TSTP Solution File: SEV148^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV148^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:12:08 EDT 2024
% Result : Theorem 1.90s 0.61s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 48
% Syntax : Number of formulae : 286 ( 38 unt; 33 typ; 0 def)
% Number of atoms : 2282 ( 237 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 6220 ( 285 ~; 405 |; 464 &;3567 @)
% ( 14 <=>; 709 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 389 ( 389 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 44 con; 0-2 aty)
% ( 776 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 916 ( 807 ^ 108 !; 0 ?; 916 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_21,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK2: a > a > $o ).
thf(func_def_23,type,
sK3: a > a > $o ).
thf(func_def_24,type,
sK4: a ).
thf(func_def_25,type,
sK5: a ).
thf(func_def_26,type,
sK6: a > $o ).
thf(func_def_27,type,
sK7: a ).
thf(func_def_28,type,
sK8: a ).
thf(func_def_29,type,
sK9: a ).
thf(func_def_30,type,
sK10: a ).
thf(func_def_31,type,
sK11: a ).
thf(func_def_32,type,
sK12: a ).
thf(func_def_33,type,
sK13: a ).
thf(func_def_34,type,
sK14: a ).
thf(func_def_35,type,
sK15: a ).
thf(func_def_36,type,
sK16: a ).
thf(func_def_37,type,
sK17: a ).
thf(func_def_38,type,
sK18: a ).
thf(func_def_39,type,
sK19: a ).
thf(func_def_40,type,
sK20: a ).
thf(func_def_41,type,
sK21: a ).
thf(func_def_42,type,
sK22: a ).
thf(func_def_43,type,
sK23: a ).
thf(func_def_44,type,
sK24: a ).
thf(func_def_45,type,
sK25: a ).
thf(func_def_46,type,
sK26: a ).
thf(func_def_47,type,
sK27: a ).
thf(func_def_48,type,
sK28: a ).
thf(func_def_49,type,
sK29: a ).
thf(func_def_50,type,
sK30: a ).
thf(func_def_51,type,
sK31: a ).
thf(f2129,plain,
$false,
inference(avatar_sat_refutation,[],[f121,f213,f307,f414,f597,f636,f935,f976,f1092,f1337,f1472,f1507,f1829,f2098,f2128]) ).
thf(f2128,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f2127]) ).
thf(f2127,plain,
( $false
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f2126]) ).
thf(f2126,plain,
( ( $true = $false )
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2123,f2125]) ).
thf(f2125,plain,
( ( ( sK6 @ sK31 )
= $false )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2124]) ).
thf(f2124,plain,
( ( ( $true
=> ( sK6 @ sK31 ) )
= $false )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f2118,f2120]) ).
thf(f2120,plain,
( ( $true
= ( sK3 @ sK5 @ sK31 ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f2118]) ).
thf(f2118,plain,
( ( $false
= ( ( sK3 @ sK5 @ sK31 )
=> ( sK6 @ sK31 ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f2114]) ).
thf(f2114,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK31 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f306]) ).
thf(f306,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f305,plain,
( spl0_9
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f2123,plain,
( ( $true
= ( sK6 @ sK31 ) )
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f2122]) ).
thf(f2122,plain,
( ( $true
= ( sK6 @ sK31 ) )
| ( $true = $false )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2121]) ).
thf(f2121,plain,
( ( $true
= ( sK6 @ sK31 ) )
| ( ( $false
=> ( sK6 @ sK31 ) )
= $false )
| ~ spl0_9 ),
inference(superposition,[],[f2118,f373]) ).
thf(f373,plain,
! [X1: a] :
( ( ( sK3 @ sK5 @ X1 )
= $false )
| ( $true
= ( sK6 @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f47]) ).
thf(f47,plain,
! [X1: a] :
( ( ( ( sK2 @ sK5 @ X1 )
| ( sK3 @ sK5 @ X1 ) )
= $false )
| ( $true
= ( sK6 @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
! [X1: a] :
( $true
= ( ( ( sK2 @ sK5 @ X1 )
| ( sK3 @ sK5 @ X1 ) )
=> ( sK6 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f43]) ).
thf(f43,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f37]) ).
thf(f37,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f27]) ).
thf(f27,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK4 ) ) ),
inference(beta_eta_normalization,[],[f24]) ).
thf(f24,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f18]) ).
thf(f18,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK4 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK4 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK3 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK4 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK4 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( sK3 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( sK3 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y2 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y2 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y2 @ Y4 )
| ( Y0 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y2 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y2 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y2 @ Y4 )
| ( Y0 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y3 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a > a > $o,X3: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X7: a,X8: a] :
( ( ( X6 @ X8 )
& ( X2 @ X8 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X9: a] :
( ( X2 @ X0 @ X9 )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) )
| ! [X10: a > $o] :
( ( ! [X11: a,X12: a] :
( ( ( X10 @ X12 )
& ( X3 @ X12 @ X11 ) )
=> ( X10 @ X11 ) )
& ! [X13: a] :
( ( X3 @ X0 @ X13 )
=> ( X10 @ X13 ) ) )
=> ( X10 @ X5 ) ) )
=> ( X4 @ X5 ) )
& ! [X14: a,X15: a] :
( ( ( X4 @ X15 )
& ( ! [X16: a > $o] :
( ( ! [X17: a] :
( ( X3 @ X15 @ X17 )
=> ( X16 @ X17 ) )
& ! [X18: a,X19: a] :
( ( ( X3 @ X19 @ X18 )
& ( X16 @ X19 ) )
=> ( X16 @ X18 ) ) )
=> ( X16 @ X14 ) )
| ! [X20: a > $o] :
( ( ! [X21: a] :
( ( X2 @ X15 @ X21 )
=> ( X20 @ X21 ) )
& ! [X22: a,X23: a] :
( ( ( X2 @ X22 @ X23 )
& ( X20 @ X22 ) )
=> ( X20 @ X23 ) ) )
=> ( X20 @ X14 ) ) ) )
=> ( X4 @ X14 ) ) )
=> ( X4 @ X1 ) )
=> ! [X24: a > $o] :
( ( ! [X25: a] :
( ( ( X2 @ X0 @ X25 )
| ( X3 @ X0 @ X25 ) )
=> ( X24 @ X25 ) )
& ! [X26: a,X27: a] :
( ( ( ( X2 @ X27 @ X26 )
| ( X3 @ X27 @ X26 ) )
& ( X24 @ X27 ) )
=> ( X24 @ X26 ) ) )
=> ( X24 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X3: a,X1: a > a > $o,X0: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X1 @ X8 @ X9 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X1 @ X2 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X0 @ X8 @ X9 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X0 @ X2 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) ) )
=> ( X4 @ X5 ) )
& ! [X9: a,X8: a] :
( ( ( X4 @ X8 )
& ( ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X6 @ X5 ) )
& ! [X11: a,X10: a] :
( ( ( X0 @ X10 @ X11 )
& ( X6 @ X10 ) )
=> ( X6 @ X11 ) ) )
=> ( X6 @ X9 ) )
| ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X6 @ X5 ) )
& ! [X10: a,X11: a] :
( ( ( X1 @ X10 @ X11 )
& ( X6 @ X10 ) )
=> ( X6 @ X11 ) ) )
=> ( X6 @ X9 ) ) ) )
=> ( X4 @ X9 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X9: a,X8: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X4 @ X8 ) )
=> ( X4 @ X9 ) ) )
=> ( X4 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X2: a,X3: a,X1: a > a > $o,X0: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X1 @ X8 @ X9 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X1 @ X2 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X0 @ X8 @ X9 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X0 @ X2 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) ) )
=> ( X4 @ X5 ) )
& ! [X9: a,X8: a] :
( ( ( X4 @ X8 )
& ( ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X6 @ X5 ) )
& ! [X11: a,X10: a] :
( ( ( X0 @ X10 @ X11 )
& ( X6 @ X10 ) )
=> ( X6 @ X11 ) ) )
=> ( X6 @ X9 ) )
| ! [X6: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X6 @ X5 ) )
& ! [X10: a,X11: a] :
( ( ( X1 @ X10 @ X11 )
& ( X6 @ X10 ) )
=> ( X6 @ X11 ) ) )
=> ( X6 @ X9 ) ) ) )
=> ( X4 @ X9 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X9: a,X8: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X4 @ X8 ) )
=> ( X4 @ X9 ) ) )
=> ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM251C_pme) ).
thf(f2098,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f2097]) ).
thf(f2097,plain,
( $false
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f2096]) ).
thf(f2096,plain,
( ( $true = $false )
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2095,f2060]) ).
thf(f2060,plain,
( ( ( sK6 @ sK30 )
= $false )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f2047]) ).
thf(f2047,plain,
( ( ( ( ( sK3 @ sK29 @ sK30 )
& ( sK6 @ sK29 ) )
=> ( sK6 @ sK30 ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f2046]) ).
thf(f2046,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK29 @ Y0 )
& ( sK6 @ sK29 ) )
=> ( sK6 @ Y0 ) )
@ sK30 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f2034]) ).
thf(f2034,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK29 @ Y0 )
& ( sK6 @ sK29 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f2032]) ).
thf(f2032,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK29 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f303]) ).
thf(f303,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f302,plain,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f2095,plain,
( ( $true
= ( sK6 @ sK30 ) )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f2094]) ).
thf(f2094,plain,
( ( ( $true
=> ( sK6 @ sK30 ) )
= $true )
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2093,f2077]) ).
thf(f2077,plain,
( ( ( sK6 @ sK29 )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f2061]) ).
thf(f2061,plain,
( ( ( ( sK3 @ sK29 @ sK30 )
& ( sK6 @ sK29 ) )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f2047]) ).
thf(f2093,plain,
( ( $true
= ( ( sK6 @ sK29 )
=> ( sK6 @ sK30 ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f2092]) ).
thf(f2092,plain,
( ( $true
= ( ( ( sK6 @ sK29 )
& $true )
=> ( sK6 @ sK30 ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f2091]) ).
thf(f2091,plain,
( ( $true
= ( ( ( sK6 @ sK29 )
& ( ( sK2 @ sK29 @ sK30 )
| $true ) )
=> ( sK6 @ sK30 ) ) )
| ~ spl0_8 ),
inference(superposition,[],[f46,f2080]) ).
thf(f2080,plain,
( ( $true
= ( sK3 @ sK29 @ sK30 ) )
| ~ spl0_8 ),
inference(boolean_simplification,[],[f2079]) ).
thf(f2079,plain,
( ( $true
= ( ( sK3 @ sK29 @ sK30 )
& $true ) )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f2061,f2077]) ).
thf(f46,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK6 @ X1 )
& ( ( sK2 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) ) )
=> ( sK6 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f45]) ).
thf(f45,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ X1 )
& ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[],[f42]) ).
thf(f42,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 )
& ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f41]) ).
thf(f41,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f40]) ).
thf(f40,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) ) ),
inference(boolean_simplification,[],[f39]) ).
thf(f39,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[],[f27,f37]) ).
thf(f1829,plain,
~ spl0_18,
inference(avatar_contradiction_clause,[],[f1828]) ).
thf(f1828,plain,
( $false
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f1827]) ).
thf(f1827,plain,
( ( $true = $false )
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1826,f1702]) ).
thf(f1702,plain,
( ( ( sK6 @ sK26 )
= $false )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f1691]) ).
thf(f1691,plain,
( ( ( ( ( sK2 @ sK25 @ sK26 )
& ( sK6 @ sK25 ) )
=> ( sK6 @ sK26 ) )
= $false )
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f1690]) ).
thf(f1690,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ sK25 @ Y0 )
& ( sK6 @ sK25 ) )
=> ( sK6 @ Y0 ) )
@ sK26 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[],[f1682]) ).
thf(f1682,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK25 @ Y0 )
& ( sK6 @ sK25 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f1678]) ).
thf(f1678,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK25 )
= $false )
| ~ spl0_18 ),
inference(sigma_clausification,[],[f596]) ).
thf(f596,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f595]) ).
thf(f595,plain,
( spl0_18
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f1826,plain,
( ( $true
= ( sK6 @ sK26 ) )
| ~ spl0_18 ),
inference(boolean_simplification,[],[f1825]) ).
thf(f1825,plain,
( ( ( $true
=> ( sK6 @ sK26 ) )
= $true )
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1824,f1782]) ).
thf(f1782,plain,
( ( $true
= ( sK6 @ sK25 ) )
| ~ spl0_18 ),
inference(boolean_simplification,[],[f1781]) ).
thf(f1781,plain,
( ( ( $true
& ( sK6 @ sK25 ) )
= $true )
| ~ spl0_18 ),
inference(backward_demodulation,[],[f1703,f1780]) ).
thf(f1780,plain,
( ( $true
= ( sK2 @ sK25 @ sK26 ) )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f1703]) ).
thf(f1703,plain,
( ( ( ( sK2 @ sK25 @ sK26 )
& ( sK6 @ sK25 ) )
= $true )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f1691]) ).
thf(f1824,plain,
( ( $true
= ( ( sK6 @ sK25 )
=> ( sK6 @ sK26 ) ) )
| ~ spl0_18 ),
inference(boolean_simplification,[],[f1823]) ).
thf(f1823,plain,
( ( $true
= ( ( ( sK6 @ sK25 )
& $true )
=> ( sK6 @ sK26 ) ) )
| ~ spl0_18 ),
inference(boolean_simplification,[],[f1822]) ).
thf(f1822,plain,
( ( ( ( ( sK6 @ sK25 )
& ( $true
| ( sK3 @ sK25 @ sK26 ) ) )
=> ( sK6 @ sK26 ) )
= $true )
| ~ spl0_18 ),
inference(superposition,[],[f46,f1780]) ).
thf(f1507,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1506]) ).
thf(f1506,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f1505]) ).
thf(f1505,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1504]) ).
thf(f1504,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1503]) ).
thf(f1503,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK13 @ sK24 ) ) ) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1496,f1487]) ).
thf(f1487,plain,
( ( $true
= ( sK2 @ sK13 @ sK24 ) )
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f1479]) ).
thf(f1479,plain,
( ( ( ( sK2 @ sK13 @ sK24 )
=> ( sK6 @ sK24 ) )
= $false )
| ~ spl0_22 ),
inference(beta_eta_normalization,[],[f1475]) ).
thf(f1475,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK24 )
= $false )
| ~ spl0_22 ),
inference(sigma_clausification,[],[f1336]) ).
thf(f1336,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1335]) ).
thf(f1335,plain,
( spl0_22
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f1496,plain,
( ( $true
= ( ~ ( ( sK2 @ sK13 @ sK24 )
| ( sK3 @ sK13 @ sK24 ) ) ) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1490]) ).
thf(f1490,plain,
( ( $true
= ( ( ( sK2 @ sK13 @ sK24 )
| ( sK3 @ sK13 @ sK24 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_22 ),
inference(superposition,[],[f1113,f1489]) ).
thf(f1489,plain,
( ( ( sK6 @ sK24 )
= $false )
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1488]) ).
thf(f1488,plain,
( ( $false
= ( $true
=> ( sK6 @ sK24 ) ) )
| ~ spl0_22 ),
inference(backward_demodulation,[],[f1479,f1487]) ).
thf(f1113,plain,
( ! [X0: a] :
( $true
= ( ( ( sK2 @ sK13 @ X0 )
| ( sK3 @ sK13 @ X0 ) )
=> ( sK6 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1110]) ).
thf(f1110,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( ( sK2 @ sK13 @ X0 )
| ( sK3 @ sK13 @ X0 ) ) )
=> ( sK6 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f46,f1097]) ).
thf(f1097,plain,
( ( ( sK6 @ sK13 )
= $true )
| ~ spl0_1
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f1095]) ).
thf(f1095,plain,
( ( ( ( sK6 @ sK13 )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1094]) ).
thf(f1094,plain,
( ( ( ( $true
& ( sK6 @ sK13 ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1093]) ).
thf(f1093,plain,
( ( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
| $true )
& ( sK6 @ sK13 ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(forward_demodulation,[],[f660,f410]) ).
thf(f410,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f409]) ).
thf(f409,plain,
( spl0_14
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f660,plain,
( ( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
& ( sK6 @ sK13 ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f659]) ).
thf(f659,plain,
( ( ( ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK13 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK13 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK13 ) )
=> ( sK6 @ Y0 ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f645]) ).
thf(f645,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK13 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK13 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK13 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f643]) ).
thf(f643,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK13 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f117]) ).
thf(f117,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f116,plain,
( spl0_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f1472,plain,
~ spl0_21,
inference(avatar_contradiction_clause,[],[f1471]) ).
thf(f1471,plain,
( $false
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f1470]) ).
thf(f1470,plain,
( ( $true = $false )
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1469,f1383]) ).
thf(f1383,plain,
( ( ( sK6 @ sK21 )
= $false )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1382]) ).
thf(f1382,plain,
( ( ( $true
=> ( sK6 @ sK21 ) )
= $false )
| ~ spl0_21 ),
inference(backward_demodulation,[],[f1370,f1381]) ).
thf(f1381,plain,
( ( $true
= ( ( sK6 @ sK20 )
& ( sK2 @ sK20 @ sK21 ) ) )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f1370]) ).
thf(f1370,plain,
( ( ( ( ( sK6 @ sK20 )
& ( sK2 @ sK20 @ sK21 ) )
=> ( sK6 @ sK21 ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1369]) ).
thf(f1369,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK20 )
& ( sK2 @ sK20 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ sK21 )
= $false )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f1354]) ).
thf(f1354,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK20 )
& ( sK2 @ sK20 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1352]) ).
thf(f1352,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) )
@ sK20 )
= $false )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f1333]) ).
thf(f1333,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1332]) ).
thf(f1332,plain,
( spl0_21
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f1469,plain,
( ( $true
= ( sK6 @ sK21 ) )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1468]) ).
thf(f1468,plain,
( ( $true
= ( $true
=> ( sK6 @ sK21 ) ) )
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1467,f1442]) ).
thf(f1442,plain,
( ( $true
= ( sK6 @ sK20 ) )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f1381]) ).
thf(f1467,plain,
( ( $true
= ( ( sK6 @ sK20 )
=> ( sK6 @ sK21 ) ) )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1466]) ).
thf(f1466,plain,
( ( $true
= ( ( ( sK6 @ sK20 )
& $true )
=> ( sK6 @ sK21 ) ) )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1465]) ).
thf(f1465,plain,
( ( $true
= ( ( ( sK6 @ sK20 )
& ( $true
| ( sK3 @ sK20 @ sK21 ) ) )
=> ( sK6 @ sK21 ) ) )
| ~ spl0_21 ),
inference(superposition,[],[f46,f1444]) ).
thf(f1444,plain,
( ( ( sK2 @ sK20 @ sK21 )
= $true )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1443]) ).
thf(f1443,plain,
( ( ( $true
& ( sK2 @ sK20 @ sK21 ) )
= $true )
| ~ spl0_21 ),
inference(backward_demodulation,[],[f1381,f1442]) ).
thf(f1337,plain,
( spl0_21
| spl0_22
| ~ spl0_1
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f1328,f409,f116,f1335,f1332]) ).
thf(f1328,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f1316]) ).
thf(f1316,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(not_proxy_clausification,[],[f1254]) ).
thf(f1254,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1250]) ).
thf(f1250,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f1239,f1099]) ).
thf(f1099,plain,
( ( ( sK6 @ sK14 )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[],[f1098]) ).
thf(f1098,plain,
( ( $false
= ( $true
=> ( sK6 @ sK14 ) ) )
| ~ spl0_1
| ~ spl0_14 ),
inference(backward_demodulation,[],[f1095,f1097]) ).
thf(f1239,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK14 ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f1238]) ).
thf(f1238,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) )
@ X1 )
= $true )
| ~ spl0_14 ),
inference(pi_clausification,[],[f410]) ).
thf(f1092,plain,
~ spl0_20,
inference(avatar_contradiction_clause,[],[f1091]) ).
thf(f1091,plain,
( $false
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f1090]) ).
thf(f1090,plain,
( ( $true = $false )
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1089,f1024]) ).
thf(f1024,plain,
( ( ( sK6 @ sK17 )
= $false )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f1006]) ).
thf(f1006,plain,
( ( ( ( ( sK6 @ sK18 )
& ( sK3 @ sK18 @ sK17 ) )
=> ( sK6 @ sK17 ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f1005]) ).
thf(f1005,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ sK17 ) )
=> ( sK6 @ sK17 ) )
@ sK18 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f992]) ).
thf(f992,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK3 @ Y0 @ sK17 ) )
=> ( sK6 @ sK17 ) ) )
= $false )
| ~ spl0_20 ),
inference(beta_eta_normalization,[],[f988]) ).
thf(f988,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
@ sK17 )
= $false )
| ~ spl0_20 ),
inference(sigma_clausification,[],[f934]) ).
thf(f934,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f933]) ).
thf(f933,plain,
( spl0_20
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f1089,plain,
( ( ( sK6 @ sK17 )
= $true )
| ~ spl0_20 ),
inference(boolean_simplification,[],[f1088]) ).
thf(f1088,plain,
( ( ( $true
=> ( sK6 @ sK17 ) )
= $true )
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1087,f1048]) ).
thf(f1048,plain,
( ( $true
= ( sK6 @ sK18 ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f1025]) ).
thf(f1025,plain,
( ( $true
= ( ( sK6 @ sK18 )
& ( sK3 @ sK18 @ sK17 ) ) )
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f1006]) ).
thf(f1087,plain,
( ( $true
= ( ( sK6 @ sK18 )
=> ( sK6 @ sK17 ) ) )
| ~ spl0_20 ),
inference(boolean_simplification,[],[f1086]) ).
thf(f1086,plain,
( ( $true
= ( ( ( sK6 @ sK18 )
& $true )
=> ( sK6 @ sK17 ) ) )
| ~ spl0_20 ),
inference(boolean_simplification,[],[f1085]) ).
thf(f1085,plain,
( ( $true
= ( ( ( sK6 @ sK18 )
& ( ( sK2 @ sK18 @ sK17 )
| $true ) )
=> ( sK6 @ sK17 ) ) )
| ~ spl0_20 ),
inference(superposition,[],[f46,f1050]) ).
thf(f1050,plain,
( ( ( sK3 @ sK18 @ sK17 )
= $true )
| ~ spl0_20 ),
inference(boolean_simplification,[],[f1049]) ).
thf(f1049,plain,
( ( $true
= ( $true
& ( sK3 @ sK18 @ sK17 ) ) )
| ~ spl0_20 ),
inference(backward_demodulation,[],[f1025,f1048]) ).
thf(f976,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f975]) ).
thf(f975,plain,
( $false
| ~ spl0_1
| ~ spl0_15
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f974]) ).
thf(f974,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_19 ),
inference(boolean_simplification,[],[f973]) ).
thf(f973,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_19 ),
inference(boolean_simplification,[],[f972]) ).
thf(f972,plain,
( ( $true
= ( ~ ( ( sK2 @ sK13 @ sK16 )
| $true ) ) )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_demodulation,[],[f969,f956]) ).
thf(f956,plain,
( ( ( sK3 @ sK13 @ sK16 )
= $true )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f952]) ).
thf(f952,plain,
( ( ( ( sK3 @ sK13 @ sK16 )
=> ( sK6 @ sK16 ) )
= $false )
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f950]) ).
thf(f950,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK16 )
= $false )
| ~ spl0_19 ),
inference(sigma_clausification,[],[f931]) ).
thf(f931,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f930]) ).
thf(f930,plain,
( spl0_19
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f969,plain,
( ( ( ~ ( ( sK2 @ sK13 @ sK16 )
| ( sK3 @ sK13 @ sK16 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_19 ),
inference(boolean_simplification,[],[f959]) ).
thf(f959,plain,
( ( $true
= ( ( ( sK2 @ sK13 @ sK16 )
| ( sK3 @ sK13 @ sK16 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[],[f689,f958]) ).
thf(f958,plain,
( ( ( sK6 @ sK16 )
= $false )
| ~ spl0_19 ),
inference(boolean_simplification,[],[f957]) ).
thf(f957,plain,
( ( ( $true
=> ( sK6 @ sK16 ) )
= $false )
| ~ spl0_19 ),
inference(backward_demodulation,[],[f952,f956]) ).
thf(f689,plain,
( ! [X0: a] :
( $true
= ( ( ( sK2 @ sK13 @ X0 )
| ( sK3 @ sK13 @ X0 ) )
=> ( sK6 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_15 ),
inference(boolean_simplification,[],[f686]) ).
thf(f686,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( ( sK2 @ sK13 @ X0 )
| ( sK3 @ sK13 @ X0 ) ) )
=> ( sK6 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_15 ),
inference(superposition,[],[f46,f673]) ).
thf(f673,plain,
( ( ( sK6 @ sK13 )
= $true )
| ~ spl0_1
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f663]) ).
thf(f663,plain,
( ( ( ( sK6 @ sK13 )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1
| ~ spl0_15 ),
inference(boolean_simplification,[],[f662]) ).
thf(f662,plain,
( ( ( ( $true
& ( sK6 @ sK13 ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1
| ~ spl0_15 ),
inference(boolean_simplification,[],[f661]) ).
thf(f661,plain,
( ( ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
& ( sK6 @ sK13 ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1
| ~ spl0_15 ),
inference(forward_demodulation,[],[f660,f413]) ).
thf(f413,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f412]) ).
thf(f412,plain,
( spl0_15
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f935,plain,
( spl0_19
| spl0_20
| ~ spl0_1
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f926,f412,f116,f933,f930]) ).
thf(f926,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_15 ),
inference(binary_proxy_clausification,[],[f911]) ).
thf(f911,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_1
| ~ spl0_15 ),
inference(not_proxy_clausification,[],[f830]) ).
thf(f830,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_15 ),
inference(boolean_simplification,[],[f827]) ).
thf(f827,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_15 ),
inference(superposition,[],[f813,f675]) ).
thf(f675,plain,
( ( ( sK6 @ sK14 )
= $false )
| ~ spl0_1
| ~ spl0_15 ),
inference(boolean_simplification,[],[f674]) ).
thf(f674,plain,
( ( $false
= ( $true
=> ( sK6 @ sK14 ) ) )
| ~ spl0_1
| ~ spl0_15 ),
inference(backward_demodulation,[],[f663,f673]) ).
thf(f813,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK13 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK14 ) ) )
| ~ spl0_15 ),
inference(beta_eta_normalization,[],[f812]) ).
thf(f812,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) )
@ X1 )
= $true )
| ~ spl0_15 ),
inference(pi_clausification,[],[f413]) ).
thf(f636,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f635]) ).
thf(f635,plain,
( $false
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f634]) ).
thf(f634,plain,
( ( $true = $false )
| ~ spl0_17 ),
inference(boolean_simplification,[],[f633]) ).
thf(f633,plain,
( ( $true = ~ $true )
| ~ spl0_17 ),
inference(boolean_simplification,[],[f632]) ).
thf(f632,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK5 @ sK15 ) ) ) )
| ~ spl0_17 ),
inference(forward_demodulation,[],[f631,f618]) ).
thf(f618,plain,
( ( ( sK2 @ sK5 @ sK15 )
= $true )
| ~ spl0_17 ),
inference(binary_proxy_clausification,[],[f614]) ).
thf(f614,plain,
( ( ( ( sK2 @ sK5 @ sK15 )
=> ( sK6 @ sK15 ) )
= $false )
| ~ spl0_17 ),
inference(beta_eta_normalization,[],[f612]) ).
thf(f612,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK15 )
= $false )
| ~ spl0_17 ),
inference(sigma_clausification,[],[f593]) ).
thf(f593,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f592]) ).
thf(f592,plain,
( spl0_17
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f631,plain,
( ( $true
= ( ~ ( ( sK2 @ sK5 @ sK15 )
| ( sK3 @ sK5 @ sK15 ) ) ) )
| ~ spl0_17 ),
inference(boolean_simplification,[],[f625]) ).
thf(f625,plain,
( ( $true
= ( ( ( sK2 @ sK5 @ sK15 )
| ( sK3 @ sK5 @ sK15 ) )
=> $false ) )
| ~ spl0_17 ),
inference(superposition,[],[f44,f620]) ).
thf(f620,plain,
( ( $false
= ( sK6 @ sK15 ) )
| ~ spl0_17 ),
inference(boolean_simplification,[],[f619]) ).
thf(f619,plain,
( ( $false
= ( $true
=> ( sK6 @ sK15 ) ) )
| ~ spl0_17 ),
inference(backward_demodulation,[],[f614,f618]) ).
thf(f597,plain,
( spl0_17
| spl0_18
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f588,f211,f119,f595,f592]) ).
thf(f119,plain,
( spl0_2
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f211,plain,
( spl0_4
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f588,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f573]) ).
thf(f573,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f439]) ).
thf(f439,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f435]) ).
thf(f435,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f315,f430]) ).
thf(f430,plain,
( ( ( sK6 @ sK7 )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f429]) ).
thf(f429,plain,
( ( ( $true
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f428]) ).
thf(f428,plain,
( ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f425,f212]) ).
thf(f212,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f425,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f423]) ).
thf(f423,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f120]) ).
thf(f120,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f315,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK5 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK7 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f314]) ).
thf(f314,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f212]) ).
thf(f414,plain,
( spl0_14
| spl0_15
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f407,f116,f412,f409]) ).
thf(f407,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f398]) ).
thf(f398,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f397]) ).
thf(f397,plain,
( ( $true
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
& $true ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f368,f395]) ).
thf(f395,plain,
( ( ( sK6 @ sK13 )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f368]) ).
thf(f368,plain,
( ( $true
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
& ( sK6 @ sK13 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f366]) ).
thf(f366,plain,
( ( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK14 ) ) ) )
& ( sK6 @ sK13 ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f365]) ).
thf(f365,plain,
( ( ( ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK13 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK13 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK13 ) )
=> ( sK6 @ Y0 ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f362]) ).
thf(f362,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK3 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK13 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK13 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( sK6 @ sK13 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f360]) ).
thf(f360,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) )
@ sK13 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f117]) ).
thf(f307,plain,
( spl0_8
| spl0_9
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f298,f208,f119,f305,f302]) ).
thf(f208,plain,
( spl0_3
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f298,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f291]) ).
thf(f291,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f284]) ).
thf(f284,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f276]) ).
thf(f276,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f272,f132]) ).
thf(f132,plain,
( ( ( sK6 @ sK7 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f131]) ).
thf(f131,plain,
( ( ( $true
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f128,f130]) ).
thf(f130,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f128]) ).
thf(f128,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( sK6 @ sK7 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f124]) ).
thf(f124,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f120]) ).
thf(f272,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK5 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK7 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f271]) ).
thf(f271,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f209]) ).
thf(f209,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f208]) ).
thf(f213,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f206,f119,f211,f208]) ).
thf(f206,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f130]) ).
thf(f121,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f112,f119,f116]) ).
thf(f112,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f94]) ).
thf(f94,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f36]) ).
thf(f36,plain,
( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f35]) ).
thf(f35,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( sK6 @ Y0 ) )
=> ( sK6 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y0 ) ) ) )
=> $false ) ),
inference(superposition,[],[f33,f26]) ).
thf(f26,plain,
( ( sK6 @ sK4 )
= $false ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f33,plain,
! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK3 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK5 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK4 ) ) ),
inference(beta_eta_normalization,[],[f32]) ).
thf(f32,plain,
! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f19]) ).
thf(f19,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ sK5 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK4 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV148^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14 % 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
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 19:09:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_NEQ_NAR problem
% 0.13/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % (28396)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.37 % (28390)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.13/0.37 % (28396)Instruction limit reached!
% 0.13/0.37 % (28396)------------------------------
% 0.13/0.37 % (28396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (28396)Termination reason: Unknown
% 0.13/0.37 % (28396)Termination phase: Property scanning
% 0.13/0.37
% 0.13/0.37 % (28396)Memory used [KB]: 1023
% 0.13/0.37 % (28396)Time elapsed: 0.004 s
% 0.13/0.37 % (28396)Instructions burned: 4 (million)
% 0.13/0.37 % (28396)------------------------------
% 0.13/0.37 % (28396)------------------------------
% 0.13/0.37 % (28391)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.13/0.37 % (28390)Instruction limit reached!
% 0.13/0.37 % (28390)------------------------------
% 0.13/0.37 % (28390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (28390)Termination reason: Unknown
% 0.13/0.37 % (28390)Termination phase: Property scanning
% 0.13/0.37
% 0.13/0.37 % (28390)Memory used [KB]: 1023
% 0.13/0.37 % (28390)Time elapsed: 0.005 s
% 0.13/0.37 % (28390)Instructions burned: 5 (million)
% 0.13/0.37 % (28390)------------------------------
% 0.13/0.37 % (28390)------------------------------
% 0.13/0.38 % (28392)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (28393)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (28395)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38 % (28394)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.13/0.38 % (28389)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.38 % (28392)Instruction limit reached!
% 0.13/0.38 % (28392)------------------------------
% 0.13/0.38 % (28392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (28392)Termination reason: Unknown
% 0.13/0.38 % (28393)Instruction limit reached!
% 0.13/0.38 % (28393)------------------------------
% 0.13/0.38 % (28393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (28393)Termination reason: Unknown
% 0.13/0.38 % (28393)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (28393)Memory used [KB]: 1023
% 0.13/0.38 % (28393)Time elapsed: 0.004 s
% 0.13/0.38 % (28393)Instructions burned: 2 (million)
% 0.13/0.38 % (28393)------------------------------
% 0.13/0.38 % (28393)------------------------------
% 0.13/0.38 % (28392)Termination phase: Preprocessing 1
% 0.13/0.38
% 0.13/0.38 % (28392)Memory used [KB]: 895
% 0.13/0.38 % (28392)Time elapsed: 0.004 s
% 0.13/0.38 % (28392)Instructions burned: 2 (million)
% 0.13/0.38 % (28392)------------------------------
% 0.13/0.38 % (28392)------------------------------
% 0.13/0.39 % (28391)Instruction limit reached!
% 0.13/0.39 % (28391)------------------------------
% 0.13/0.39 % (28391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (28391)Termination reason: Unknown
% 0.13/0.39 % (28391)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (28391)Memory used [KB]: 5628
% 0.13/0.39 % (28391)Time elapsed: 0.016 s
% 0.13/0.39 % (28391)Instructions burned: 28 (million)
% 0.13/0.39 % (28391)------------------------------
% 0.13/0.39 % (28391)------------------------------
% 0.13/0.39 % (28398)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.13/0.40 % (28397)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.13/0.40 % (28395)Instruction limit reached!
% 0.13/0.40 % (28395)------------------------------
% 0.13/0.40 % (28395)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (28395)Termination reason: Unknown
% 0.13/0.40 % (28395)Termination phase: Saturation
% 0.13/0.40
% 0.13/0.40 % (28395)Memory used [KB]: 5628
% 0.13/0.40 % (28395)Time elapsed: 0.019 s
% 0.13/0.40 % (28395)Instructions burned: 18 (million)
% 0.13/0.40 % (28395)------------------------------
% 0.13/0.40 % (28395)------------------------------
% 0.13/0.40 % (28398)Instruction limit reached!
% 0.13/0.40 % (28398)------------------------------
% 0.13/0.40 % (28398)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (28398)Termination reason: Unknown
% 0.13/0.40 % (28398)Termination phase: Saturation
% 0.13/0.40
% 0.13/0.40 % (28398)Memory used [KB]: 5628
% 0.13/0.40 % (28398)Time elapsed: 0.012 s
% 0.13/0.40 % (28398)Instructions burned: 15 (million)
% 0.13/0.40 % (28398)------------------------------
% 0.13/0.40 % (28398)------------------------------
% 0.13/0.41 % (28400)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.13/0.41 % (28399)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.41 % (28399)Instruction limit reached!
% 0.13/0.41 % (28399)------------------------------
% 0.13/0.41 % (28399)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (28399)Termination reason: Unknown
% 0.13/0.41 % (28399)Termination phase: Preprocessing 3
% 0.13/0.41
% 0.13/0.41 % (28399)Memory used [KB]: 1023
% 0.13/0.41 % (28399)Time elapsed: 0.005 s
% 0.13/0.41 % (28399)Instructions burned: 3 (million)
% 0.13/0.41 % (28399)------------------------------
% 0.13/0.41 % (28399)------------------------------
% 0.13/0.41 % (28403)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.41 % (28401)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.13/0.41 % (28403)Instruction limit reached!
% 0.13/0.41 % (28403)------------------------------
% 0.13/0.41 % (28403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (28403)Termination reason: Unknown
% 0.13/0.41 % (28403)Termination phase: Preprocessing 3
% 0.13/0.41
% 0.13/0.41 % (28403)Memory used [KB]: 1023
% 0.13/0.41 % (28403)Time elapsed: 0.004 s
% 0.13/0.41 % (28403)Instructions burned: 4 (million)
% 0.13/0.41 % (28403)------------------------------
% 0.13/0.41 % (28403)------------------------------
% 0.13/0.42 % (28401)Instruction limit reached!
% 0.13/0.42 % (28401)------------------------------
% 0.13/0.42 % (28401)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.42 % (28401)Termination reason: Unknown
% 0.13/0.42 % (28401)Termination phase: Saturation
% 0.13/0.42
% 0.13/0.42 % (28401)Memory used [KB]: 1023
% 0.13/0.42 % (28401)Time elapsed: 0.007 s
% 0.13/0.42 % (28401)Instructions burned: 8 (million)
% 0.13/0.42 % (28401)------------------------------
% 0.13/0.42 % (28401)------------------------------
% 0.13/0.42 % (28402)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.13/0.42 % (28397)Instruction limit reached!
% 0.13/0.42 % (28397)------------------------------
% 0.13/0.42 % (28397)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.42 % (28397)Termination reason: Unknown
% 0.13/0.42 % (28397)Termination phase: Saturation
% 0.13/0.42
% 0.13/0.42 % (28397)Memory used [KB]: 5628
% 0.13/0.42 % (28397)Time elapsed: 0.030 s
% 0.13/0.42 % (28397)Instructions burned: 37 (million)
% 0.13/0.42 % (28397)------------------------------
% 0.13/0.42 % (28397)------------------------------
% 0.13/0.43 % (28405)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.43 % (28404)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43 % (28402)Instruction limit reached!
% 0.21/0.43 % (28402)------------------------------
% 0.21/0.43 % (28402)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (28402)Termination reason: Unknown
% 0.21/0.43 % (28402)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (28402)Memory used [KB]: 5628
% 0.21/0.43 % (28402)Time elapsed: 0.010 s
% 0.21/0.43 % (28402)Instructions burned: 16 (million)
% 0.21/0.43 % (28402)------------------------------
% 0.21/0.43 % (28402)------------------------------
% 0.21/0.43 % (28404)Instruction limit reached!
% 0.21/0.43 % (28404)------------------------------
% 0.21/0.43 % (28404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (28404)Termination reason: Unknown
% 0.21/0.43 % (28404)Termination phase: Preprocessing 3
% 0.21/0.43
% 0.21/0.43 % (28404)Memory used [KB]: 1023
% 0.21/0.43 % (28404)Time elapsed: 0.004 s
% 0.21/0.43 % (28404)Instructions burned: 4 (million)
% 0.21/0.43 % (28404)------------------------------
% 0.21/0.43 % (28404)------------------------------
% 0.21/0.43 % (28405)Instruction limit reached!
% 0.21/0.43 % (28405)------------------------------
% 0.21/0.43 % (28405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (28405)Termination reason: Unknown
% 0.21/0.43 % (28405)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (28405)Memory used [KB]: 5500
% 0.21/0.43 % (28405)Time elapsed: 0.006 s
% 0.21/0.43 % (28405)Instructions burned: 7 (million)
% 0.21/0.43 % (28405)------------------------------
% 0.21/0.43 % (28405)------------------------------
% 0.21/0.43 % (28406)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43 % (28406)Instruction limit reached!
% 0.21/0.43 % (28406)------------------------------
% 0.21/0.43 % (28406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (28406)Termination reason: Unknown
% 0.21/0.43 % (28406)Termination phase: Property scanning
% 0.21/0.43
% 0.21/0.43 % (28406)Memory used [KB]: 1023
% 0.21/0.43 % (28406)Time elapsed: 0.003 s
% 0.21/0.43 % (28406)Instructions burned: 4 (million)
% 0.21/0.43 % (28406)------------------------------
% 0.21/0.43 % (28406)------------------------------
% 0.21/0.44 % (28407)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.44 % (28407)Instruction limit reached!
% 0.21/0.44 % (28407)------------------------------
% 0.21/0.44 % (28407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (28407)Termination reason: Unknown
% 0.21/0.44 % (28407)Termination phase: Property scanning
% 0.21/0.44
% 0.21/0.44 % (28407)Memory used [KB]: 1023
% 0.21/0.44 % (28407)Time elapsed: 0.004 s
% 0.21/0.44 % (28407)Instructions burned: 4 (million)
% 0.21/0.44 % (28407)------------------------------
% 0.21/0.44 % (28407)------------------------------
% 0.21/0.45 % (28409)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.45 % (28410)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.45 % (28408)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.45 % (28410)Instruction limit reached!
% 0.21/0.45 % (28410)------------------------------
% 0.21/0.45 % (28410)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (28410)Termination reason: Unknown
% 0.21/0.45 % (28410)Termination phase: Property scanning
% 0.21/0.45
% 0.21/0.45 % (28410)Memory used [KB]: 1023
% 0.21/0.45 % (28410)Time elapsed: 0.005 s
% 0.21/0.45 % (28410)Instructions burned: 6 (million)
% 0.21/0.45 % (28410)------------------------------
% 0.21/0.45 % (28410)------------------------------
% 0.21/0.46 % (28411)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.46 % (28408)Instruction limit reached!
% 0.21/0.46 % (28408)------------------------------
% 0.21/0.46 % (28408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (28408)Termination reason: Unknown
% 0.21/0.46 % (28408)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (28408)Memory used [KB]: 5628
% 0.21/0.46 % (28408)Time elapsed: 0.012 s
% 0.21/0.46 % (28408)Instructions burned: 19 (million)
% 0.21/0.46 % (28408)------------------------------
% 0.21/0.46 % (28408)------------------------------
% 0.21/0.46 % (28412)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.47 % (28413)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.47 % (28413)Instruction limit reached!
% 0.21/0.47 % (28413)------------------------------
% 0.21/0.47 % (28413)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (28413)Termination reason: Unknown
% 0.21/0.47 % (28413)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (28413)Memory used [KB]: 5500
% 0.21/0.47 % (28413)Time elapsed: 0.005 s
% 0.21/0.47 % (28413)Instructions burned: 6 (million)
% 0.21/0.47 % (28413)------------------------------
% 0.21/0.47 % (28413)------------------------------
% 0.21/0.47 % (28412)Instruction limit reached!
% 0.21/0.47 % (28412)------------------------------
% 0.21/0.47 % (28412)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (28412)Termination reason: Unknown
% 0.21/0.47 % (28412)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (28412)Memory used [KB]: 5756
% 0.21/0.47 % (28412)Time elapsed: 0.035 s
% 0.21/0.47 % (28412)Instructions burned: 21 (million)
% 0.21/0.47 % (28412)------------------------------
% 0.21/0.47 % (28412)------------------------------
% 0.21/0.48 % (28414)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.48 % (28414)Instruction limit reached!
% 0.21/0.48 % (28414)------------------------------
% 0.21/0.48 % (28414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (28414)Termination reason: Unknown
% 0.21/0.48 % (28414)Termination phase: Saturation
% 0.21/0.48
% 0.21/0.48 % (28414)Memory used [KB]: 5500
% 0.21/0.48 % (28414)Time elapsed: 0.005 s
% 0.21/0.48 % (28414)Instructions burned: 6 (million)
% 0.21/0.48 % (28414)------------------------------
% 0.21/0.48 % (28414)------------------------------
% 0.21/0.49 % (28416)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2998ds/779Mi)
% 0.21/0.49 % (28415)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.21/0.49 % (28389)Instruction limit reached!
% 0.21/0.49 % (28389)------------------------------
% 0.21/0.49 % (28389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (28389)Termination reason: Unknown
% 0.21/0.49 % (28389)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (28389)Memory used [KB]: 6524
% 0.21/0.49 % (28389)Time elapsed: 0.111 s
% 0.21/0.49 % (28389)Instructions burned: 183 (million)
% 0.21/0.49 % (28389)------------------------------
% 0.21/0.49 % (28389)------------------------------
% 0.21/0.50 % (28417)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.21/0.50 % (28418)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.21/0.51 % (28417)Instruction limit reached!
% 0.21/0.51 % (28417)------------------------------
% 0.21/0.51 % (28417)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51 % (28417)Termination reason: Unknown
% 0.21/0.51 % (28417)Termination phase: Saturation
% 0.21/0.51
% 0.21/0.51 % (28417)Memory used [KB]: 5500
% 0.21/0.51 % (28417)Time elapsed: 0.011 s
% 0.21/0.51 % (28417)Instructions burned: 19 (million)
% 0.21/0.51 % (28417)------------------------------
% 0.21/0.51 % (28417)------------------------------
% 0.21/0.52 % (28419)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.21/0.53 % (28419)Instruction limit reached!
% 0.21/0.53 % (28419)------------------------------
% 0.21/0.53 % (28419)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53 % (28419)Termination reason: Unknown
% 0.21/0.53 % (28419)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (28419)Memory used [KB]: 5628
% 0.21/0.53 % (28419)Time elapsed: 0.034 s
% 0.21/0.53 % (28419)Instructions burned: 17 (million)
% 0.21/0.53 % (28419)------------------------------
% 0.21/0.53 % (28419)------------------------------
% 0.21/0.54 % (28394)Instruction limit reached!
% 0.21/0.54 % (28394)------------------------------
% 0.21/0.54 % (28394)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.54 % (28394)Termination reason: Unknown
% 0.21/0.54 % (28394)Termination phase: Saturation
% 0.21/0.54
% 0.21/0.54 % (28394)Memory used [KB]: 6140
% 0.21/0.54 % (28394)Time elapsed: 0.159 s
% 0.21/0.54 % (28394)Instructions burned: 275 (million)
% 0.21/0.54 % (28394)------------------------------
% 0.21/0.54 % (28394)------------------------------
% 0.21/0.55 % (28420)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.21/0.55 % (28420)Instruction limit reached!
% 0.21/0.55 % (28420)------------------------------
% 0.21/0.55 % (28420)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.55 % (28420)Termination reason: Unknown
% 0.21/0.55 % (28420)Termination phase: Preprocessing 3
% 0.21/0.55
% 0.21/0.55 % (28420)Memory used [KB]: 1023
% 0.21/0.55 % (28420)Time elapsed: 0.004 s
% 0.21/0.55 % (28420)Instructions burned: 4 (million)
% 0.21/0.55 % (28420)------------------------------
% 0.21/0.55 % (28420)------------------------------
% 0.21/0.56 % (28421)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 1.71/0.57 % (28421)Instruction limit reached!
% 1.71/0.57 % (28421)------------------------------
% 1.71/0.57 % (28421)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.71/0.57 % (28421)Termination reason: Unknown
% 1.71/0.57 % (28421)Termination phase: Saturation
% 1.71/0.57
% 1.71/0.57 % (28421)Memory used [KB]: 5756
% 1.71/0.57 % (28421)Time elapsed: 0.018 s
% 1.71/0.57 % (28421)Instructions burned: 30 (million)
% 1.71/0.57 % (28421)------------------------------
% 1.71/0.57 % (28421)------------------------------
% 1.71/0.58 % (28422)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2997ds/127Mi)
% 1.71/0.59 % (28423)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2997ds/100Mi)
% 1.90/0.59 % (28400)First to succeed.
% 1.90/0.61 % (28400)Refutation found. Thanks to Tanya!
% 1.90/0.61 % SZS status Theorem for theBenchmark
% 1.90/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.90/0.61 % (28400)------------------------------
% 1.90/0.61 % (28400)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.90/0.61 % (28400)Termination reason: Refutation
% 1.90/0.61
% 1.90/0.61 % (28400)Memory used [KB]: 6780
% 1.90/0.61 % (28400)Time elapsed: 0.204 s
% 1.90/0.61 % (28400)Instructions burned: 319 (million)
% 1.90/0.61 % (28400)------------------------------
% 1.90/0.61 % (28400)------------------------------
% 1.90/0.61 % (28388)Success in time 0.263 s
% 1.90/0.61 % Vampire---4.8 exiting
%------------------------------------------------------------------------------