s
% 0.22/0.52 % (22212)Instructions burned: 5 (million)
% 0.22/0.52 % (22212)------------------------------
% 0.22/0.52 % (22212)------------------------------
% 1.29/0.53 % (22213)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 1.29/0.54 % (22213)Instruction limit reached!
% 1.29/0.54 % (22213)------------------------------
% 1.29/0.54 % (22213)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.54 % (22213)Termination reason: Unknown
% 1.29/0.54 % (22213)Termination phase: Saturation
% 1.29/0.54
% 1.29/0.54 % (22213)Memory used [KB]: 5756
% 1.29/0.54 % (22213)Time elapsed: 0.012 s
% 1.29/0.54 % (22213)Instructions burned: 30 (million)
% 1.29/0.54 % (22213)------------------------------
% 1.29/0.54 % (22213)------------------------------
% 1.45/0.55 % (22186)Instruction limit reached!
% 1.45/0.55 % (22186)------------------------------
% 1.45/0.55 % (22186)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.45/0.55 % (22186)Termination reason: Unknown
% 1.45/0.55 % (22214)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 1.45/0.55 % (22186)Termination phase: Saturation
% 1.45/0.55
% 1.45/0.55 % (22186)Memory used [KB]: 6524
% 1.45/0.55 % (22186)Time elapsed: 0.164 s
% 1.45/0.55 % (22186)Instructions burned: 276 (million)
% 1.45/0.55 % (22186)------------------------------
% 1.45/0.55 % (22186)------------------------------
% 1.45/0.56 % (22215)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 1.45/0.59 % (22214)Instruction limit reached!
% 1.45/0.59 % (22214)------------------------------
% 1.45/0.59 % (22214)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.45/0.59 % (22214)Termination reason: Unknown
% 1.45/0.59 % (22214)Termination phase: Saturation
% 1.45/0.59
% 1.45/0.59 % (22214)Memory used [KB]: 6268
% 1.45/0.59 % (22214)Time elapsed: 0.042 s
% 1.45/0.59 % (22214)Instructions burned: 127 (million)
% 1.45/0.59 % (22214)------------------------------
% 1.45/0.59 % (22214)------------------------------
% 1.45/0.60 % (22215)Instruction limit reached!
% 1.45/0.60 % (22215)------------------------------
% 1.45/0.60 % (22215)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.45/0.60 % (22215)Termination reason: Unknown
% 1.45/0.60 % (22215)Termination phase: Saturation
% 1.45/0.60
% 1.45/0.60 % (22215)Memory used [KB]: 6140
% 1.45/0.60 % (22215)Time elapsed: 0.038 s
% 1.45/0.60 % (22215)Instructions burned: 102 (million)
% 1.45/0.60 % (22215)------------------------------
% 1.45/0.60 % (22215)------------------------------
% 1.45/0.60 % (22216)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2997ds/3Mi)
% 1.45/0.60 % (22216)Instruction limit reached!
% 1.45/0.60 % (22216)------------------------------
% 1.45/0.60 % (22216)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.45/0.60 % (22216)Termination reason: Unknown
% 1.45/0.60 % (22216)Termination phase: Naming
% 1.45/0.60
% 1.45/0.60 % (22216)Memory used [KB]: 1023
% 1.45/0.60 % (22216)Time elapsed: 0.003 s
% 1.45/0.60 % (22216)Instructions burned: 5 (million)
% 1.45/0.60 % (22216)------------------------------
% 1.45/0.60 % (22216)------------------------------
% 1.45/0.61 % (22217)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2997ds/20Mi)
% 1.45/0.61 % (22218)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2997ds/86Mi)
% 1.45/0.61 % (22217)Instruction limit reached!
% 1.45/0.61 % (22217)------------------------------
% 1.45/0.61 % (22217)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.45/0.61 % (22217)Termination reason: Unknown
% 1.45/0.61 % (22217)Termination phase: Saturation
% 1.45/0.61
% 1.45/0.61 % (22217)Memory used [KB]: 5628
% 1.45/0.61 % (22217)Time elapsed: 0.008 s
% 1.45/0.61 % (22217)Instructions burned: 21 (million)
% 1.45/0.61 % (22217)------------------------------
% 1.45/0.61 % (22217)------------------------------
% 1.45/0.61 % (22192)First to succeed.
% 1.45/0.62 % (22219)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2997ds/107Mi)
% 1.99/0.63 % (22192)Refutation found. Thanks to Tanya!
% 1.99/0.63 % SZS status Theorem for theBenchmark
% 1.99/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 1.99/0.64 % (22192)------------------------------
% 1.99/0.64 % (22192)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.99/0.64 % (22192)Termination reason: Refutation
% 1.99/0.64
% 1.99/0.64 % (22192)Memory used [KB]: 7291
% 1.99/0.64 % (22192)Time elapsed: 0.237 s
% 1.99/0.64 % (22192)Instructions burned: 428 (million)
% 1.99/0.64 % (22192)------------------------------
% 1.99/0.64 % (22192)------------------------------
% 1.99/0.64 % (22180)Success in time 0.252 s
% 1.99/0.64 % Vampire---4.8 exiting
%------------------------------------------------------------------------------