TSTP Solution File: SEV152^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV152^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:41:31 EDT 2024
% Result : Theorem 2.24s 0.67s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 59
% Syntax : Number of formulae : 412 ( 27 unt; 36 typ; 0 def)
% Number of atoms : 4010 ( 348 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 11675 ( 535 ~;1098 |; 781 &;6763 @)
% ( 22 <=>;1163 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 613 ( 613 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 56 usr; 53 con; 0-2 aty)
% (1313 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1534 (1370 ^ 163 !; 0 ?;1534 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a ).
thf(func_def_24,type,
sK5: a > a > $o ).
thf(func_def_25,type,
sK6: a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a > $o ).
thf(func_def_32,type,
sK13: a ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a > $o ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a ).
thf(func_def_50,type,
sK31: a ).
thf(func_def_51,type,
sK32: a ).
thf(func_def_52,type,
sK33: a ).
thf(func_def_53,type,
sK34: a ).
thf(f3037,plain,
$false,
inference(avatar_sat_refutation,[],[f57,f182,f192,f202,f220,f248,f386,f495,f623,f667,f825,f959,f1876,f1920,f1965,f1982,f2032,f2043,f2049,f2308,f2536,f2993,f3036]) ).
thf(f3036,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f3035]) ).
thf(f3035,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f3034]) ).
thf(f3034,plain,
( ( $false = $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(boolean_simplification,[],[f3033]) ).
thf(f3033,plain,
( ( ~ $true = $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(boolean_simplification,[],[f3032]) ).
thf(f3032,plain,
( ( $true
= ( ~ ( ( sK5 @ sK10 @ sK34 )
| $true ) ) )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f3031,f3022]) ).
thf(f3022,plain,
( ( ( sK3 @ sK10 @ sK34 )
= $true )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f3011]) ).
thf(f3011,plain,
( ( $false
= ( ( sK3 @ sK10 @ sK34 )
=> ( sK12 @ sK34 ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f3009]) ).
thf(f3009,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) )
@ sK34 ) )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f491]) ).
thf(f491,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f490]) ).
thf(f490,plain,
( spl0_13
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f3031,plain,
( ( ( ~ ( ( sK5 @ sK10 @ sK34 )
| ( sK3 @ sK10 @ sK34 ) ) )
= $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(boolean_simplification,[],[f3027]) ).
thf(f3027,plain,
( ( ( ( ( sK5 @ sK10 @ sK34 )
| ( sK3 @ sK10 @ sK34 ) )
=> $false )
= $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f2646,f3024]) ).
thf(f3024,plain,
( ( $false
= ( sK12 @ sK34 ) )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f3023]) ).
thf(f3023,plain,
( ( $false
= ( $true
=> ( sK12 @ sK34 ) ) )
| ~ spl0_13 ),
inference(backward_demodulation,[],[f3011,f3022]) ).
thf(f2646,plain,
( ! [X1: a] :
( ( ( ( sK5 @ sK10 @ X1 )
| ( sK3 @ sK10 @ X1 ) )
=> ( sK12 @ X1 ) )
= $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f2645]) ).
thf(f2645,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(pi_clausification,[],[f2626]) ).
thf(f2626,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) )
= $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2625]) ).
thf(f2625,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) ) )
= $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f2579,f2624]) ).
thf(f2624,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) ) )
= $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f2579]) ).
thf(f2579,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f2561]) ).
thf(f2561,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) ) )
=> ( sK12 @ sK11 ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f2560]) ).
thf(f2560,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) )
@ sK12 )
= $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(sigma_clausification,[],[f2548]) ).
thf(f2548,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2547]) ).
thf(f2547,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2546]) ).
thf(f2546,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f2061,f244]) ).
thf(f244,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f243,plain,
( spl0_9
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f2061,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f2060]) ).
thf(f2060,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK10 @ Y2 )
| ( sK3 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK11 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f2059]) ).
thf(f2059,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK10 @ Y2 )
| ( sK3 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f2058]) ).
thf(f2058,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK10 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f216]) ).
thf(f216,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f215,plain,
( spl0_7
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f2993,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f2992]) ).
thf(f2992,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f2991]) ).
thf(f2991,plain,
( ( $false = $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f2990,f2791]) ).
thf(f2791,plain,
( ( $false
= ( sK12 @ sK33 ) )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f2790]) ).
thf(f2790,plain,
( ( $false
= ( $true
=> ( sK12 @ sK33 ) ) )
| ~ spl0_14 ),
inference(backward_demodulation,[],[f2771,f2789]) ).
thf(f2789,plain,
( ( ( ( sK3 @ sK32 @ sK33 )
& ( sK12 @ sK32 ) )
= $true )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f2771]) ).
thf(f2771,plain,
( ( $false
= ( ( ( sK3 @ sK32 @ sK33 )
& ( sK12 @ sK32 ) )
=> ( sK12 @ sK33 ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f2770]) ).
thf(f2770,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK3 @ sK32 @ Y0 )
& ( sK12 @ sK32 ) )
=> ( sK12 @ Y0 ) )
@ sK33 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f2758]) ).
thf(f2758,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK32 @ Y0 )
& ( sK12 @ sK32 ) )
=> ( sK12 @ Y0 ) ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f2754]) ).
thf(f2754,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK12 @ Y0 ) )
=> ( sK12 @ Y1 ) ) )
@ sK32 ) )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f494]) ).
thf(f494,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK12 @ Y0 ) )
=> ( sK12 @ Y1 ) ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f493]) ).
thf(f493,plain,
( spl0_14
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK12 @ Y0 ) )
=> ( sK12 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f2990,plain,
( ( ( sK12 @ sK33 )
= $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(boolean_simplification,[],[f2989]) ).
thf(f2989,plain,
( ( $true
= ( $true
=> ( sK12 @ sK33 ) ) )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[],[f2974,f2814]) ).
thf(f2814,plain,
( ( $true
= ( sK12 @ sK32 ) )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f2789]) ).
thf(f2974,plain,
( ( ( ( sK12 @ sK32 )
=> ( sK12 @ sK33 ) )
= $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(boolean_simplification,[],[f2973]) ).
thf(f2973,plain,
( ( ( ( ( sK12 @ sK32 )
& $true )
=> ( sK12 @ sK33 ) )
= $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(boolean_simplification,[],[f2969]) ).
thf(f2969,plain,
( ( ( ( ( sK12 @ sK32 )
& ( ( sK5 @ sK32 @ sK33 )
| $true ) )
=> ( sK12 @ sK33 ) )
= $true )
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(superposition,[],[f2813,f2817]) ).
thf(f2817,plain,
( ( $true
= ( sK3 @ sK32 @ sK33 ) )
| ~ spl0_14 ),
inference(boolean_simplification,[],[f2816]) ).
thf(f2816,plain,
( ( ( ( sK3 @ sK32 @ sK33 )
& $true )
= $true )
| ~ spl0_14 ),
inference(backward_demodulation,[],[f2789,f2814]) ).
thf(f2813,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK12 @ X2 )
& ( ( sK5 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) ) )
=> ( sK12 @ X1 ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f2812]) ).
thf(f2812,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK12 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) ) )
=> ( sK12 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(pi_clausification,[],[f2795]) ).
thf(f2795,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK12 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) ) )
=> ( sK12 @ X1 ) ) )
= $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f2794]) ).
thf(f2794,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(pi_clausification,[],[f2624]) ).
thf(f2536,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f2535]) ).
thf(f2535,plain,
( $false
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f2534]) ).
thf(f2534,plain,
( ( $false = $true )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f2533,f2346]) ).
thf(f2346,plain,
( ( $false
= ( sK12 @ sK29 ) )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f2329]) ).
thf(f2329,plain,
( ( $false
= ( ( ( sK5 @ sK30 @ sK29 )
& ( sK12 @ sK30 ) )
=> ( sK12 @ sK29 ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f2328]) ).
thf(f2328,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK29 )
& ( sK12 @ Y0 ) )
=> ( sK12 @ sK29 ) )
@ sK30 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f2316]) ).
thf(f2316,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK29 )
& ( sK12 @ Y0 ) )
=> ( sK12 @ sK29 ) ) )
= $false )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f2312]) ).
thf(f2312,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK12 @ Y1 ) )
=> ( sK12 @ Y0 ) ) )
@ sK29 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f619]) ).
thf(f619,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK12 @ Y1 ) )
=> ( sK12 @ Y0 ) ) ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f618]) ).
thf(f618,plain,
( spl0_15
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK12 @ Y1 ) )
=> ( sK12 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f2533,plain,
( ( $true
= ( sK12 @ sK29 ) )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15 ),
inference(boolean_simplification,[],[f2532]) ).
thf(f2532,plain,
( ( ( $true
=> ( sK12 @ sK29 ) )
= $true )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15 ),
inference(forward_demodulation,[],[f2459,f2377]) ).
thf(f2377,plain,
( ( ( sK12 @ sK31 )
= $true )
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f2374]) ).
thf(f2374,plain,
( ( $true
= ( ( sK5 @ sK31 @ sK29 )
& ( sK12 @ sK31 ) ) )
| ~ spl0_15 ),
inference(not_proxy_clausification,[],[f2357]) ).
thf(f2357,plain,
( ( $false
= ( ~ ( ( sK5 @ sK31 @ sK29 )
& ( sK12 @ sK31 ) ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f2356]) ).
thf(f2356,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK5 @ Y0 @ sK29 )
& ( sK12 @ Y0 ) )
@ sK31 ) )
| ~ spl0_15 ),
inference(sigma_clausification,[],[f2350]) ).
thf(f2350,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK5 @ Y0 @ sK29 )
& ( sK12 @ Y0 ) ) ) )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f2349]) ).
thf(f2349,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ Y0 @ sK29 )
& ( sK12 @ Y0 ) )
=> $false ) ) )
| ~ spl0_15 ),
inference(backward_demodulation,[],[f2316,f2346]) ).
thf(f2459,plain,
( ( ( ( sK12 @ sK31 )
=> ( sK12 @ sK29 ) )
= $true )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15 ),
inference(boolean_simplification,[],[f2458]) ).
thf(f2458,plain,
( ( $true
= ( ( ( sK12 @ sK31 )
& $true )
=> ( sK12 @ sK29 ) ) )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15 ),
inference(boolean_simplification,[],[f2449]) ).
thf(f2449,plain,
( ( ( ( ( sK12 @ sK31 )
& ( $true
| ( sK3 @ sK31 @ sK29 ) ) )
=> ( sK12 @ sK29 ) )
= $true )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f2417,f2380]) ).
thf(f2380,plain,
( ( ( sK5 @ sK31 @ sK29 )
= $true )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f2379]) ).
thf(f2379,plain,
( ( $true
= ( ( sK5 @ sK31 @ sK29 )
& $true ) )
| ~ spl0_15 ),
inference(backward_demodulation,[],[f2374,f2377]) ).
thf(f2417,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK12 @ X2 )
& ( ( sK5 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) ) )
=> ( sK12 @ X1 ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f2416]) ).
thf(f2416,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK12 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) ) )
=> ( sK12 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_7
| ~ spl0_10 ),
inference(pi_clausification,[],[f2403]) ).
thf(f2403,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK12 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) ) )
=> ( sK12 @ X1 ) ) )
= $true )
| ~ spl0_7
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f2402]) ).
thf(f2402,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(pi_clausification,[],[f2133]) ).
thf(f2133,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) ) )
= $true )
| ~ spl0_7
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f2086]) ).
thf(f2086,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f2066]) ).
thf(f2066,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) ) )
=> ( sK12 @ sK11 ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f2065]) ).
thf(f2065,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) )
@ sK12 )
= $false )
| ~ spl0_7
| ~ spl0_10 ),
inference(sigma_clausification,[],[f2064]) ).
thf(f2064,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f2063]) ).
thf(f2063,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f2062]) ).
thf(f2062,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| $true )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f2061,f247]) ).
thf(f247,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f246,plain,
( spl0_10
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f2308,plain,
( ~ spl0_7
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f2307]) ).
thf(f2307,plain,
( $false
| ~ spl0_7
| ~ spl0_10
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f2306]) ).
thf(f2306,plain,
( ( $false = $true )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_16 ),
inference(boolean_simplification,[],[f2305]) ).
thf(f2305,plain,
( ( ~ $true = $true )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_16 ),
inference(boolean_simplification,[],[f2304]) ).
thf(f2304,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK10 @ sK28 ) ) ) )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_demodulation,[],[f2303,f2299]) ).
thf(f2299,plain,
( ( $true
= ( sK5 @ sK10 @ sK28 ) )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f2282]) ).
thf(f2282,plain,
( ( $false
= ( ( sK5 @ sK10 @ sK28 )
=> ( sK12 @ sK28 ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f2278]) ).
thf(f2278,plain,
( ( ( ^ [Y0: a] :
( ( sK5 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) )
@ sK28 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f622]) ).
thf(f622,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f621]) ).
thf(f621,plain,
( spl0_16
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f2303,plain,
( ( $true
= ( ~ ( ( sK5 @ sK10 @ sK28 )
| ( sK3 @ sK10 @ sK28 ) ) ) )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_16 ),
inference(boolean_simplification,[],[f2302]) ).
thf(f2302,plain,
( ( ( ( ( sK5 @ sK10 @ sK28 )
| ( sK3 @ sK10 @ sK28 ) )
=> $false )
= $true )
| ~ spl0_7
| ~ spl0_10
| ~ spl0_16 ),
inference(superposition,[],[f2148,f2301]) ).
thf(f2301,plain,
( ( ( sK12 @ sK28 )
= $false )
| ~ spl0_16 ),
inference(boolean_simplification,[],[f2300]) ).
thf(f2300,plain,
( ( $false
= ( $true
=> ( sK12 @ sK28 ) ) )
| ~ spl0_16 ),
inference(backward_demodulation,[],[f2282,f2299]) ).
thf(f2148,plain,
( ! [X1: a] :
( ( ( ( sK5 @ sK10 @ X1 )
| ( sK3 @ sK10 @ X1 ) )
=> ( sK12 @ X1 ) )
= $true )
| ~ spl0_7
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f2147]) ).
thf(f2147,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_7
| ~ spl0_10 ),
inference(pi_clausification,[],[f2135]) ).
thf(f2135,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) )
= $true )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f2134]) ).
thf(f2134,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) ) )
= $true )
| ~ spl0_7
| ~ spl0_10 ),
inference(backward_demodulation,[],[f2086,f2133]) ).
thf(f2049,plain,
( ~ spl0_12
| ~ spl0_18
| ~ spl0_57 ),
inference(avatar_contradiction_clause,[],[f2048]) ).
thf(f2048,plain,
( $false
| ~ spl0_12
| ~ spl0_18
| ~ spl0_57 ),
inference(trivial_inequality_removal,[],[f2047]) ).
thf(f2047,plain,
( ( $false = $true )
| ~ spl0_12
| ~ spl0_18
| ~ spl0_57 ),
inference(boolean_simplification,[],[f2046]) ).
thf(f2046,plain,
( ( ( ( sK16 @ sK17 )
=> $true )
= $false )
| ~ spl0_12
| ~ spl0_18
| ~ spl0_57 ),
inference(forward_demodulation,[],[f2039,f2031]) ).
thf(f2031,plain,
( ( ( sK16 @ sK18 )
= $true )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f2030]) ).
thf(f2030,plain,
( spl0_57
<=> ( ( sK16 @ sK18 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
thf(f2039,plain,
( ( $false
= ( ( sK16 @ sK17 )
=> ( sK16 @ sK18 ) ) )
| ~ spl0_12
| ~ spl0_18 ),
inference(boolean_simplification,[],[f2038]) ).
thf(f2038,plain,
( ( ( ( $true
& ( sK16 @ sK17 ) )
=> ( sK16 @ sK18 ) )
= $false )
| ~ spl0_12
| ~ spl0_18 ),
inference(boolean_simplification,[],[f2037]) ).
thf(f2037,plain,
( ( $false
= ( ( ( $true
| ( sK3 @ sK17 @ sK18 ) )
& ( sK16 @ sK17 ) )
=> ( sK16 @ sK18 ) ) )
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_demodulation,[],[f2036,f666]) ).
thf(f666,plain,
( ( $true
= ( sK5 @ sK17 @ sK18 ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f665]) ).
thf(f665,plain,
( spl0_18
<=> ( $true
= ( sK5 @ sK17 @ sK18 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f2036,plain,
( ( $false
= ( ( ( ( sK5 @ sK17 @ sK18 )
| ( sK3 @ sK17 @ sK18 ) )
& ( sK16 @ sK17 ) )
=> ( sK16 @ sK18 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f2035]) ).
thf(f2035,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK5 @ sK17 @ Y0 )
| ( sK3 @ sK17 @ Y0 ) )
& ( sK16 @ sK17 ) )
=> ( sK16 @ Y0 ) )
@ sK18 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f2022]) ).
thf(f2022,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK5 @ sK17 @ Y0 )
| ( sK3 @ sK17 @ Y0 ) )
& ( sK16 @ sK17 ) )
=> ( sK16 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f2020]) ).
thf(f2020,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) )
@ sK17 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f385]) ).
thf(f385,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f384]) ).
thf(f384,plain,
( spl0_12
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f2043,plain,
( ~ spl0_12
| ~ spl0_18
| ~ spl0_56 ),
inference(avatar_contradiction_clause,[],[f2042]) ).
thf(f2042,plain,
( $false
| ~ spl0_12
| ~ spl0_18
| ~ spl0_56 ),
inference(trivial_inequality_removal,[],[f2041]) ).
thf(f2041,plain,
( ( $false = $true )
| ~ spl0_12
| ~ spl0_18
| ~ spl0_56 ),
inference(boolean_simplification,[],[f2040]) ).
thf(f2040,plain,
( ( $false
= ( $false
=> ( sK16 @ sK18 ) ) )
| ~ spl0_12
| ~ spl0_18
| ~ spl0_56 ),
inference(forward_demodulation,[],[f2039,f2028]) ).
thf(f2028,plain,
( ( $false
= ( sK16 @ sK17 ) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f2027]) ).
thf(f2027,plain,
( spl0_56
<=> ( $false
= ( sK16 @ sK17 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
thf(f2032,plain,
( spl0_56
| spl0_57
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f2025,f665,f218,f2030,f2027]) ).
thf(f218,plain,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f2025,plain,
( ( ( sK16 @ sK18 )
= $true )
| ( $false
= ( sK16 @ sK17 ) )
| ~ spl0_8
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f2004]) ).
thf(f2004,plain,
( ( $true
= ( ( sK16 @ sK17 )
=> ( sK16 @ sK18 ) ) )
| ~ spl0_8
| ~ spl0_18 ),
inference(boolean_simplification,[],[f2003]) ).
thf(f2003,plain,
( ( ( ( $true
& ( sK16 @ sK17 ) )
=> ( sK16 @ sK18 ) )
= $true )
| ~ spl0_8
| ~ spl0_18 ),
inference(boolean_simplification,[],[f1996]) ).
thf(f1996,plain,
( ( ( ( ( $true
| ( sK3 @ sK17 @ sK18 ) )
& ( sK16 @ sK17 ) )
=> ( sK16 @ sK18 ) )
= $true )
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[],[f776,f666]) ).
thf(f776,plain,
( ! [X2: a,X1: a] :
( ( ( ( ( sK5 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
& ( sK16 @ X2 ) )
=> ( sK16 @ X1 ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f775]) ).
thf(f775,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_8 ),
inference(pi_clausification,[],[f771]) ).
thf(f771,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ X1 ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f770]) ).
thf(f770,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK16 @ Y1 ) )
=> ( sK16 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_8 ),
inference(pi_clausification,[],[f655]) ).
thf(f655,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK16 @ Y1 ) )
=> ( sK16 @ Y0 ) ) ) )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f651]) ).
thf(f651,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK16 @ Y1 ) )
=> ( sK16 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK15 @ Y0 )
| ( sK5 @ sK15 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f649]) ).
thf(f649,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK16 @ Y1 ) )
=> ( sK16 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK15 @ Y0 )
| ( sK5 @ sK15 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) )
=> ( sK16 @ sK14 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f648]) ).
thf(f648,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) )
@ sK16 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f643]) ).
thf(f643,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f642]) ).
thf(f642,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f639,f641]) ).
thf(f641,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK13 @ Y1 )
| ( sK3 @ sK13 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f639]) ).
thf(f639,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK13 @ Y1 )
| ( sK3 @ sK13 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f638]) ).
thf(f638,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK13 @ Y2 )
| ( sK3 @ sK13 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK14 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK5 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK5 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK14 ) ) ) )
@ sK15 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f633]) ).
thf(f633,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK13 @ Y2 )
| ( sK3 @ sK13 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK14 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK5 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK5 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK14 ) ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f632]) ).
thf(f632,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ sK13 @ Y3 )
| ( sK3 @ sK13 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK5 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK5 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK14 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f629]) ).
thf(f629,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ sK13 @ Y3 )
| ( sK3 @ sK13 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK5 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK5 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f628]) ).
thf(f628,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK13 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f219]) ).
thf(f219,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f1982,plain,
( ~ spl0_8
| ~ spl0_22
| ~ spl0_51 ),
inference(avatar_contradiction_clause,[],[f1981]) ).
thf(f1981,plain,
( $false
| ~ spl0_8
| ~ spl0_22
| ~ spl0_51 ),
inference(trivial_inequality_removal,[],[f1980]) ).
thf(f1980,plain,
( ( $false = $true )
| ~ spl0_8
| ~ spl0_22
| ~ spl0_51 ),
inference(forward_demodulation,[],[f1973,f1968]) ).
thf(f1968,plain,
( ( $false
= ( ( sK16 @ sK19 )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_22
| ~ spl0_51 ),
inference(boolean_simplification,[],[f1967]) ).
thf(f1967,plain,
( ( $false
= ( ( $true
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_22
| ~ spl0_51 ),
inference(boolean_simplification,[],[f1966]) ).
thf(f1966,plain,
( ( $false
= ( ( ( ( sK3 @ sK19 @ sK20 )
| $true )
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_22
| ~ spl0_51 ),
inference(forward_demodulation,[],[f1959,f1872]) ).
thf(f1872,plain,
( ( $true
= ( sK5 @ sK19 @ sK20 ) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1871]) ).
thf(f1871,plain,
( spl0_51
<=> ( $true
= ( sK5 @ sK19 @ sK20 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
thf(f1959,plain,
( ( $false
= ( ( ( ( sK3 @ sK19 @ sK20 )
| ( sK5 @ sK19 @ sK20 ) )
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f1958]) ).
thf(f1958,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK3 @ sK19 @ Y0 )
| ( sK5 @ sK19 @ Y0 ) )
& ( sK16 @ sK19 ) )
=> ( sK16 @ Y0 ) )
@ sK20 ) )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f1942]) ).
thf(f1942,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK3 @ sK19 @ Y0 )
| ( sK5 @ sK19 @ Y0 ) )
& ( sK16 @ sK19 ) )
=> ( sK16 @ Y0 ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f1940]) ).
thf(f1940,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) )
@ sK19 )
= $false )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f958]) ).
thf(f958,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) )
= $false )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f957]) ).
thf(f957,plain,
( spl0_22
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f1973,plain,
( ( ( ( sK16 @ sK19 )
=> ( sK16 @ sK20 ) )
= $true )
| ~ spl0_8
| ~ spl0_51 ),
inference(boolean_simplification,[],[f1972]) ).
thf(f1972,plain,
( ( $true
= ( ( $true
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_8
| ~ spl0_51 ),
inference(boolean_simplification,[],[f1969]) ).
thf(f1969,plain,
( ( ( ( ( $true
| ( sK3 @ sK19 @ sK20 ) )
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) )
= $true )
| ~ spl0_8
| ~ spl0_51 ),
inference(superposition,[],[f776,f1872]) ).
thf(f1965,plain,
( ~ spl0_8
| ~ spl0_22
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f1964]) ).
thf(f1964,plain,
( $false
| ~ spl0_8
| ~ spl0_22
| ~ spl0_52 ),
inference(trivial_inequality_removal,[],[f1963]) ).
thf(f1963,plain,
( ( $false = $true )
| ~ spl0_8
| ~ spl0_22
| ~ spl0_52 ),
inference(backward_demodulation,[],[f1933,f1962]) ).
thf(f1962,plain,
( ( $false
= ( ( sK16 @ sK19 )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_22
| ~ spl0_52 ),
inference(boolean_simplification,[],[f1961]) ).
thf(f1961,plain,
( ( $false
= ( ( $true
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_22
| ~ spl0_52 ),
inference(boolean_simplification,[],[f1960]) ).
thf(f1960,plain,
( ( $false
= ( ( ( $true
| ( sK5 @ sK19 @ sK20 ) )
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_22
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1959,f1875]) ).
thf(f1875,plain,
( ( ( sK3 @ sK19 @ sK20 )
= $true )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1874]) ).
thf(f1874,plain,
( spl0_52
<=> ( ( sK3 @ sK19 @ sK20 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
thf(f1933,plain,
( ( ( ( sK16 @ sK19 )
=> ( sK16 @ sK20 ) )
= $true )
| ~ spl0_8
| ~ spl0_52 ),
inference(boolean_simplification,[],[f1932]) ).
thf(f1932,plain,
( ( $true
= ( ( $true
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_8
| ~ spl0_52 ),
inference(boolean_simplification,[],[f1925]) ).
thf(f1925,plain,
( ( $true
= ( ( ( ( sK5 @ sK19 @ sK20 )
| $true )
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_8
| ~ spl0_52 ),
inference(superposition,[],[f776,f1875]) ).
thf(f1920,plain,
( ~ spl0_8
| ~ spl0_11
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1919]) ).
thf(f1919,plain,
( $false
| ~ spl0_8
| ~ spl0_11
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f1916]) ).
thf(f1916,plain,
( ( $false = $true )
| ~ spl0_8
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[],[f832,f1900]) ).
thf(f1900,plain,
( ( ( ( ( sK5 @ sK13 @ sK27 )
| ( sK3 @ sK13 @ sK27 ) )
=> ( sK16 @ sK27 ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1898]) ).
thf(f1898,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK5 @ sK13 @ Y0 )
| ( sK3 @ sK13 @ Y0 ) )
=> ( sK16 @ Y0 ) )
@ sK27 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f955]) ).
thf(f955,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK13 @ Y0 )
| ( sK3 @ sK13 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f954]) ).
thf(f954,plain,
( spl0_21
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK13 @ Y0 )
| ( sK3 @ sK13 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f832,plain,
( ! [X0: a] :
( $true
= ( ( ( sK5 @ sK13 @ X0 )
| ( sK3 @ sK13 @ X0 ) )
=> ( sK16 @ X0 ) ) )
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[],[f828]) ).
thf(f828,plain,
( ! [X0: a] :
( $true
= ( ( ( ( sK5 @ sK13 @ X0 )
| ( sK3 @ sK13 @ X0 ) )
& $true )
=> ( sK16 @ X0 ) ) )
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f776,f382]) ).
thf(f382,plain,
( ( $true
= ( sK16 @ sK13 ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f381]) ).
thf(f381,plain,
( spl0_11
<=> ( $true
= ( sK16 @ sK13 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f1876,plain,
( spl0_51
| spl0_52
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1869,f957,f1874,f1871]) ).
thf(f1869,plain,
( ( ( sK3 @ sK19 @ sK20 )
= $true )
| ( $true
= ( sK5 @ sK19 @ sK20 ) )
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f1272]) ).
thf(f1272,plain,
( ( $true
= ( ( sK3 @ sK19 @ sK20 )
| ( sK5 @ sK19 @ sK20 ) ) )
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f1027]) ).
thf(f1027,plain,
( ( ( ( ( sK3 @ sK19 @ sK20 )
| ( sK5 @ sK19 @ sK20 ) )
& ( sK16 @ sK19 ) )
= $true )
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f1008]) ).
thf(f1008,plain,
( ( $false
= ( ( ( ( sK3 @ sK19 @ sK20 )
| ( sK5 @ sK19 @ sK20 ) )
& ( sK16 @ sK19 ) )
=> ( sK16 @ sK20 ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f1007]) ).
thf(f1007,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK3 @ sK19 @ Y0 )
| ( sK5 @ sK19 @ Y0 ) )
& ( sK16 @ sK19 ) )
=> ( sK16 @ Y0 ) )
@ sK20 ) )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f986]) ).
thf(f986,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK3 @ sK19 @ Y0 )
| ( sK5 @ sK19 @ Y0 ) )
& ( sK16 @ sK19 ) )
=> ( sK16 @ Y0 ) ) ) )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f982]) ).
thf(f982,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) )
@ sK19 )
= $false )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f958]) ).
thf(f959,plain,
( spl0_21
| spl0_22
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f950,f218,f957,f954]) ).
thf(f950,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK13 @ Y0 )
| ( sK3 @ sK13 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f933]) ).
thf(f933,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK13 @ Y0 )
| ( sK3 @ sK13 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) ) )
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f848]) ).
thf(f848,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK13 @ Y0 )
| ( sK3 @ sK13 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f844]) ).
thf(f844,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK13 @ Y0 )
| ( sK3 @ sK13 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_8 ),
inference(superposition,[],[f837,f653]) ).
thf(f653,plain,
( ( $false
= ( sK16 @ sK14 ) )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f652]) ).
thf(f652,plain,
( ( $false
= ( $true
=> ( sK16 @ sK14 ) ) )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f649,f651]) ).
thf(f837,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK3 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK13 @ Y0 )
| ( sK3 @ sK13 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK14 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f836]) ).
thf(f836,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK13 @ Y1 )
| ( sK3 @ sK13 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) )
@ X1 )
= $true )
| ~ spl0_8 ),
inference(pi_clausification,[],[f693]) ).
thf(f693,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK13 @ Y1 )
| ( sK3 @ sK13 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f641]) ).
thf(f825,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f824]) ).
thf(f824,plain,
( $false
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f823]) ).
thf(f823,plain,
( ( $false = $true )
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f822,f637]) ).
thf(f637,plain,
( ( $false
= ( sK16 @ sK18 ) )
| ~ spl0_12 ),
inference(boolean_simplification,[],[f636]) ).
thf(f636,plain,
( ( $false
= ( $true
=> ( sK16 @ sK18 ) ) )
| ~ spl0_12 ),
inference(backward_demodulation,[],[f631,f635]) ).
thf(f635,plain,
( ( ( ( ( sK5 @ sK17 @ sK18 )
| ( sK3 @ sK17 @ sK18 ) )
& ( sK16 @ sK17 ) )
= $true )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f631]) ).
thf(f631,plain,
( ( $false
= ( ( ( ( sK5 @ sK17 @ sK18 )
| ( sK3 @ sK17 @ sK18 ) )
& ( sK16 @ sK17 ) )
=> ( sK16 @ sK18 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f630]) ).
thf(f630,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( sK5 @ sK17 @ Y0 )
| ( sK3 @ sK17 @ Y0 ) )
& ( sK16 @ sK17 ) )
=> ( sK16 @ Y0 ) )
@ sK18 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f627]) ).
thf(f627,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK5 @ sK17 @ Y0 )
| ( sK3 @ sK17 @ Y0 ) )
& ( sK16 @ sK17 ) )
=> ( sK16 @ Y0 ) ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f626]) ).
thf(f626,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) )
@ sK17 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f385]) ).
thf(f822,plain,
( ( ( sK16 @ sK18 )
= $true )
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(boolean_simplification,[],[f821]) ).
thf(f821,plain,
( ( $true
= ( $true
=> ( sK16 @ sK18 ) ) )
| ~ spl0_8
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f796,f644]) ).
thf(f644,plain,
( ( ( sK16 @ sK17 )
= $true )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f635]) ).
thf(f796,plain,
( ( $true
= ( ( sK16 @ sK17 )
=> ( sK16 @ sK18 ) ) )
| ~ spl0_8
| ~ spl0_17 ),
inference(boolean_simplification,[],[f795]) ).
thf(f795,plain,
( ( ( ( $true
& ( sK16 @ sK17 ) )
=> ( sK16 @ sK18 ) )
= $true )
| ~ spl0_8
| ~ spl0_17 ),
inference(boolean_simplification,[],[f792]) ).
thf(f792,plain,
( ( ( ( ( ( sK5 @ sK17 @ sK18 )
| $true )
& ( sK16 @ sK17 ) )
=> ( sK16 @ sK18 ) )
= $true )
| ~ spl0_8
| ~ spl0_17 ),
inference(superposition,[],[f776,f663]) ).
thf(f663,plain,
( ( ( sK3 @ sK17 @ sK18 )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f662]) ).
thf(f662,plain,
( spl0_17
<=> ( ( sK3 @ sK17 @ sK18 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f667,plain,
( spl0_17
| spl0_18
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f658,f384,f665,f662]) ).
thf(f658,plain,
( ( $true
= ( sK5 @ sK17 @ sK18 ) )
| ( ( sK3 @ sK17 @ sK18 )
= $true )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f647]) ).
thf(f647,plain,
( ( ( ( sK5 @ sK17 @ sK18 )
| ( sK3 @ sK17 @ sK18 ) )
= $true )
| ~ spl0_12 ),
inference(boolean_simplification,[],[f646]) ).
thf(f646,plain,
( ( ( ( ( sK5 @ sK17 @ sK18 )
| ( sK3 @ sK17 @ sK18 ) )
& $true )
= $true )
| ~ spl0_12 ),
inference(backward_demodulation,[],[f635,f644]) ).
thf(f623,plain,
( spl0_15
| spl0_16
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f614,f246,f215,f621,f618]) ).
thf(f614,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK12 @ Y1 ) )
=> ( sK12 @ Y0 ) ) ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f608]) ).
thf(f608,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK12 @ Y1 ) )
=> ( sK12 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(not_proxy_clausification,[],[f511]) ).
thf(f511,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK12 @ Y1 ) )
=> ( sK12 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f510]) ).
thf(f510,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( sK12 @ Y1 ) )
=> ( sK12 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f500,f504]) ).
thf(f504,plain,
( ( $false
= ( sK12 @ sK11 ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(binary_proxy_clausification,[],[f502]) ).
thf(f502,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) ) )
=> ( sK12 @ sK11 ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f501]) ).
thf(f501,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) )
@ sK12 )
= $false )
| ~ spl0_7
| ~ spl0_10 ),
inference(sigma_clausification,[],[f498]) ).
thf(f498,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f497]) ).
thf(f497,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[],[f496]) ).
thf(f496,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| $true )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f394,f247]) ).
thf(f394,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f393]) ).
thf(f393,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK10 @ Y2 )
| ( sK3 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK11 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f390]) ).
thf(f390,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK10 @ Y2 )
| ( sK3 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f389]) ).
thf(f389,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK10 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f216]) ).
thf(f500,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK10 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK11 ) )
= $true )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f499]) ).
thf(f499,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) )
@ X1 )
= $true )
| ~ spl0_10 ),
inference(pi_clausification,[],[f247]) ).
thf(f495,plain,
( spl0_13
| spl0_14
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f486,f243,f215,f493,f490]) ).
thf(f486,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK12 @ Y0 ) )
=> ( sK12 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f409]) ).
thf(f409,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK12 @ Y0 ) )
=> ( sK12 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(not_proxy_clausification,[],[f408]) ).
thf(f408,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK12 @ Y0 ) )
=> ( sK12 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f407]) ).
thf(f407,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK12 @ Y0 ) )
=> ( sK12 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK10 @ Y0 )
=> ( sK12 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f392,f401]) ).
thf(f401,plain,
( ( $false
= ( sK12 @ sK11 ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f400]) ).
thf(f400,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK12 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ sK10 @ Y0 )
| ( sK3 @ sK10 @ Y0 ) )
=> ( sK12 @ Y0 ) ) ) )
=> ( sK12 @ sK11 ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f399]) ).
thf(f399,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) )
@ sK12 )
= $false )
| ~ spl0_7
| ~ spl0_9 ),
inference(sigma_clausification,[],[f397]) ).
thf(f397,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f396]) ).
thf(f396,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f395]) ).
thf(f395,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f394,f244]) ).
thf(f392,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK10 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK11 ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f391]) ).
thf(f391,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) )
@ X1 )
= $true )
| ~ spl0_9 ),
inference(pi_clausification,[],[f244]) ).
thf(f386,plain,
( spl0_11
| spl0_12
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f379,f218,f384,f381]) ).
thf(f379,plain,
( ( $true
= ( sK16 @ sK13 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f341]) ).
thf(f341,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) )
=> ( sK16 @ sK13 ) )
= $true )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f340]) ).
thf(f340,plain,
( ( $true
= ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( sK16 @ Y0 ) )
=> ( sK16 @ Y1 ) ) ) ) )
=> ( sK16 @ sK13 ) ) )
| ~ spl0_8 ),
inference(superposition,[],[f324,f267]) ).
thf(f267,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK15 @ Y0 )
| ( sK5 @ sK15 @ Y0 ) )
=> ( sK16 @ Y0 ) ) )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f264]) ).
thf(f264,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK16 @ Y1 ) )
=> ( sK16 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK15 @ Y0 )
| ( sK5 @ sK15 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f262]) ).
thf(f262,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK16 @ Y1 ) )
=> ( sK16 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK15 @ Y0 )
| ( sK5 @ sK15 @ Y0 ) )
=> ( sK16 @ Y0 ) ) ) )
=> ( sK16 @ sK14 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f261]) ).
thf(f261,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) )
@ sK16 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f260]) ).
thf(f260,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f259]) ).
thf(f259,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f256,f258]) ).
thf(f258,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK13 @ Y1 )
| ( sK3 @ sK13 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f256]) ).
thf(f256,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK13 @ Y1 )
| ( sK3 @ sK13 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f255]) ).
thf(f255,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK13 @ Y2 )
| ( sK3 @ sK13 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK14 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK5 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK5 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK14 ) ) ) )
@ sK15 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f254]) ).
thf(f254,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK3 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK13 @ Y2 )
| ( sK3 @ sK13 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK14 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK5 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK5 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK14 ) ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f253]) ).
thf(f253,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ sK13 @ Y3 )
| ( sK3 @ sK13 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK5 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK5 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK14 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f252]) ).
thf(f252,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK3 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ sK13 @ Y3 )
| ( sK3 @ sK13 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK5 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK5 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f251]) ).
thf(f251,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK13 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f219]) ).
thf(f324,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK15 @ Y0 )
| ( sK5 @ sK15 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK5 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK13 ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f323]) ).
thf(f323,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[],[f308]) ).
thf(f308,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f307]) ).
thf(f307,plain,
( ( ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK15 @ Y1 )
| ( sK5 @ sK15 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK5 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
= $true )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f258,f306]) ).
thf(f306,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK3 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK13 @ Y1 )
| ( sK3 @ sK13 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f258]) ).
thf(f248,plain,
( spl0_9
| spl0_10
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f241,f215,f246,f243]) ).
thf(f241,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
= $true )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f228]) ).
thf(f228,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f226]) ).
thf(f226,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ sK10 @ Y1 )
| ( sK3 @ sK10 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f225]) ).
thf(f225,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK10 @ Y2 )
| ( sK3 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK11 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f224]) ).
thf(f224,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ sK10 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK5 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ sK10 @ Y2 )
| ( sK3 @ sK10 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f223]) ).
thf(f223,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK10 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f216]) ).
thf(f220,plain,
( spl0_7
| spl0_8
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f213,f52,f218,f215]) ).
thf(f52,plain,
( spl0_1
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f213,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f53]) ).
thf(f53,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f202,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f201]) ).
thf(f201,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f200,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f199,f138]) ).
thf(f138,plain,
( ( ( sK6 @ sK7 )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f137]) ).
thf(f137,plain,
( ( $false
= ( ( ( sK6 @ sK8 )
& ( ( sK3 @ sK8 @ sK7 )
| ( sK5 @ sK8 @ sK7 ) ) )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f136]) ).
thf(f136,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK7 )
| ( sK5 @ Y0 @ sK7 ) ) )
=> ( sK6 @ sK7 ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f135]) ).
thf(f135,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK7 )
| ( sK5 @ Y0 @ sK7 ) ) )
=> ( sK6 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f131]) ).
thf(f131,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f128]) ).
thf(f128,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f85]) ).
thf(f85,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f84]) ).
thf(f84,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& $true ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f82,f29]) ).
thf(f29,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK5 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK5 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK5 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> ( sK6 @ sK2 ) ) ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f21]) ).
thf(f21,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) )
= $false ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) ) )
= $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] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( $false
= ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK5 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 ) ) ) ) ),
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] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( sK3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK4 @ Y2 )
| ( Y0 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK4 @ Y2 )
| ( Y0 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( Y0 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( sK3 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y1 @ Y5 )
| ( sK3 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( Y0 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK4 @ Y2 )
| ( Y0 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK4 @ Y2 )
| ( Y0 @ sK4 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( Y0 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [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] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK3 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y2 @ Y6 )
| ( sK3 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y4 @ Y6 )
| ( Y1 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y7 @ Y6 )
| ( sK3 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y4 @ Y6 )
| ( Y1 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( Y1 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( Y1 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( Y1 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( Y1 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ 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] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( sK3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK3 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y2 @ Y6 )
| ( sK3 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y4 @ Y6 )
| ( Y1 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y7 @ Y6 )
| ( sK3 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y4 @ Y6 )
| ( Y1 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( Y1 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( Y1 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( Y1 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( Y1 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ 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] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y3 @ Y7 )
| ( Y0 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y5 @ Y7 )
| ( Y2 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y5 @ Y7 )
| ( Y2 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( Y2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ sK2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( Y2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ sK2 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ 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] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( Y2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y3 @ Y7 )
| ( Y0 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y5 @ Y7 )
| ( Y2 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y5 @ Y7 )
| ( Y2 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( Y2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ sK2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( Y2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ sK2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ 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] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y3 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y4 @ Y8 )
| ( Y1 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ 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] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y3 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y4 @ Y8 )
| ( Y1 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ 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] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y3 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y4 @ Y8 )
| ( Y1 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ 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] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y3 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y3 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y3 @ Y4 @ Y8 )
| ( Y1 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( ( Y3 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
& ( Y7 @ Y9 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y3 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a,X2: a > a > $o,X3: a] :
( ( ( ! [X4: a,X5: a,X6: a] :
( ( ! [X7: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X7 @ X9 )
& ( ( X2 @ X9 @ X8 )
| ( X0 @ X9 @ X8 ) ) )
=> ( X7 @ X8 ) )
& ! [X10: a] :
( ( ( X0 @ X4 @ X10 )
| ( X2 @ X4 @ X10 ) )
=> ( X7 @ X10 ) ) )
=> ( X7 @ X6 ) )
& ! [X11: a > $o] :
( ( ! [X12: a] :
( ( ( X2 @ X6 @ X12 )
| ( X0 @ X6 @ X12 ) )
=> ( X11 @ X12 ) )
& ! [X13: a,X14: a] :
( ( ( X11 @ X14 )
& ( ( X0 @ X14 @ X13 )
| ( X2 @ X14 @ X13 ) ) )
=> ( X11 @ X13 ) ) )
=> ( X11 @ X5 ) ) )
=> ! [X15: a > $o] :
( ( ! [X16: a] :
( ( ( X0 @ X4 @ X16 )
| ( X2 @ X4 @ X16 ) )
=> ( X15 @ X16 ) )
& ! [X17: a,X18: a] :
( ( ( X15 @ X17 )
& ( ( X2 @ X17 @ X18 )
| ( X0 @ X17 @ X18 ) ) )
=> ( X15 @ X18 ) ) )
=> ( X15 @ X5 ) ) )
& ! [X19: a,X20: a] :
( ( ! [X21: a > $o] :
( ( ! [X22: a] :
( ( X0 @ X20 @ X22 )
=> ( X21 @ X22 ) )
& ! [X23: a,X24: a] :
( ( ( X21 @ X23 )
& ( X0 @ X23 @ X24 ) )
=> ( X21 @ X24 ) ) )
=> ( X21 @ X19 ) )
| ! [X25: a > $o] :
( ( ! [X26: a] :
( ( X2 @ X20 @ X26 )
=> ( X25 @ X26 ) )
& ! [X27: a,X28: a] :
( ( ( X25 @ X28 )
& ( X2 @ X28 @ X27 ) )
=> ( X25 @ X27 ) ) )
=> ( X25 @ X19 ) ) )
=> ! [X29: a > $o] :
( ( ! [X30: a] :
( ( ( X2 @ X20 @ X30 )
| ( X0 @ X20 @ X30 ) )
=> ( X29 @ X30 ) )
& ! [X31: a,X32: a] :
( ( ( ( X2 @ X31 @ X32 )
| ( X0 @ X31 @ X32 ) )
& ( X29 @ X31 ) )
=> ( X29 @ X32 ) ) )
=> ( X29 @ X19 ) ) ) )
=> ! [X33: a > $o] :
( ( ! [X34: a] :
( ( ( X0 @ X1 @ X34 )
| ( X2 @ X1 @ X34 ) )
=> ( X33 @ X34 ) )
& ! [X35: a,X36: a] :
( ( ( ( X0 @ X35 @ X36 )
| ( X2 @ X35 @ X36 ) )
& ( X33 @ X35 ) )
=> ( X33 @ X36 ) ) )
=> ( X33 @ X3 ) ) )
=> ! [X37: a > $o] :
( ( ! [X38: a,X39: a] :
( ( ( ( X2 @ X38 @ X39 )
| ( X0 @ X38 @ X39 ) )
& ( X37 @ X38 ) )
=> ( X37 @ X39 ) )
& ! [X40: a] :
( ( ( X0 @ X1 @ X40 )
| ( X2 @ X1 @ X40 ) )
=> ( X37 @ X40 ) ) )
=> ( X37 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > $o,X2: a,X0: a > a > $o,X3: a] :
( ( ( ! [X4: a,X10: a,X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
& ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X0 @ X5 @ X7 )
| ( X1 @ X5 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
& ! [X5: a,X4: a] :
( ( ! [X6: a > $o] :
( ( ! [X7: a] :
( ( X1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X1 @ X8 @ X9 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X7: a] :
( ( X0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X0 @ X8 @ X9 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X0 @ X4 @ X7 )
| ( X1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X2 @ X7 )
| ( X0 @ X2 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X3 ) ) )
=> ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X2 @ X7 )
| ( X0 @ X2 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: a > a > $o,X2: a,X0: a > a > $o,X3: a] :
( ( ( ! [X4: a,X10: a,X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
& ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X0 @ X5 @ X7 )
| ( X1 @ X5 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
& ! [X5: a,X4: a] :
( ( ! [X6: a > $o] :
( ( ! [X7: a] :
( ( X1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X1 @ X8 @ X9 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X7: a] :
( ( X0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X0 @ X8 @ X9 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X0 @ X4 @ X7 )
| ( X1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X2 @ X7 )
| ( X0 @ X2 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X3 ) ) )
=> ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X2 @ X7 )
| ( X0 @ X2 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2qUpj2rD0D/Vampire---4.8_21833',cTHM251D_pme) ).
thf(f82,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK5 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f78]) ).
thf(f78,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK5 @ sK4 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f67,f27]) ).
thf(f27,plain,
( ( sK6 @ sK2 )
= $false ),
inference(boolean_simplification,[],[f26]) ).
thf(f26,plain,
( $false
= ( $true
=> ( sK6 @ sK2 ) ) ),
inference(backward_demodulation,[],[f23,f25]) ).
thf(f67,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK4 @ Y0 )
| ( sK5 @ sK4 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK2 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f66]) ).
thf(f66,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f56]) ).
thf(f56,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f55,plain,
( spl0_2
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f199,plain,
( ( ( sK6 @ sK7 )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f198]) ).
thf(f198,plain,
( ( $true
= ( $true
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f197,f166]) ).
thf(f166,plain,
( ( ( sK6 @ sK9 )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f165]) ).
thf(f165,plain,
( ( ( ( sK6 @ sK9 )
& $true )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f157,f163]) ).
thf(f163,plain,
( ( ( ( sK3 @ sK9 @ sK7 )
| ( sK5 @ sK9 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f157]) ).
thf(f157,plain,
( ( ( ( sK6 @ sK9 )
& ( ( sK3 @ sK9 @ sK7 )
| ( sK5 @ sK9 @ sK7 ) ) )
= $true )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f147,plain,
( ( $false
= ( ~ ( ( sK6 @ sK9 )
& ( ( sK3 @ sK9 @ sK7 )
| ( sK5 @ sK9 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f146]) ).
thf(f146,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK7 )
| ( sK5 @ Y0 @ sK7 ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f142]) ).
thf(f142,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK7 )
| ( sK5 @ Y0 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f141]) ).
thf(f141,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ sK7 )
| ( sK5 @ Y0 @ sK7 ) ) )
=> $false ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f135,f138]) ).
thf(f197,plain,
( ( $true
= ( ( sK6 @ sK9 )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f196]) ).
thf(f196,plain,
( ( $true
= ( ( ( sK6 @ sK9 )
& $true )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f195]) ).
thf(f195,plain,
( ( $true
= ( ( ( sK6 @ sK9 )
& ( ( sK5 @ sK9 @ sK7 )
| $true ) )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_4 ),
inference(superposition,[],[f37,f181]) ).
thf(f181,plain,
( ( $true
= ( sK3 @ sK9 @ sK7 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f180]) ).
thf(f180,plain,
( spl0_4
<=> ( $true
= ( sK3 @ sK9 @ sK7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f37,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 )
& ( ( sK5 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) ) )
=> ( sK6 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f36]) ).
thf(f36,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[],[f33]) ).
thf(f33,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK5 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f32]) ).
thf(f32,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f30]) ).
thf(f30,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK5 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $true ),
inference(backward_demodulation,[],[f25,f29]) ).
thf(f192,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f191]) ).
thf(f191,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f190,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f189,f138]) ).
thf(f189,plain,
( ( ( sK6 @ sK7 )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f188]) ).
thf(f188,plain,
( ( $true
= ( $true
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f187,f166]) ).
thf(f187,plain,
( ( $true
= ( ( sK6 @ sK9 )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f186]) ).
thf(f186,plain,
( ( $true
= ( ( ( sK6 @ sK9 )
& $true )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f185]) ).
thf(f185,plain,
( ( ( ( ( sK6 @ sK9 )
& ( $true
| ( sK3 @ sK9 @ sK7 ) ) )
=> ( sK6 @ sK7 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[],[f37,f178]) ).
thf(f178,plain,
( ( ( sK5 @ sK9 @ sK7 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f177,plain,
( spl0_3
<=> ( ( sK5 @ sK9 @ sK7 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f182,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f175,f55,f180,f177]) ).
thf(f175,plain,
( ( ( sK5 @ sK9 @ sK7 )
= $true )
| ( $true
= ( sK3 @ sK9 @ sK7 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f163]) ).
thf(f57,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f50,f55,f52]) ).
thf(f50,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( 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] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK5 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y0 @ Y3 )
| ( sK3 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK3 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y0 @ Y4 )
| ( sK3 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK5 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK5 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK4 @ Y1 )
| ( sK5 @ sK4 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV152^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 11:22:36 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_NEQ_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.2qUpj2rD0D/Vampire---4.8_21833
% 0.14/0.38 % (22055)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.14/0.38 % (22056)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.14/0.38 % (22060)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.14/0.38 % (22061)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.14/0.38 % (22058)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.38 % (22058)Instruction limit reached!
% 0.14/0.38 % (22058)------------------------------
% 0.14/0.38 % (22058)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22062)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.14/0.38 % (22058)Termination reason: Unknown
% 0.14/0.38 % (22058)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (22058)Memory used [KB]: 1023
% 0.14/0.38 % (22058)Time elapsed: 0.003 s
% 0.14/0.38 % (22058)Instructions burned: 3 (million)
% 0.14/0.38 % (22058)------------------------------
% 0.14/0.38 % (22058)------------------------------
% 0.14/0.38 % (22057)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on Vampire---4 for (2999ds/27Mi)
% 0.14/0.38 % (22056)Instruction limit reached!
% 0.14/0.38 % (22056)------------------------------
% 0.14/0.38 % (22056)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22056)Termination reason: Unknown
% 0.14/0.38 % (22056)Termination phase: Preprocessing 3
% 0.14/0.38
% 0.14/0.38 % (22056)Memory used [KB]: 1023
% 0.14/0.38 % (22056)Time elapsed: 0.004 s
% 0.14/0.38 % (22056)Instructions burned: 4 (million)
% 0.14/0.38 % (22056)------------------------------
% 0.14/0.38 % (22056)------------------------------
% 0.14/0.38 % (22062)Instruction limit reached!
% 0.14/0.38 % (22062)------------------------------
% 0.14/0.38 % (22062)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22062)Termination reason: Unknown
% 0.14/0.38 % (22062)Termination phase: Naming
% 0.14/0.38
% 0.14/0.38 % (22062)Memory used [KB]: 1023
% 0.14/0.38 % (22062)Time elapsed: 0.004 s
% 0.14/0.38 % (22062)Instructions burned: 3 (million)
% 0.14/0.38 % (22062)------------------------------
% 0.14/0.38 % (22062)------------------------------
% 0.14/0.38 % (22059)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.38 % (22059)Instruction limit reached!
% 0.14/0.38 % (22059)------------------------------
% 0.14/0.38 % (22059)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22059)Termination reason: Unknown
% 0.14/0.38 % (22059)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (22059)Memory used [KB]: 1023
% 0.14/0.38 % (22059)Time elapsed: 0.003 s
% 0.14/0.38 % (22059)Instructions burned: 2 (million)
% 0.14/0.38 % (22059)------------------------------
% 0.14/0.38 % (22059)------------------------------
% 0.14/0.39 % (22061)Instruction limit reached!
% 0.14/0.39 % (22061)------------------------------
% 0.14/0.39 % (22061)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (22061)Termination reason: Unknown
% 0.14/0.39 % (22061)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (22061)Memory used [KB]: 5628
% 0.14/0.39 % (22061)Time elapsed: 0.013 s
% 0.14/0.39 % (22061)Instructions burned: 19 (million)
% 0.14/0.39 % (22061)------------------------------
% 0.14/0.39 % (22061)------------------------------
% 0.14/0.39 % (22057)Instruction limit reached!
% 0.14/0.39 % (22057)------------------------------
% 0.14/0.39 % (22057)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (22057)Termination reason: Unknown
% 0.14/0.39 % (22057)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (22057)Memory used [KB]: 5756
% 0.14/0.39 % (22057)Time elapsed: 0.018 s
% 0.14/0.39 % (22057)Instructions burned: 27 (million)
% 0.14/0.39 % (22057)------------------------------
% 0.14/0.39 % (22057)------------------------------
% 0.14/0.39 % (22065)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.14/0.39 % (22066)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.14/0.40 % (22066)Instruction limit reached!
% 0.14/0.40 % (22066)------------------------------
% 0.14/0.40 % (22066)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (22066)Termination reason: Unknown
% 0.14/0.40 % (22066)Termination phase: Naming
% 0.14/0.40
% 0.14/0.40 % (22066)Memory used [KB]: 1023
% 0.14/0.40 % (22066)Time elapsed: 0.004 s
% 0.14/0.40 % (22066)Instructions burned: 4 (million)
% 0.14/0.40 % (22066)------------------------------
% 0.14/0.40 % (22066)------------------------------
% 0.14/0.40 % (22069)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.14/0.40 % (22063)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (2999ds/37Mi)
% 0.14/0.40 % (22070)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.14/0.40 % (22065)Instruction limit reached!
% 0.14/0.40 % (22065)------------------------------
% 0.14/0.40 % (22065)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (22065)Termination reason: Unknown
% 0.14/0.40 % (22065)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (22065)Memory used [KB]: 5756
% 0.14/0.40 % (22065)Time elapsed: 0.011 s
% 0.14/0.40 % (22065)Instructions burned: 15 (million)
% 0.14/0.40 % (22065)------------------------------
% 0.14/0.40 % (22065)------------------------------
% 0.14/0.41 % (22070)Instruction limit reached!
% 0.14/0.41 % (22070)------------------------------
% 0.14/0.41 % (22070)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (22070)Termination reason: Unknown
% 0.14/0.41 % (22070)Termination phase: Property scanning
% 0.14/0.41
% 0.14/0.41 % (22070)Memory used [KB]: 1151
% 0.14/0.41 % (22070)Time elapsed: 0.006 s
% 0.14/0.41 % (22070)Instructions burned: 7 (million)
% 0.14/0.41 % (22070)------------------------------
% 0.14/0.41 % (22070)------------------------------
% 0.14/0.41 % (22071)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.22/0.41 % (22072)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.41 % (22072)Instruction limit reached!
% 0.22/0.41 % (22072)------------------------------
% 0.22/0.41 % (22072)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (22072)Termination reason: Unknown
% 0.22/0.41 % (22072)Termination phase: Naming
% 0.22/0.41
% 0.22/0.41 % (22072)Memory used [KB]: 1023
% 0.22/0.41 % (22072)Time elapsed: 0.004 s
% 0.22/0.41 % (22072)Instructions burned: 3 (million)
% 0.22/0.41 % (22072)------------------------------
% 0.22/0.41 % (22072)------------------------------
% 0.22/0.42 % (22071)Instruction limit reached!
% 0.22/0.42 % (22071)------------------------------
% 0.22/0.42 % (22071)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (22071)Termination reason: Unknown
% 0.22/0.42 % (22071)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (22071)Memory used [KB]: 1151
% 0.22/0.42 % (22071)Time elapsed: 0.010 s
% 0.22/0.42 % (22071)Instructions burned: 16 (million)
% 0.22/0.42 % (22071)------------------------------
% 0.22/0.42 % (22071)------------------------------
% 0.22/0.42 % (22073)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.42 % (22073)Instruction limit reached!
% 0.22/0.42 % (22073)------------------------------
% 0.22/0.42 % (22073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (22073)Termination reason: Unknown
% 0.22/0.42 % (22073)Termination phase: Naming
% 0.22/0.42
% 0.22/0.42 % (22073)Memory used [KB]: 1023
% 0.22/0.42 % (22073)Time elapsed: 0.004 s
% 0.22/0.42 % (22073)Instructions burned: 4 (million)
% 0.22/0.42 % (22073)------------------------------
% 0.22/0.42 % (22073)------------------------------
% 0.22/0.42 % (22074)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.42 % (22063)Instruction limit reached!
% 0.22/0.42 % (22063)------------------------------
% 0.22/0.42 % (22063)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (22063)Termination reason: Unknown
% 0.22/0.42 % (22063)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (22063)Memory used [KB]: 5628
% 0.22/0.42 % (22063)Time elapsed: 0.027 s
% 0.22/0.42 % (22063)Instructions burned: 37 (million)
% 0.22/0.42 % (22063)------------------------------
% 0.22/0.42 % (22063)------------------------------
% 0.22/0.43 % (22075)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.43 % (22074)Instruction limit reached!
% 0.22/0.43 % (22074)------------------------------
% 0.22/0.43 % (22074)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (22074)Termination reason: Unknown
% 0.22/0.43 % (22074)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (22074)Memory used [KB]: 1151
% 0.22/0.43 % (22074)Time elapsed: 0.009 s
% 0.22/0.43 % (22074)Instructions burned: 9 (million)
% 0.22/0.43 % (22074)------------------------------
% 0.22/0.43 % (22074)------------------------------
% 0.22/0.43 % (22075)Instruction limit reached!
% 0.22/0.43 % (22075)------------------------------
% 0.22/0.43 % (22075)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (22075)Termination reason: Unknown
% 0.22/0.43 % (22075)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (22075)Memory used [KB]: 1023
% 0.22/0.43 % (22075)Time elapsed: 0.004 s
% 0.22/0.43 % (22075)Instructions burned: 3 (million)
% 0.22/0.43 % (22075)------------------------------
% 0.22/0.43 % (22075)------------------------------
% 0.22/0.43 % (22076)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.22/0.43 % (22076)Instruction limit reached!
% 0.22/0.43 % (22076)------------------------------
% 0.22/0.43 % (22076)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (22076)Termination reason: Unknown
% 0.22/0.43 % (22076)Termination phase: Preprocessing 3
% 0.22/0.43
% 0.22/0.43 % (22076)Memory used [KB]: 1023
% 0.22/0.43 % (22076)Time elapsed: 0.005 s
% 0.22/0.43 % (22076)Instructions burned: 5 (million)
% 0.22/0.43 % (22076)------------------------------
% 0.22/0.43 % (22076)------------------------------
% 0.22/0.44 % (22077)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.22/0.44 % (22078)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.22/0.44 % (22079)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.44 % (22080)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on Vampire---4 for (2999ds/902Mi)
% 0.22/0.45 % (22077)Instruction limit reached!
% 0.22/0.45 % (22077)------------------------------
% 0.22/0.45 % (22077)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (22077)Termination reason: Unknown
% 0.22/0.45 % (22077)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (22077)Memory used [KB]: 5756
% 0.22/0.45 % (22077)Time elapsed: 0.013 s
% 0.22/0.45 % (22077)Instructions burned: 19 (million)
% 0.22/0.45 % (22077)------------------------------
% 0.22/0.45 % (22077)------------------------------
% 0.22/0.45 % (22079)Instruction limit reached!
% 0.22/0.45 % (22079)------------------------------
% 0.22/0.45 % (22079)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (22079)Termination reason: Unknown
% 0.22/0.45 % (22079)Termination phase: Preprocessing 3
% 0.22/0.45
% 0.22/0.45 % (22079)Memory used [KB]: 1023
% 0.22/0.45 % (22079)Time elapsed: 0.005 s
% 0.22/0.45 % (22079)Instructions burned: 6 (million)
% 0.22/0.45 % (22079)------------------------------
% 0.22/0.45 % (22079)------------------------------
% 0.22/0.45 % (22081)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (2999ds/21Mi)
% 0.22/0.46 % (22082)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.22/0.46 % (22081)Instruction limit reached!
% 0.22/0.46 % (22081)------------------------------
% 0.22/0.46 % (22081)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (22081)Termination reason: Unknown
% 0.22/0.46 % (22081)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (22081)Memory used [KB]: 5884
% 0.22/0.46 % (22081)Time elapsed: 0.014 s
% 0.22/0.46 % (22081)Instructions burned: 21 (million)
% 0.22/0.46 % (22081)------------------------------
% 0.22/0.46 % (22081)------------------------------
% 0.22/0.46 % (22083)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.46 % (22082)Instruction limit reached!
% 0.22/0.46 % (22082)------------------------------
% 0.22/0.46 % (22082)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (22082)Termination reason: Unknown
% 0.22/0.46 % (22082)Termination phase: Property scanning
% 0.22/0.46
% 0.22/0.46 % (22082)Memory used [KB]: 1023
% 0.22/0.46 % (22082)Time elapsed: 0.005 s
% 0.22/0.46 % (22082)Instructions burned: 6 (million)
% 0.22/0.46 % (22082)------------------------------
% 0.22/0.46 % (22082)------------------------------
% 0.22/0.47 % (22083)Instruction limit reached!
% 0.22/0.47 % (22083)------------------------------
% 0.22/0.47 % (22083)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (22083)Termination reason: Unknown
% 0.22/0.47 % (22083)Termination phase: Property scanning
% 0.22/0.47
% 0.22/0.47 % (22083)Memory used [KB]: 1023
% 0.22/0.47 % (22083)Time elapsed: 0.007 s
% 0.22/0.47 % (22083)Instructions burned: 6 (million)
% 0.22/0.47 % (22083)------------------------------
% 0.22/0.47 % (22083)------------------------------
% 0.22/0.48 % (22084)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.22/0.48 % (22086)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on Vampire---4 for (2998ds/779Mi)
% 0.22/0.49 % (22055)Instruction limit reached!
% 0.22/0.49 % (22055)------------------------------
% 0.22/0.49 % (22055)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (22055)Termination reason: Unknown
% 0.22/0.49 % (22055)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (22055)Memory used [KB]: 6652
% 0.22/0.49 % (22055)Time elapsed: 0.113 s
% 0.22/0.49 % (22055)Instructions burned: 184 (million)
% 0.22/0.49 % (22055)------------------------------
% 0.22/0.49 % (22055)------------------------------
% 0.22/0.49 % (22088)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (2998ds/19Mi)
% 0.22/0.50 % (22088)Instruction limit reached!
% 0.22/0.50 % (22088)------------------------------
% 0.22/0.50 % (22088)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50 % (22088)Termination reason: Unknown
% 0.22/0.50 % (22088)Termination phase: Saturation
% 0.22/0.50
% 0.22/0.50 % (22088)Memory used [KB]: 5500
% 0.22/0.50 % (22088)Time elapsed: 0.009 s
% 0.22/0.50 % (22088)Instructions burned: 19 (million)
% 0.22/0.50 % (22088)------------------------------
% 0.22/0.50 % (22088)------------------------------
% 0.22/0.50 % (22093)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2998ds/879Mi)
% 0.22/0.51 % (22095)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.22/0.52 % (22095)Instruction limit reached!
% 0.22/0.52 % (22095)------------------------------
% 0.22/0.52 % (22095)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (22095)Termination reason: Unknown
% 0.22/0.52 % (22095)Termination phase: Saturation
% 0.22/0.52
% 0.22/0.52 % (22095)Memory used [KB]: 5756
% 0.22/0.52 % (22095)Time elapsed: 0.010 s
% 0.22/0.52 % (22095)Instructions burned: 18 (million)
% 0.22/0.52 % (22095)------------------------------
% 0.22/0.52 % (22095)------------------------------
% 0.22/0.53 % (22135)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.22/0.53 % (22135)Instruction limit reached!
% 0.22/0.53 % (22135)------------------------------
% 0.22/0.53 % (22135)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53 % (22135)Termination reason: Unknown
% 0.22/0.53 % (22135)Termination phase: Preprocessing 3
% 0.22/0.53
% 0.22/0.53 % (22135)Memory used [KB]: 1023
% 0.22/0.53 % (22135)Time elapsed: 0.003 s
% 0.22/0.53 % (22135)Instructions burned: 4 (million)
% 0.22/0.53 % (22135)------------------------------
% 0.22/0.53 % (22135)------------------------------
% 0.22/0.54 % (22060)Instruction limit reached!
% 0.22/0.54 % (22060)------------------------------
% 0.22/0.54 % (22060)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.54 % (22060)Termination reason: Unknown
% 0.22/0.54 % (22060)Termination phase: Saturation
% 0.22/0.54
% 0.22/0.54 % (22060)Memory used [KB]: 6396
% 0.22/0.54 % (22060)Time elapsed: 0.164 s
% 0.22/0.54 % (22060)Instructions burned: 276 (million)
% 0.22/0.54 % (22060)------------------------------
% 0.22/0.54 % (22060)------------------------------
% 0.22/0.54 % (22140)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2998ds/30Mi)
% 0.22/0.55 % (22141)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2998ds/127Mi)
% 0.22/0.55 % (22140)Instruction limit reached!
% 0.22/0.55 % (22140)------------------------------
% 0.22/0.55 % (22140)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (22140)Termination reason: Unknown
% 0.22/0.55 % (22140)Termination phase: Saturation
% 0.22/0.55
% 0.22/0.55 % (22140)Memory used [KB]: 5756
% 0.22/0.55 % (22140)Time elapsed: 0.012 s
% 0.22/0.55 % (22140)Instructions burned: 32 (million)
% 0.22/0.55 % (22140)------------------------------
% 0.22/0.55 % (22140)------------------------------
% 0.22/0.56 % (22142)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on Vampire---4 for (2998ds/100Mi)
% 1.93/0.60 % (22141)Instruction limit reached!
% 1.93/0.60 % (22141)------------------------------
% 1.93/0.60 % (22141)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.93/0.60 % (22141)Termination reason: Unknown
% 1.93/0.60 % (22141)Termination phase: Saturation
% 1.93/0.60
% 1.93/0.60 % (22141)Memory used [KB]: 6396
% 1.93/0.60 % (22141)Time elapsed: 0.052 s
% 1.93/0.60 % (22141)Instructions burned: 127 (million)
% 1.93/0.60 % (22141)------------------------------
% 1.93/0.60 % (22141)------------------------------
% 1.93/0.61 % (22142)Instruction limit reached!
% 1.93/0.61 % (22142)------------------------------
% 1.93/0.61 % (22142)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.93/0.61 % (22142)Termination reason: Unknown
% 1.93/0.61 % (22142)Termination phase: Saturation
% 1.93/0.61
% 1.93/0.61 % (22142)Memory used [KB]: 6140
% 1.93/0.61 % (22142)Time elapsed: 0.060 s
% 1.93/0.61 % (22142)Instructions burned: 100 (million)
% 1.93/0.61 % (22142)------------------------------
% 1.93/0.61 % (22142)------------------------------
% 1.93/0.61 % (22146)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 Vampire---4 for (2997ds/3Mi)
% 1.93/0.62 % (22146)Instruction limit reached!
% 1.93/0.62 % (22146)------------------------------
% 1.93/0.62 % (22146)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.93/0.62 % (22146)Termination reason: Unknown
% 1.93/0.62 % (22146)Termination phase: Property scanning
% 1.93/0.62
% 1.93/0.62 % (22146)Memory used [KB]: 1023
% 1.93/0.62 % (22146)Time elapsed: 0.004 s
% 1.93/0.62 % (22146)Instructions burned: 4 (million)
% 1.93/0.62 % (22146)------------------------------
% 1.93/0.62 % (22146)------------------------------
% 1.93/0.62 % (22147)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 Vampire---4 for (2997ds/20Mi)
% 2.22/0.62 % (22147)Instruction limit reached!
% 2.22/0.62 % (22147)------------------------------
% 2.22/0.62 % (22147)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.22/0.62 % (22147)Termination reason: Unknown
% 2.22/0.62 % (22147)Termination phase: Saturation
% 2.22/0.62
% 2.22/0.62 % (22147)Memory used [KB]: 5756
% 2.22/0.62 % (22147)Time elapsed: 0.008 s
% 2.22/0.62 % (22147)Instructions burned: 20 (million)
% 2.22/0.62 % (22147)------------------------------
% 2.22/0.62 % (22147)------------------------------
% 2.24/0.63 % (22149)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 Vampire---4 for (2997ds/107Mi)
% 2.24/0.63 % (22084)Instruction limit reached!
% 2.24/0.63 % (22084)------------------------------
% 2.24/0.63 % (22084)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.24/0.63 % (22084)Termination reason: Unknown
% 2.24/0.63 % (22084)Termination phase: Saturation
% 2.24/0.63
% 2.24/0.63 % (22084)Memory used [KB]: 6652
% 2.24/0.63 % (22084)Time elapsed: 0.160 s
% 2.24/0.63 % (22084)Instructions burned: 377 (million)
% 2.24/0.63 % (22084)------------------------------
% 2.24/0.63 % (22084)------------------------------
% 2.24/0.64 % (22148)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 Vampire---4 for (2997ds/86Mi)
% 2.24/0.64 % (22150)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on Vampire---4 for (2997ds/39Mi)
% 2.24/0.65 % (22069)First to succeed.
% 2.24/0.66 % (22150)Instruction limit reached!
% 2.24/0.66 % (22150)------------------------------
% 2.24/0.66 % (22150)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.24/0.66 % (22150)Termination reason: Unknown
% 2.24/0.66 % (22150)Termination phase: Saturation
% 2.24/0.66
% 2.24/0.66 % (22150)Memory used [KB]: 5628
% 2.24/0.66 % (22150)Time elapsed: 0.014 s
% 2.24/0.66 % (22150)Instructions burned: 41 (million)
% 2.24/0.66 % (22150)------------------------------
% 2.24/0.66 % (22150)------------------------------
% 2.24/0.66 % (22151)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on Vampire---4 for (2996ds/448Mi)
% 2.24/0.67 % (22149)Instruction limit reached!
% 2.24/0.67 % (22149)------------------------------
% 2.24/0.67 % (22149)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.24/0.67 % (22149)Termination reason: Unknown
% 2.24/0.67 % (22149)Termination phase: Saturation
% 2.24/0.67
% 2.24/0.67 % (22149)Memory used [KB]: 6140
% 2.24/0.67 % (22149)Time elapsed: 0.041 s
% 2.24/0.67 % (22149)Instructions burned: 109 (million)
% 2.24/0.67 % (22149)------------------------------
% 2.24/0.67 % (22149)------------------------------
% 2.24/0.67 % (22069)Refutation found. Thanks to Tanya!
% 2.24/0.67 % SZS status Theorem for Vampire---4
% 2.24/0.67 % SZS output start Proof for Vampire---4
% See solution above
% 2.24/0.68 % (22069)------------------------------
% 2.24/0.68 % (22069)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.24/0.68 % (22069)Termination reason: Refutation
% 2.24/0.68
% 2.24/0.68 % (22069)Memory used [KB]: 7291
% 2.24/0.68 % (22069)Time elapsed: 0.297 s
% 2.24/0.68 % (22069)Instructions burned: 416 (million)
% 2.24/0.68 % (22069)------------------------------
% 2.24/0.68 % (22069)------------------------------
% 2.24/0.68 % (22050)Success in time 0.32 s
% 2.24/0.68 % Vampire---4.8 exiting
%------------------------------------------------------------------------------