%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV155^5 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n027.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 04:12:11 EDT 2024
% Result : Theorem 0.14s 0.56s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 63
% Syntax : Number of formulae : 384 ( 33 unt; 42 typ; 0 def)
% Number of atoms : 3751 ( 316 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 12421 ( 448 ~; 710 |; 659 &;7877 @)
% ( 20 <=>;1016 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 958 ( 958 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 57 con; 0-2 aty)
% (1691 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2011 (1758 ^ 252 !; 0 ?;2011 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a > a > $o ).
thf(func_def_22,type,
sK3: a ).
thf(func_def_23,type,
sK4: a > a > $o ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a > a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a > a > $o ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a > a > $o ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a ).
thf(func_def_50,type,
sK31: a ).
thf(func_def_51,type,
sK32: a ).
thf(func_def_52,type,
sK33: a ).
thf(func_def_53,type,
sK34: a ).
thf(func_def_54,type,
sK35: a ).
thf(func_def_55,type,
sK36: a ).
thf(func_def_56,type,
sK37: a ).
thf(func_def_57,type,
sK38: a ).
thf(func_def_58,type,
sK39: a ).
thf(func_def_59,type,
sK40: a ).
thf(f2135,plain,
$false,
inference(avatar_sat_refutation,[],[f56,f75,f173,f275,f337,f368,f374,f424,f602,f841,f954,f985,f992,f1011,f1103,f1318,f1618,f1654,f1708,f2048,f2128]) ).
thf(f2128,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f2127]) ).
thf(f2127,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f2123]) ).
thf(f2123,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f2117,f1972]) ).
thf(f1972,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK13 @ X3 @ X1 )
& ( sK13 @ X1 @ X2 ) )
=> ( sK13 @ X3 @ X2 ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1971]) ).
thf(f1971,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK13 @ Y0 @ X1 )
& ( sK13 @ X1 @ X2 ) )
=> ( sK13 @ Y0 @ X2 ) )
@ X3 )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1962]) ).
thf(f1962,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ Y0 @ X1 )
& ( sK13 @ X1 @ X2 ) )
=> ( sK13 @ Y0 @ X2 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1961]) ).
thf(f1961,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ X1 )
& ( sK13 @ X1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1957]) ).
thf(f1957,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ X1 )
& ( sK13 @ X1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1956]) ).
thf(f1956,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y0 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1745]) ).
thf(f1745,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y0 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1740]) ).
thf(f1740,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y0 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f1713]) ).
thf(f1713,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y0 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK13 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1712]) ).
thf(f1712,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[],[f1711]) ).
thf(f1711,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1710]) ).
thf(f1710,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1709]) ).
thf(f1709,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1339,f169]) ).
thf(f169,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f168,plain,
( spl0_7
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f1339,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1338]) ).
thf(f1338,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f1337]) ).
thf(f1337,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f1336]) ).
thf(f1336,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f74]) ).
thf(f74,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f73,plain,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f2117,plain,
( ( ( ( ( sK13 @ sK39 @ sK40 )
& ( sK13 @ sK40 @ sK38 ) )
=> ( sK13 @ sK39 @ sK38 ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f2116]) ).
thf(f2116,plain,
( ( ( ^ [Y0: a] :
( ( ( sK13 @ sK39 @ Y0 )
& ( sK13 @ Y0 @ sK38 ) )
=> ( sK13 @ sK39 @ sK38 ) )
@ sK40 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f2094]) ).
thf(f2094,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ sK39 @ Y0 )
& ( sK13 @ Y0 @ sK38 ) )
=> ( sK13 @ sK39 @ sK38 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f2093]) ).
thf(f2093,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y1 @ sK38 ) )
=> ( sK13 @ Y0 @ sK38 ) ) )
@ sK39 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f2057]) ).
thf(f2057,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 @ Y1 )
& ( sK13 @ Y1 @ sK38 ) )
=> ( sK13 @ Y0 @ sK38 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f2055]) ).
thf(f2055,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
@ sK38 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f274]) ).
thf(f274,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f273,plain,
( spl0_10
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f2048,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2047]) ).
thf(f2047,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f2046]) ).
thf(f2046,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2045]) ).
thf(f2045,plain,
( ( ~ $true = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2044]) ).
thf(f2044,plain,
( ( ( ~ ( $true
| ( sK2 @ sK36 @ sK37 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2038,f2031]) ).
thf(f2031,plain,
( ( $true
= ( sK4 @ sK36 @ sK37 ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f2029]) ).
thf(f2029,plain,
( ( ( ( sK4 @ sK36 @ sK37 )
=> ( sK13 @ sK36 @ sK37 ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f2028]) ).
thf(f2028,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK4 @ sK36 @ Y0 )
=> ( sK13 @ sK36 @ Y0 ) )
@ sK37 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f2024]) ).
thf(f2024,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK36 @ Y0 )
=> ( sK13 @ sK36 @ Y0 ) ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f2020]) ).
thf(f2020,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK13 @ Y0 @ Y1 ) ) )
@ sK36 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f271]) ).
thf(f271,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK13 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f270,plain,
( spl0_9
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK13 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f2038,plain,
( ( ( ~ ( ( sK4 @ sK36 @ sK37 )
| ( sK2 @ sK36 @ sK37 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2037]) ).
thf(f2037,plain,
( ( $true
= ( ( ( sK4 @ sK36 @ sK37 )
| ( sK2 @ sK36 @ sK37 ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f1772,f2033]) ).
thf(f2033,plain,
( ( ( sK13 @ sK36 @ sK37 )
= $false )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f2032]) ).
thf(f2032,plain,
( ( $false
= ( $true
=> ( sK13 @ sK36 @ sK37 ) ) )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f2029,f2031]) ).
thf(f1772,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK4 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) )
=> ( sK13 @ X2 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1771]) ).
thf(f1771,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1767]) ).
thf(f1767,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f1766]) ).
thf(f1766,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[],[f1748]) ).
thf(f1748,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f1747]) ).
thf(f1747,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[],[f1740,f1745]) ).
thf(f1708,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f1707]) ).
thf(f1707,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_37 ),
inference(trivial_inequality_removal,[],[f1706]) ).
thf(f1706,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_37 ),
inference(boolean_simplification,[],[f1705]) ).
thf(f1705,plain,
( ( ~ $true = $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_37 ),
inference(boolean_simplification,[],[f1704]) ).
thf(f1704,plain,
( ( ( ~ ( ( sK4 @ sK35 @ sK34 )
| $true ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1702,f1689]) ).
thf(f1689,plain,
( ( ( sK2 @ sK35 @ sK34 )
= $true )
| ~ spl0_37 ),
inference(binary_proxy_clausification,[],[f1679]) ).
thf(f1679,plain,
( ( ( ( sK2 @ sK35 @ sK34 )
=> ( sK13 @ sK35 @ sK34 ) )
= $false )
| ~ spl0_37 ),
inference(beta_eta_normalization,[],[f1678]) ).
thf(f1678,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK34 )
=> ( sK13 @ Y0 @ sK34 ) )
@ sK35 )
= $false )
| ~ spl0_37 ),
inference(sigma_clausification,[],[f1669]) ).
thf(f1669,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK34 )
=> ( sK13 @ Y0 @ sK34 ) ) )
= $false )
| ~ spl0_37 ),
inference(beta_eta_normalization,[],[f1665]) ).
thf(f1665,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK13 @ Y1 @ Y0 ) ) )
@ sK34 ) )
| ~ spl0_37 ),
inference(sigma_clausification,[],[f1614]) ).
thf(f1614,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1613]) ).
thf(f1613,plain,
( spl0_37
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
thf(f1702,plain,
( ( $true
= ( ~ ( ( sK4 @ sK35 @ sK34 )
| ( sK2 @ sK35 @ sK34 ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_37 ),
inference(boolean_simplification,[],[f1697]) ).
thf(f1697,plain,
( ( ( ( ( sK4 @ sK35 @ sK34 )
| ( sK2 @ sK35 @ sK34 ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_37 ),
inference(superposition,[],[f1443,f1688]) ).
thf(f1688,plain,
( ( ( sK13 @ sK35 @ sK34 )
= $false )
| ~ spl0_37 ),
inference(binary_proxy_clausification,[],[f1679]) ).
thf(f1443,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK4 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) )
=> ( sK13 @ X2 @ X1 ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1442]) ).
thf(f1442,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1421]) ).
thf(f1421,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK13 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1420]) ).
thf(f1420,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1394]) ).
thf(f1394,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1393]) ).
thf(f1393,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[],[f1386,f1391]) ).
thf(f1391,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y0 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1386]) ).
thf(f1386,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y0 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1364]) ).
thf(f1364,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y0 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK13 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1363]) ).
thf(f1363,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(sigma_clausification,[],[f1342]) ).
thf(f1342,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1341]) ).
thf(f1341,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1340]) ).
thf(f1340,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1339,f172]) ).
thf(f172,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f171]) ).
thf(f171,plain,
( spl0_8
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f1654,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[],[f1653]) ).
thf(f1653,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_38 ),
inference(trivial_inequality_removal,[],[f1649]) ).
thf(f1649,plain,
( ( $false = $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_38 ),
inference(superposition,[],[f1545,f1643]) ).
thf(f1643,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ Y0 @ sK32 )
& ( sK13 @ sK32 @ sK31 ) )
=> ( sK13 @ Y0 @ sK31 ) ) )
= $false )
| ~ spl0_38 ),
inference(beta_eta_normalization,[],[f1642]) ).
thf(f1642,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ Y0 )
& ( sK13 @ Y0 @ sK31 ) )
=> ( sK13 @ Y1 @ sK31 ) ) )
@ sK32 )
= $false )
| ~ spl0_38 ),
inference(sigma_clausification,[],[f1634]) ).
thf(f1634,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ Y0 )
& ( sK13 @ Y0 @ sK31 ) )
=> ( sK13 @ Y1 @ sK31 ) ) ) )
= $false )
| ~ spl0_38 ),
inference(beta_eta_normalization,[],[f1630]) ).
thf(f1630,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) )
@ sK31 )
= $false )
| ~ spl0_38 ),
inference(sigma_clausification,[],[f1617]) ).
thf(f1617,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1616]) ).
thf(f1616,plain,
( spl0_38
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
thf(f1545,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ Y0 @ X1 )
& ( sK13 @ X1 @ X2 ) )
=> ( sK13 @ Y0 @ X2 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1544]) ).
thf(f1544,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ X1 )
& ( sK13 @ X1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1533]) ).
thf(f1533,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y1 @ X1 )
& ( sK13 @ X1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1532]) ).
thf(f1532,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y0 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[],[f1391]) ).
thf(f1618,plain,
( spl0_37
| spl0_38
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1609,f171,f73,f1616,f1613]) ).
thf(f1609,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1603]) ).
thf(f1603,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f1505]) ).
thf(f1505,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1503]) ).
thf(f1503,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y1 )
& ( sK13 @ Y1 @ Y0 ) )
=> ( sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f1495,f1385]) ).
thf(f1385,plain,
( ( $false
= ( sK13 @ sK11 @ sK12 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1364]) ).
thf(f1495,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK11 @ sK12 ) )
= $true )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1494]) ).
thf(f1494,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[],[f172]) ).
thf(f1318,plain,
( ~ spl0_3
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f1317]) ).
thf(f1317,plain,
( $false
| ~ spl0_3
| ~ spl0_23
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f1316]) ).
thf(f1316,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_23
| ~ spl0_25 ),
inference(backward_demodulation,[],[f1140,f1315]) ).
thf(f1315,plain,
( ( $false
= ( sK10 @ sK23 @ sK22 ) )
| ~ spl0_23
| ~ spl0_25 ),
inference(boolean_simplification,[],[f1314]) ).
thf(f1314,plain,
( ( $false
= ( $true
=> ( sK10 @ sK23 @ sK22 ) ) )
| ~ spl0_23
| ~ spl0_25 ),
inference(boolean_simplification,[],[f1313]) ).
thf(f1313,plain,
( ( $false
= ( ( ( sK2 @ sK23 @ sK22 )
| $true )
=> ( sK10 @ sK23 @ sK22 ) ) )
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1312,f981]) ).
thf(f981,plain,
( ( ( sK4 @ sK23 @ sK22 )
= $true )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f980]) ).
thf(f980,plain,
( spl0_25
<=> ( ( sK4 @ sK23 @ sK22 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f1312,plain,
( ( $false
= ( ( ( sK2 @ sK23 @ sK22 )
| ( sK4 @ sK23 @ sK22 ) )
=> ( sK10 @ sK23 @ sK22 ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[],[f1311]) ).
thf(f1311,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK22 )
| ( sK4 @ Y0 @ sK22 ) )
=> ( sK10 @ Y0 @ sK22 ) )
@ sK23 ) )
| ~ spl0_23 ),
inference(sigma_clausification,[],[f1283]) ).
thf(f1283,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK22 )
| ( sK4 @ Y0 @ sK22 ) )
=> ( sK10 @ Y0 @ sK22 ) ) )
= $false )
| ~ spl0_23 ),
inference(beta_eta_normalization,[],[f1281]) ).
thf(f1281,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ sK22 )
= $false )
| ~ spl0_23 ),
inference(sigma_clausification,[],[f950]) ).
thf(f950,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f949]) ).
thf(f949,plain,
( spl0_23
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f1140,plain,
( ( $true
= ( sK10 @ sK23 @ sK22 ) )
| ~ spl0_3
| ~ spl0_25 ),
inference(boolean_simplification,[],[f1139]) ).
thf(f1139,plain,
( ( $true
= ( $true
=> ( sK10 @ sK23 @ sK22 ) ) )
| ~ spl0_3
| ~ spl0_25 ),
inference(boolean_simplification,[],[f1135]) ).
thf(f1135,plain,
( ( ( ( $true
| ( sK2 @ sK23 @ sK22 ) )
=> ( sK10 @ sK23 @ sK22 ) )
= $true )
| ~ spl0_3
| ~ spl0_25 ),
inference(superposition,[],[f787,f981]) ).
thf(f787,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK4 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) )
=> ( sK10 @ X2 @ X1 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f786]) ).
thf(f786,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK10 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f784]) ).
thf(f784,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK10 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f782]) ).
thf(f782,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f733]) ).
thf(f733,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f671]) ).
thf(f671,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f663]) ).
thf(f663,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
=> ( sK10 @ sK7 @ sK9 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f662]) ).
thf(f662,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) )
@ sK10 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f653]) ).
thf(f653,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f638]) ).
thf(f638,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK9 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f637]) ).
thf(f637,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ sK8 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
@ sK9 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f622]) ).
thf(f622,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ sK8 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK8 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f621]) ).
thf(f621,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y1 ) ) ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f617]) ).
thf(f617,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK7 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f616]) ).
thf(f616,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f71]) ).
thf(f71,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f70,plain,
( spl0_3
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f1103,plain,
( ~ spl0_3
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1102]) ).
thf(f1102,plain,
( $false
| ~ spl0_3
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f1101]) ).
thf(f1101,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1094,f1030]) ).
thf(f1030,plain,
( ( ( sK10 @ sK27 @ sK28 )
= $false )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1029]) ).
thf(f1029,plain,
( ( $false
= ( $true
=> ( sK10 @ sK27 @ sK28 ) ) )
| ~ spl0_21 ),
inference(backward_demodulation,[],[f1026,f1028]) ).
thf(f1028,plain,
( ( ( ( sK10 @ sK27 @ sK29 )
& ( sK10 @ sK29 @ sK28 ) )
= $true )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f1026]) ).
thf(f1026,plain,
( ( $false
= ( ( ( sK10 @ sK27 @ sK29 )
& ( sK10 @ sK29 @ sK28 ) )
=> ( sK10 @ sK27 @ sK28 ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1025]) ).
thf(f1025,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ sK27 @ Y0 )
& ( sK10 @ Y0 @ sK28 ) )
=> ( sK10 @ sK27 @ sK28 ) )
@ sK29 )
= $false )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f1024]) ).
thf(f1024,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK27 @ Y0 )
& ( sK10 @ Y0 @ sK28 ) )
=> ( sK10 @ sK27 @ sK28 ) ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1023]) ).
thf(f1023,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ sK27 @ Y1 )
& ( sK10 @ Y1 @ Y0 ) )
=> ( sK10 @ sK27 @ Y0 ) ) )
@ sK28 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f1020]) ).
thf(f1020,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ sK27 @ Y1 )
& ( sK10 @ Y1 @ Y0 ) )
=> ( sK10 @ sK27 @ Y0 ) ) ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1018]) ).
thf(f1018,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y0 @ Y2 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) )
@ sK27 ) )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f837]) ).
thf(f837,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y0 @ Y2 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f836]) ).
thf(f836,plain,
( spl0_21
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y0 @ Y2 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f1094,plain,
( ( ( sK10 @ sK27 @ sK28 )
= $true )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1092]) ).
thf(f1092,plain,
( ( $true
= ( $true
=> ( sK10 @ sK27 @ sK28 ) ) )
| ~ spl0_3
| ~ spl0_21 ),
inference(superposition,[],[f1068,f1060]) ).
thf(f1060,plain,
( ( ( sK10 @ sK30 @ sK28 )
= $true )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[],[f1049]) ).
thf(f1049,plain,
( ( $true
= ( ( sK10 @ sK27 @ sK30 )
& ( sK10 @ sK30 @ sK28 ) ) )
| ~ spl0_21 ),
inference(not_proxy_clausification,[],[f1044]) ).
thf(f1044,plain,
( ( ( ~ ( ( sK10 @ sK27 @ sK30 )
& ( sK10 @ sK30 @ sK28 ) ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[],[f1043]) ).
thf(f1043,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK10 @ sK27 @ Y0 )
& ( sK10 @ Y0 @ sK28 ) )
@ sK30 )
= $false )
| ~ spl0_21 ),
inference(sigma_clausification,[],[f1032]) ).
thf(f1032,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK10 @ sK27 @ Y0 )
& ( sK10 @ Y0 @ sK28 ) ) ) )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1031]) ).
thf(f1031,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK27 @ Y0 )
& ( sK10 @ Y0 @ sK28 ) )
=> $false ) )
= $false )
| ~ spl0_21 ),
inference(backward_demodulation,[],[f1024,f1030]) ).
thf(f1068,plain,
( ! [X0: a] :
( ( ( sK10 @ sK30 @ X0 )
=> ( sK10 @ sK27 @ X0 ) )
= $true )
| ~ spl0_3
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1066]) ).
thf(f1066,plain,
( ! [X0: a] :
( $true
= ( ( ( sK10 @ sK30 @ X0 )
& $true )
=> ( sK10 @ sK27 @ X0 ) ) )
| ~ spl0_3
| ~ spl0_21 ),
inference(superposition,[],[f753,f1063]) ).
thf(f1063,plain,
( ( ( sK10 @ sK27 @ sK30 )
= $true )
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1062]) ).
thf(f1062,plain,
( ( $true
= ( ( sK10 @ sK27 @ sK30 )
& $true ) )
| ~ spl0_21 ),
inference(backward_demodulation,[],[f1049,f1060]) ).
thf(f753,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK10 @ X2 @ X3 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X1 @ X3 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f752]) ).
thf(f752,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK10 @ X2 @ Y0 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X1 @ Y0 ) )
@ X3 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f751]) ).
thf(f751,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X2 @ Y0 )
& ( sK10 @ X1 @ X2 ) )
=> ( sK10 @ X1 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f750]) ).
thf(f750,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ Y1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ X1 @ Y1 ) ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f749]) ).
thf(f749,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ Y1 )
& ( sK10 @ X1 @ Y0 ) )
=> ( sK10 @ X1 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f748]) ).
thf(f748,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f736]) ).
thf(f736,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f735]) ).
thf(f735,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y2 )
& ( sK10 @ Y0 @ Y1 ) )
=> ( sK10 @ Y0 @ Y2 ) ) ) ) )
& $true ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f671,f733]) ).
thf(f1011,plain,
( ~ spl0_3
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f1010]) ).
thf(f1010,plain,
( $false
| ~ spl0_3
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f1006]) ).
thf(f1006,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_24 ),
inference(superposition,[],[f1003,f753]) ).
thf(f1003,plain,
( ( ( ( ( sK10 @ sK25 @ sK24 )
& ( sK10 @ sK26 @ sK25 ) )
=> ( sK10 @ sK26 @ sK24 ) )
= $false )
| ~ spl0_24 ),
inference(beta_eta_normalization,[],[f1002]) ).
thf(f1002,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ sK25 @ sK24 )
& ( sK10 @ Y0 @ sK25 ) )
=> ( sK10 @ Y0 @ sK24 ) )
@ sK26 )
= $false )
| ~ spl0_24 ),
inference(sigma_clausification,[],[f1001]) ).
thf(f1001,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK25 @ sK24 )
& ( sK10 @ Y0 @ sK25 ) )
=> ( sK10 @ Y0 @ sK24 ) ) ) )
| ~ spl0_24 ),
inference(beta_eta_normalization,[],[f1000]) ).
thf(f1000,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ sK24 )
& ( sK10 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ sK24 ) ) )
@ sK25 ) )
| ~ spl0_24 ),
inference(sigma_clausification,[],[f999]) ).
thf(f999,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 @ sK24 )
& ( sK10 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ sK24 ) ) ) )
= $false )
| ~ spl0_24 ),
inference(beta_eta_normalization,[],[f995]) ).
thf(f995,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y0 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y2 @ Y0 ) ) ) )
@ sK24 )
= $false )
| ~ spl0_24 ),
inference(sigma_clausification,[],[f953]) ).
thf(f953,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y0 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y2 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f952]) ).
thf(f952,plain,
( spl0_24
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y0 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y2 @ Y0 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f992,plain,
( ~ spl0_3
| ~ spl0_23
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f991]) ).
thf(f991,plain,
( $false
| ~ spl0_3
| ~ spl0_23
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f990]) ).
thf(f990,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_23
| ~ spl0_26 ),
inference(boolean_simplification,[],[f989]) ).
thf(f989,plain,
( ( ~ $true = $true )
| ~ spl0_3
| ~ spl0_23
| ~ spl0_26 ),
inference(boolean_simplification,[],[f986]) ).
thf(f986,plain,
( ( ( ~ ( ( sK4 @ sK23 @ sK22 )
| $true ) )
= $true )
| ~ spl0_3
| ~ spl0_23
| ~ spl0_26 ),
inference(backward_demodulation,[],[f972,f984]) ).
thf(f984,plain,
( ( ( sK2 @ sK23 @ sK22 )
= $true )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f983]) ).
thf(f983,plain,
( spl0_26
<=> ( ( sK2 @ sK23 @ sK22 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f972,plain,
( ( $true
= ( ~ ( ( sK4 @ sK23 @ sK22 )
| ( sK2 @ sK23 @ sK22 ) ) ) )
| ~ spl0_3
| ~ spl0_23 ),
inference(boolean_simplification,[],[f968]) ).
thf(f968,plain,
( ( ( ( ( sK4 @ sK23 @ sK22 )
| ( sK2 @ sK23 @ sK22 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_23 ),
inference(superposition,[],[f787,f967]) ).
thf(f967,plain,
( ( $false
= ( sK10 @ sK23 @ sK22 ) )
| ~ spl0_23 ),
inference(boolean_simplification,[],[f966]) ).
thf(f966,plain,
( ( $false
= ( $true
=> ( sK10 @ sK23 @ sK22 ) ) )
| ~ spl0_23 ),
inference(backward_demodulation,[],[f963,f965]) ).
thf(f965,plain,
( ( ( ( sK2 @ sK23 @ sK22 )
| ( sK4 @ sK23 @ sK22 ) )
= $true )
| ~ spl0_23 ),
inference(binary_proxy_clausification,[],[f963]) ).
thf(f963,plain,
( ( $false
= ( ( ( sK2 @ sK23 @ sK22 )
| ( sK4 @ sK23 @ sK22 ) )
=> ( sK10 @ sK23 @ sK22 ) ) )
| ~ spl0_23 ),
inference(beta_eta_normalization,[],[f962]) ).
thf(f962,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK22 )
| ( sK4 @ Y0 @ sK22 ) )
=> ( sK10 @ Y0 @ sK22 ) )
@ sK23 ) )
| ~ spl0_23 ),
inference(sigma_clausification,[],[f961]) ).
thf(f961,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK22 )
| ( sK4 @ Y0 @ sK22 ) )
=> ( sK10 @ Y0 @ sK22 ) ) )
= $false )
| ~ spl0_23 ),
inference(beta_eta_normalization,[],[f957]) ).
thf(f957,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) )
@ sK22 )
= $false )
| ~ spl0_23 ),
inference(sigma_clausification,[],[f950]) ).
thf(f985,plain,
( spl0_25
| spl0_26
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f978,f949,f983,f980]) ).
thf(f978,plain,
( ( ( sK4 @ sK23 @ sK22 )
= $true )
| ( ( sK2 @ sK23 @ sK22 )
= $true )
| ~ spl0_23 ),
inference(binary_proxy_clausification,[],[f965]) ).
thf(f954,plain,
( spl0_23
| spl0_24
| ~ spl0_3
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f945,f839,f70,f952,f949]) ).
thf(f839,plain,
( spl0_22
<=> ( ( sK10 @ sK8 @ sK9 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f945,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y0 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y2 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_3
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f942]) ).
thf(f942,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y0 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_22 ),
inference(not_proxy_clausification,[],[f875]) ).
thf(f875,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y0 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_22 ),
inference(boolean_simplification,[],[f869]) ).
thf(f869,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y1 @ Y0 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( sK10 @ Y1 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_22 ),
inference(superposition,[],[f764,f855]) ).
thf(f855,plain,
( ( ( sK10 @ sK7 @ sK8 )
= $false )
| ~ spl0_3
| ~ spl0_22 ),
inference(boolean_simplification,[],[f844]) ).
thf(f844,plain,
( ( $false
= ( $true
& ( sK10 @ sK7 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_22 ),
inference(superposition,[],[f765,f840]) ).
thf(f840,plain,
( ( ( sK10 @ sK8 @ sK9 )
= $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f839]) ).
thf(f765,plain,
( ! [X0: a] :
( ( ( sK10 @ X0 @ sK9 )
& ( sK10 @ sK7 @ X0 ) )
= $false )
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f762]) ).
thf(f762,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK10 @ X0 @ sK9 )
& ( sK10 @ sK7 @ X0 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f755]) ).
thf(f755,plain,
( ! [X0: a] :
( $true
= ( ( ( sK10 @ X0 @ sK9 )
& ( sK10 @ sK7 @ X0 ) )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[],[f753,f673]) ).
thf(f673,plain,
( ( $false
= ( sK10 @ sK7 @ sK9 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f672]) ).
thf(f672,plain,
( ( ( $true
=> ( sK10 @ sK7 @ sK9 ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f663,f671]) ).
thf(f764,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y0 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK7 @ sK8 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f763]) ).
thf(f763,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f675]) ).
thf(f675,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f654]) ).
thf(f654,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f638]) ).
thf(f841,plain,
( spl0_21
| spl0_22
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f834,f70,f839,f836]) ).
thf(f834,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y0 @ Y2 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( sK10 @ sK8 @ sK9 )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f785]) ).
thf(f785,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y0 @ Y2 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) )
=> ( sK10 @ sK8 @ sK9 ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f783]) ).
thf(f783,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK10 @ Y0 @ Y2 )
& ( sK10 @ Y2 @ Y1 ) )
=> ( sK10 @ Y0 @ Y1 ) ) ) ) ) )
=> ( sK10 @ sK8 @ sK9 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[],[f683,f733]) ).
thf(f683,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK8 @ sK9 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f682]) ).
thf(f682,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f677]) ).
thf(f677,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f676]) ).
thf(f676,plain,
( ( ( $true
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK9 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f654,f675]) ).
thf(f602,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f601]) ).
thf(f601,plain,
( $false
| ~ spl0_13
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f600]) ).
thf(f600,plain,
( ( $false = $true )
| ~ spl0_13
| ~ spl0_15 ),
inference(backward_demodulation,[],[f550,f599]) ).
thf(f599,plain,
( ( $false
= ( sK6 @ sK14 @ sK15 ) )
| ~ spl0_13
| ~ spl0_15 ),
inference(boolean_simplification,[],[f598]) ).
thf(f598,plain,
( ( $false
= ( $true
=> ( sK6 @ sK14 @ sK15 ) ) )
| ~ spl0_13
| ~ spl0_15 ),
inference(boolean_simplification,[],[f597]) ).
thf(f597,plain,
( ( ( ( ( sK2 @ sK14 @ sK15 )
| $true )
=> ( sK6 @ sK14 @ sK15 ) )
= $false )
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f596,f364]) ).
thf(f364,plain,
( ( $true
= ( sK4 @ sK14 @ sK15 ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f363]) ).
thf(f363,plain,
( spl0_15
<=> ( $true
= ( sK4 @ sK14 @ sK15 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f596,plain,
( ( ( ( ( sK2 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
=> ( sK6 @ sK14 @ sK15 ) )
= $false )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f595]) ).
thf(f595,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
=> ( sK6 @ sK14 @ Y0 ) )
@ sK15 ) )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f581]) ).
thf(f581,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
=> ( sK6 @ sK14 @ Y0 ) ) )
= $false )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f579]) ).
thf(f579,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK14 ) )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f333]) ).
thf(f333,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f332]) ).
thf(f332,plain,
( spl0_13
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f550,plain,
( ( $true
= ( sK6 @ sK14 @ sK15 ) )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f549]) ).
thf(f549,plain,
( ( $true
= ( $true
=> ( sK6 @ sK14 @ sK15 ) ) )
| ~ spl0_15 ),
inference(boolean_simplification,[],[f548]) ).
thf(f548,plain,
( ( $true
= ( ( $true
| ( sK2 @ sK14 @ sK15 ) )
=> ( sK6 @ sK14 @ sK15 ) ) )
| ~ spl0_15 ),
inference(superposition,[],[f92,f364]) ).
thf(f92,plain,
! [X2: a,X1: a] :
( ( ( ( sK4 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) )
=> ( sK6 @ X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f91]) ).
thf(f91,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f88]) ).
thf(f88,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f87]) ).
thf(f87,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK6 @ sK3 @ sK5 ) )
= $false ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f21]) ).
thf(f21,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) )
= $false ),
inference(backward_demodulation,[],[f17,f19]) ).
thf(f19,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK4 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK3 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( Y0 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
| ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( Y0 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ sK3 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
| ( sK2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y7 @ Y6 )
| ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y6 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y0 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y7 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a,X3: a > a > $o] :
( ( ( ! [X4: a,X5: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X1 @ X8 @ X7 )
=> ( X6 @ X8 @ X7 ) )
& ! [X9: a,X10: a,X11: a] :
( ( ( X6 @ X9 @ X11 )
& ( X6 @ X10 @ X9 ) )
=> ( X6 @ X10 @ X11 ) ) )
=> ( X6 @ X5 @ X4 ) )
| ! [X12: a > a > $o] :
( ( ! [X13: a,X14: a] :
( ( X3 @ X13 @ X14 )
=> ( X12 @ X13 @ X14 ) )
& ! [X15: a,X16: a,X17: a] :
( ( ( X12 @ X16 @ X17 )
& ( X12 @ X15 @ X16 ) )
=> ( X12 @ X15 @ X17 ) ) )
=> ( X12 @ X5 @ X4 ) ) )
=> ! [X18: a > a > $o] :
( ( ! [X19: a,X20: a,X21: a] :
( ( ( X18 @ X21 @ X20 )
& ( X18 @ X19 @ X21 ) )
=> ( X18 @ X19 @ X20 ) )
& ! [X22: a,X23: a] :
( ( ( X3 @ X22 @ X23 )
| ( X1 @ X22 @ X23 ) )
=> ( X18 @ X22 @ X23 ) ) )
=> ( X18 @ X5 @ X4 ) ) )
& ! [X24: a,X25: a,X26: a] :
( ( ! [X27: a > a > $o] :
( ( ! [X28: a,X29: a,X30: a] :
( ( ( X27 @ X28 @ X29 )
& ( X27 @ X30 @ X28 ) )
=> ( X27 @ X30 @ X29 ) )
& ! [X31: a,X32: a] :
( ( ( X3 @ X31 @ X32 )
| ( X1 @ X31 @ X32 ) )
=> ( X27 @ X31 @ X32 ) ) )
=> ( X27 @ X25 @ X24 ) )
& ! [X33: a > a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( X1 @ X34 @ X35 )
| ( X3 @ X34 @ X35 ) )
=> ( X33 @ X34 @ X35 ) )
& ! [X36: a,X37: a,X38: a] :
( ( ( X33 @ X36 @ X37 )
& ( X33 @ X37 @ X38 ) )
=> ( X33 @ X36 @ X38 ) ) )
=> ( X33 @ X26 @ X25 ) ) )
=> ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a] :
( ( ( X3 @ X40 @ X41 )
| ( X1 @ X40 @ X41 ) )
=> ( X39 @ X40 @ X41 ) )
& ! [X42: a,X43: a,X44: a] :
( ( ( X39 @ X44 @ X43 )
& ( X39 @ X43 @ X42 ) )
=> ( X39 @ X44 @ X42 ) ) )
=> ( X39 @ X26 @ X24 ) ) ) )
=> ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a,X48: a] :
( ( ( X45 @ X47 @ X46 )
& ( X45 @ X48 @ X47 ) )
=> ( X45 @ X48 @ X46 ) )
& ! [X49: a,X50: a] :
( ( ( X1 @ X50 @ X49 )
| ( X3 @ X50 @ X49 ) )
=> ( X45 @ X50 @ X49 ) ) )
=> ( X45 @ X2 @ X0 ) ) )
=> ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a,X54: a] :
( ( ( X51 @ X53 @ X54 )
& ( X51 @ X52 @ X53 ) )
=> ( X51 @ X52 @ X54 ) )
& ! [X55: a,X56: a] :
( ( ( X3 @ X55 @ X56 )
| ( X1 @ X55 @ X56 ) )
=> ( X51 @ X55 @ X56 ) ) )
=> ( X51 @ X2 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X0: a > a > $o,X2: a,X1: a > a > $o] :
( ( ( ! [X5: a,X4: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X8: a,X7: a] :
( ( X0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X8: a,X7: a,X9: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
| ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X7: a,X9: a,X8: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) )
& ! [X7: a,X8: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
& ! [X9: a,X5: a,X4: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X8: a,X10: a,X7: a] :
( ( ( X6 @ X8 @ X10 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X7: a,X8: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X5 @ X9 ) )
& ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
& ! [X7: a,X8: a,X10: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
& ! [X10: a,X8: a,X7: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) ) )
=> ( X6 @ X4 @ X9 ) ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X9: a,X5: a,X4: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) )
& ! [X5: a,X4: a] :
( ( ( X0 @ X4 @ X5 )
| ( X1 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X6 @ X2 @ X3 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X4: a,X5: a,X9: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) )
& ! [X4: a,X5: a] :
( ( ( X1 @ X4 @ X5 )
| ( X0 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X6 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X3: a,X0: a > a > $o,X2: a,X1: a > a > $o] :
( ( ( ! [X5: a,X4: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X8: a,X7: a] :
( ( X0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X8: a,X7: a,X9: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
| ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X7: a,X9: a,X8: a] :
( ( ( X6 @ X8 @ X9 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X9 ) )
& ! [X7: a,X8: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
& ! [X9: a,X5: a,X4: a] :
( ( ! [X6: a > a > $o] :
( ( ! [X8: a,X10: a,X7: a] :
( ( ( X6 @ X8 @ X10 )
& ( X6 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X10 ) )
& ! [X7: a,X8: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X5 @ X9 ) )
& ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( ( X0 @ X7 @ X8 )
| ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
& ! [X7: a,X8: a,X10: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X7: a,X8: a] :
( ( ( X1 @ X7 @ X8 )
| ( X0 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
& ! [X10: a,X8: a,X7: a] :
( ( ( X6 @ X7 @ X8 )
& ( X6 @ X8 @ X10 ) )
=> ( X6 @ X7 @ X10 ) ) )
=> ( X6 @ X4 @ X9 ) ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X9: a,X5: a,X4: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) )
& ! [X5: a,X4: a] :
( ( ( X0 @ X4 @ X5 )
| ( X1 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X6 @ X2 @ X3 ) ) )
=> ! [X6: a > a > $o] :
( ( ! [X4: a,X5: a,X9: a] :
( ( ( X6 @ X5 @ X9 )
& ( X6 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X9 ) )
& ! [X4: a,X5: a] :
( ( ( X1 @ X4 @ X5 )
| ( X0 @ X4 @ X5 ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ( X6 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM250D_pme) ).
thf(f424,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[],[f423]) ).
thf(f423,plain,
( $false
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f419]) ).
thf(f419,plain,
( ( $false = $true )
| ~ spl0_14 ),
inference(superposition,[],[f411,f39]) ).
thf(f39,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK6 @ X3 @ X2 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ X3 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f38]) ).
thf(f38,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ X2 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f37]) ).
thf(f37,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ X2 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f36]) ).
thf(f36,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y1 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f35]) ).
thf(f35,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y1 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f34]) ).
thf(f34,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f33]) ).
thf(f33,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f32]) ).
thf(f32,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) )
= $true ),
inference(backward_demodulation,[],[f25,f31]) ).
thf(f411,plain,
( ( $false
= ( ( ( sK6 @ sK16 @ sK17 )
& ( sK6 @ sK17 @ sK18 ) )
=> ( sK6 @ sK16 @ sK18 ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f410]) ).
thf(f410,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK16 @ sK17 )
& ( sK6 @ sK17 @ Y0 ) )
=> ( sK6 @ sK16 @ Y0 ) )
@ sK18 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f395]) ).
thf(f395,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK16 @ sK17 )
& ( sK6 @ sK17 @ Y0 ) )
=> ( sK6 @ sK16 @ Y0 ) ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f394]) ).
thf(f394,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK16 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ sK16 @ Y1 ) ) )
@ sK17 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f385]) ).
thf(f385,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK16 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ sK16 @ Y1 ) ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[],[f381]) ).
thf(f381,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) )
@ sK16 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[],[f336]) ).
thf(f336,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f335]) ).
thf(f335,plain,
( spl0_14
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f374,plain,
( ~ spl0_13
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f373]) ).
thf(f373,plain,
( $false
| ~ spl0_13
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f372]) ).
thf(f372,plain,
( ( $false = $true )
| ~ spl0_13
| ~ spl0_16 ),
inference(boolean_simplification,[],[f371]) ).
thf(f371,plain,
( ( ~ $true = $true )
| ~ spl0_13
| ~ spl0_16 ),
inference(boolean_simplification,[],[f369]) ).
thf(f369,plain,
( ( ( ~ ( ( sK4 @ sK14 @ sK15 )
| $true ) )
= $true )
| ~ spl0_13
| ~ spl0_16 ),
inference(backward_demodulation,[],[f357,f367]) ).
thf(f367,plain,
( ( $true
= ( sK2 @ sK14 @ sK15 ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f366]) ).
thf(f366,plain,
( spl0_16
<=> ( $true
= ( sK2 @ sK14 @ sK15 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f357,plain,
( ( ( ~ ( ( sK4 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) ) )
= $true )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f351]) ).
thf(f351,plain,
( ( $true
= ( ( ( sK4 @ sK14 @ sK15 )
| ( sK2 @ sK14 @ sK15 ) )
=> $false ) )
| ~ spl0_13 ),
inference(superposition,[],[f92,f350]) ).
thf(f350,plain,
( ( $false
= ( sK6 @ sK14 @ sK15 ) )
| ~ spl0_13 ),
inference(boolean_simplification,[],[f349]) ).
thf(f349,plain,
( ( $false
= ( $true
=> ( sK6 @ sK14 @ sK15 ) ) )
| ~ spl0_13 ),
inference(backward_demodulation,[],[f346,f348]) ).
thf(f348,plain,
( ( ( ( sK2 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
= $true )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f346]) ).
thf(f346,plain,
( ( ( ( ( sK2 @ sK14 @ sK15 )
| ( sK4 @ sK14 @ sK15 ) )
=> ( sK6 @ sK14 @ sK15 ) )
= $false )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f345]) ).
thf(f345,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
=> ( sK6 @ sK14 @ Y0 ) )
@ sK15 ) )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f342]) ).
thf(f342,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK14 @ Y0 )
| ( sK4 @ sK14 @ Y0 ) )
=> ( sK6 @ sK14 @ Y0 ) ) )
= $false )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f340]) ).
thf(f340,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK14 ) )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f333]) ).
thf(f368,plain,
( spl0_15
| spl0_16
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f361,f332,f366,f363]) ).
thf(f361,plain,
( ( $true
= ( sK2 @ sK14 @ sK15 ) )
| ( $true
= ( sK4 @ sK14 @ sK15 ) )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f348]) ).
thf(f337,plain,
( spl0_13
| spl0_14
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f328,f51,f335,f332]) ).
thf(f51,plain,
( spl0_1
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f328,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f325]) ).
thf(f325,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f323]) ).
thf(f323,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f317]) ).
thf(f317,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f301,f24]) ).
thf(f24,plain,
( ( sK6 @ sK3 @ sK5 )
= $false ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f301,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK4 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK3 @ sK5 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f300]) ).
thf(f300,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f52]) ).
thf(f52,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f275,plain,
( spl0_9
| spl0_10
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f266,f168,f73,f273,f270]) ).
thf(f266,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK13 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f256]) ).
thf(f256,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f186,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[],[f185]) ).
thf(f185,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y1 @ Y2 )
& ( sK13 @ Y2 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK13 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f181,f160]) ).
thf(f160,plain,
( ( $false
= ( sK13 @ sK11 @ sK12 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f159]) ).
thf(f159,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK13 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK13 @ Y2 @ Y0 )
& ( sK13 @ Y0 @ Y1 ) )
=> ( sK13 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK13 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f158]) ).
thf(f158,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) )
@ sK13 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f152]) ).
thf(f152,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f151]) ).
thf(f151,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f150]) ).
thf(f150,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f149]) ).
thf(f149,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK11 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f148]) ).
thf(f148,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f74]) ).
thf(f181,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK11 @ sK12 ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f180]) ).
thf(f180,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f169]) ).
thf(f173,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f166,f73,f171,f168]) ).
thf(f166,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f153]) ).
thf(f153,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 @ sK12 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f151]) ).
thf(f75,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f68,f54,f73,f70]) ).
thf(f54,plain,
( spl0_2
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f68,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f55]) ).
thf(f55,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f56,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f49,f54,f51]) ).
thf(f49,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK5 ) ) )
= $true )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK4 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV155^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.09/0.30 % Computer : n027.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun May 19 18:41:07 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.30 This is a TH0_THM_NEQ_NAR problem
% 0.09/0.30 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.31 % (7285)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.31 % (7287)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)
% 0.14/0.32 % (7286)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)
% 0.14/0.32 % (7289)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)
% 0.14/0.32 % (7290)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)
% 0.14/0.32 % (7292)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)
% 0.14/0.32 % (7286)Instruction limit reached!
% 0.14/0.32 % (7286)------------------------------
% 0.14/0.32 % (7286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (7286)Termination reason: Unknown
% 0.14/0.32 % (7286)Termination phase: Preprocessing 3
% 0.14/0.32
% 0.14/0.32 % (7286)Memory used [KB]: 1023
% 0.14/0.32 % (7286)Time elapsed: 0.003 s
% 0.14/0.32 % (7286)Instructions burned: 4 (million)
% 0.14/0.32 % (7286)------------------------------
% 0.14/0.32 % (7286)------------------------------
% 0.14/0.32 % (7289)Instruction limit reached!
% 0.14/0.32 % (7289)------------------------------
% 0.14/0.32 % (7289)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (7289)Termination reason: Unknown
% 0.14/0.32 % (7289)Termination phase: shuffling
% 0.14/0.32
% 0.14/0.32 % (7289)Memory used [KB]: 1023
% 0.14/0.32 % (7289)Time elapsed: 0.003 s
% 0.14/0.32 % (7289)Instructions burned: 3 (million)
% 0.14/0.32 % (7289)------------------------------
% 0.14/0.32 % (7289)------------------------------
% 0.14/0.32 % (7292)Instruction limit reached!
% 0.14/0.32 % (7292)------------------------------
% 0.14/0.32 % (7292)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (7292)Termination reason: Unknown
% 0.14/0.32 % (7292)Termination phase: Naming
% 0.14/0.32
% 0.14/0.32 % (7292)Memory used [KB]: 1023
% 0.14/0.32 % (7292)Time elapsed: 0.003 s
% 0.14/0.32 % (7292)Instructions burned: 4 (million)
% 0.14/0.32 % (7292)------------------------------
% 0.14/0.32 % (7292)------------------------------
% 0.14/0.32 % (7288)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.32 % (7288)Instruction limit reached!
% 0.14/0.32 % (7288)------------------------------
% 0.14/0.32 % (7288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (7288)Termination reason: Unknown
% 0.14/0.32 % (7288)Termination phase: shuffling
% 0.14/0.32
% 0.14/0.32 % (7288)Memory used [KB]: 1023
% 0.14/0.32 % (7288)Time elapsed: 0.002 s
% 0.14/0.32 % (7288)Instructions burned: 2 (million)
% 0.14/0.32 % (7288)------------------------------
% 0.14/0.32 % (7288)------------------------------
% 0.14/0.32 % (7291)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.32 % (7287)Instruction limit reached!
% 0.14/0.32 % (7287)------------------------------
% 0.14/0.32 % (7287)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (7287)Termination reason: Unknown
% 0.14/0.32 % (7287)Termination phase: Saturation
% 0.14/0.32
% 0.14/0.32 % (7287)Memory used [KB]: 5756
% 0.14/0.32 % (7287)Time elapsed: 0.011 s
% 0.14/0.32 % (7287)Instructions burned: 28 (million)
% 0.14/0.32 % (7287)------------------------------
% 0.14/0.32 % (7287)------------------------------
% 0.14/0.33 % (7291)Instruction limit reached!
% 0.14/0.33 % (7291)------------------------------
% 0.14/0.33 % (7291)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (7291)Termination reason: Unknown
% 0.14/0.33 % (7291)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (7291)Memory used [KB]: 5628
% 0.14/0.33 % (7291)Time elapsed: 0.007 s
% 0.14/0.33 % (7291)Instructions burned: 18 (million)
% 0.14/0.33 % (7291)------------------------------
% 0.14/0.33 % (7291)------------------------------
% 0.14/0.33 % (7293)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.33 % (7295)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.33 % (7294)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.14/0.33 % (7295)Instruction limit reached!
% 0.14/0.33 % (7295)------------------------------
% 0.14/0.33 % (7295)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (7295)Termination reason: Unknown
% 0.14/0.33 % (7295)Termination phase: Naming
% 0.14/0.33
% 0.14/0.33 % (7295)Memory used [KB]: 1023
% 0.14/0.33 % (7295)Time elapsed: 0.003 s
% 0.14/0.33 % (7295)Instructions burned: 4 (million)
% 0.14/0.33 % (7295)------------------------------
% 0.14/0.33 % (7295)------------------------------
% 0.14/0.33 % (7296)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.14/0.34 % (7298)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.34 % (7294)Instruction limit reached!
% 0.14/0.34 % (7294)------------------------------
% 0.14/0.34 % (7294)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (7294)Termination reason: Unknown
% 0.14/0.34 % (7294)Termination phase: Saturation
% 0.14/0.34
% 0.14/0.34 % (7294)Memory used [KB]: 5756
% 0.14/0.34 % (7294)Time elapsed: 0.007 s
% 0.14/0.34 % (7294)Instructions burned: 15 (million)
% 0.14/0.34 % (7294)------------------------------
% 0.14/0.34 % (7294)------------------------------
% 0.14/0.34 % (7297)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.34 % (7298)Instruction limit reached!
% 0.14/0.34 % (7298)------------------------------
% 0.14/0.34 % (7298)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (7298)Termination reason: Unknown
% 0.14/0.34 % (7298)Termination phase: Property scanning
% 0.14/0.34
% 0.14/0.34 % (7298)Memory used [KB]: 1151
% 0.14/0.34 % (7298)Time elapsed: 0.006 s
% 0.14/0.34 % (7298)Instructions burned: 18 (million)
% 0.14/0.34 % (7298)------------------------------
% 0.14/0.34 % (7298)------------------------------
% 0.14/0.34 % (7297)Instruction limit reached!
% 0.14/0.34 % (7297)------------------------------
% 0.14/0.34 % (7297)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (7297)Termination reason: Unknown
% 0.14/0.34 % (7297)Termination phase: Property scanning
% 0.14/0.34
% 0.14/0.34 % (7297)Memory used [KB]: 1151
% 0.14/0.34 % (7297)Time elapsed: 0.005 s
% 0.14/0.34 % (7297)Instructions burned: 8 (million)
% 0.14/0.34 % (7297)------------------------------
% 0.14/0.34 % (7297)------------------------------
% 0.14/0.34 % (7293)Instruction limit reached!
% 0.14/0.34 % (7293)------------------------------
% 0.14/0.34 % (7293)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (7293)Termination reason: Unknown
% 0.14/0.34 % (7293)Termination phase: Saturation
% 0.14/0.34
% 0.14/0.34 % (7293)Memory used [KB]: 5628
% 0.14/0.34 % (7293)Time elapsed: 0.017 s
% 0.14/0.34 % (7293)Instructions burned: 38 (million)
% 0.14/0.34 % (7293)------------------------------
% 0.14/0.34 % (7293)------------------------------
% 0.14/0.35 % (7300)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.35 % (7300)Instruction limit reached!
% 0.14/0.35 % (7300)------------------------------
% 0.14/0.35 % (7300)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (7300)Termination reason: Unknown
% 0.14/0.35 % (7300)Termination phase: Preprocessing 2
% 0.14/0.35
% 0.14/0.35 % (7300)Memory used [KB]: 1023
% 0.14/0.35 % (7300)Time elapsed: 0.003 s
% 0.14/0.35 % (7300)Instructions burned: 4 (million)
% 0.14/0.35 % (7300)------------------------------
% 0.14/0.35 % (7300)------------------------------
% 0.14/0.35 % (7301)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.35 % (7299)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.35 % (7301)Instruction limit reached!
% 0.14/0.35 % (7301)------------------------------
% 0.14/0.35 % (7301)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (7301)Termination reason: Unknown
% 0.14/0.35 % (7301)Termination phase: Property scanning
% 0.14/0.35
% 0.14/0.35 % (7301)Memory used [KB]: 1151
% 0.14/0.35 % (7301)Time elapsed: 0.004 s
% 0.14/0.35 % (7301)Instructions burned: 9 (million)
% 0.14/0.35 % (7301)------------------------------
% 0.14/0.35 % (7301)------------------------------
% 0.14/0.35 % (7299)Instruction limit reached!
% 0.14/0.35 % (7299)------------------------------
% 0.14/0.35 % (7299)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (7299)Termination reason: Unknown
% 0.14/0.35 % (7299)Termination phase: Preprocessing 2
% 0.14/0.35
% 0.14/0.35 % (7299)Memory used [KB]: 1023
% 0.14/0.35 % (7299)Time elapsed: 0.003 s
% 0.14/0.35 % (7299)Instructions burned: 4 (million)
% 0.14/0.35 % (7299)------------------------------
% 0.14/0.35 % (7299)------------------------------
% 0.14/0.36 % (7304)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)
% 0.14/0.36 % (7305)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.14/0.36 % (7302)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.36 % (7302)Instruction limit reached!
% 0.14/0.36 % (7302)------------------------------
% 0.14/0.36 % (7302)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (7302)Termination reason: Unknown
% 0.14/0.36 % (7302)Termination phase: shuffling
% 0.14/0.36
% 0.14/0.36 % (7302)Memory used [KB]: 1023
% 0.14/0.36 % (7302)Time elapsed: 0.003 s
% 0.14/0.36 % (7302)Instructions burned: 3 (million)
% 0.14/0.36 % (7302)------------------------------
% 0.14/0.36 % (7302)------------------------------
% 0.14/0.36 % (7304)Instruction limit reached!
% 0.14/0.36 % (7304)------------------------------
% 0.14/0.36 % (7304)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (7304)Termination reason: Unknown
% 0.14/0.36 % (7304)Termination phase: Saturation
% 0.14/0.36
% 0.14/0.36 % (7304)Memory used [KB]: 5628
% 0.14/0.36 % (7304)Time elapsed: 0.007 s
% 0.14/0.36 % (7304)Instructions burned: 18 (million)
% 0.14/0.36 % (7304)------------------------------
% 0.14/0.36 % (7304)------------------------------
% 0.14/0.37 % (7303)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (7303)Instruction limit reached!
% 0.14/0.37 % (7303)------------------------------
% 0.14/0.37 % (7303)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (7303)Termination reason: Unknown
% 0.14/0.37 % (7303)Termination phase: Preprocessing 3
% 0.14/0.37
% 0.14/0.37 % (7303)Memory used [KB]: 1023
% 0.14/0.37 % (7303)Time elapsed: 0.003 s
% 0.14/0.37 % (7303)Instructions burned: 4 (million)
% 0.14/0.37 % (7303)------------------------------
% 0.14/0.37 % (7303)------------------------------
% 0.14/0.37 % (7307)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)
% 0.14/0.38 % (7306)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.14/0.38 % (7308)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)
% 0.14/0.38 % (7309)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.14/0.38 % (7306)Instruction limit reached!
% 0.14/0.38 % (7306)------------------------------
% 0.14/0.38 % (7306)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (7306)Termination reason: Unknown
% 0.14/0.38 % (7306)Termination phase: Preprocessing 3
% 0.14/0.38
% 0.14/0.38 % (7306)Memory used [KB]: 1151
% 0.14/0.38 % (7306)Time elapsed: 0.003 s
% 0.14/0.38 % (7306)Instructions burned: 6 (million)
% 0.14/0.38 % (7306)------------------------------
% 0.14/0.38 % (7306)------------------------------
% 0.14/0.38 % (7309)Instruction limit reached!
% 0.14/0.38 % (7309)------------------------------
% 0.14/0.38 % (7309)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (7309)Termination reason: Unknown
% 0.14/0.38 % (7309)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (7309)Memory used [KB]: 1023
% 0.14/0.38 % (7309)Time elapsed: 0.003 s
% 0.14/0.38 % (7309)Instructions burned: 5 (million)
% 0.14/0.38 % (7309)------------------------------
% 0.14/0.38 % (7309)------------------------------
% 0.14/0.39 % (7308)Instruction limit reached!
% 0.14/0.39 % (7308)------------------------------
% 0.14/0.39 % (7308)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (7308)Termination reason: Unknown
% 0.14/0.39 % (7308)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (7310)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)
% 0.14/0.39 % (7308)Memory used [KB]: 5756
% 0.14/0.39 % (7308)Time elapsed: 0.011 s
% 0.14/0.39 % (7308)Instructions burned: 21 (million)
% 0.14/0.39 % (7308)------------------------------
% 0.14/0.39 % (7308)------------------------------
% 0.14/0.39 % (7310)Instruction limit reached!
% 0.14/0.39 % (7310)------------------------------
% 0.14/0.39 % (7310)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (7310)Termination reason: Unknown
% 0.14/0.39 % (7310)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (7310)Memory used [KB]: 5500
% 0.14/0.39 % (7310)Time elapsed: 0.004 s
% 0.14/0.39 % (7310)Instructions burned: 9 (million)
% 0.14/0.39 % (7310)------------------------------
% 0.14/0.39 % (7310)------------------------------
% 0.14/0.39 % (7285)Instruction limit reached!
% 0.14/0.39 % (7285)------------------------------
% 0.14/0.39 % (7285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (7285)Termination reason: Unknown
% 0.14/0.39 % (7285)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (7285)Memory used [KB]: 6140
% 0.14/0.39 % (7285)Time elapsed: 0.076 s
% 0.14/0.39 % (7285)Instructions burned: 183 (million)
% 0.14/0.39 % (7285)------------------------------
% 0.14/0.39 % (7285)------------------------------
% 0.14/0.40 % (7313)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.14/0.40 % (7311)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.14/0.40 % (7312)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.14/0.40 % (7313)Instruction limit reached!
% 0.14/0.40 % (7313)------------------------------
% 0.14/0.40 % (7313)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (7313)Termination reason: Unknown
% 0.14/0.40 % (7313)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (7313)Memory used [KB]: 5500
% 0.14/0.40 % (7313)Time elapsed: 0.007 s
% 0.14/0.40 % (7313)Instructions burned: 23 (million)
% 0.14/0.40 % (7313)------------------------------
% 0.14/0.40 % (7313)------------------------------
% 0.14/0.41 % (7314)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.14/0.41 % (7315)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.14/0.42 % (7315)Instruction limit reached!
% 0.14/0.42 % (7315)------------------------------
% 0.14/0.42 % (7315)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (7315)Termination reason: Unknown
% 0.14/0.42 % (7315)Termination phase: Saturation
% 0.14/0.42
% 0.14/0.42 % (7315)Memory used [KB]: 5756
% 0.14/0.42 % (7315)Time elapsed: 0.029 s
% 0.14/0.42 % (7315)Instructions burned: 18 (million)
% 0.14/0.42 % (7315)------------------------------
% 0.14/0.42 % (7315)------------------------------
% 0.14/0.43 % (7316)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.43 % (7290)Instruction limit reached!
% 0.14/0.43 % (7290)------------------------------
% 0.14/0.43 % (7290)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.43 % (7290)Termination reason: Unknown
% 0.14/0.43 % (7290)Termination phase: Saturation
% 0.14/0.43
% 0.14/0.43 % (7290)Memory used [KB]: 6396
% 0.14/0.43 % (7290)Time elapsed: 0.110 s
% 0.14/0.43 % (7290)Instructions burned: 275 (million)
% 0.14/0.43 % (7290)------------------------------
% 0.14/0.43 % (7290)------------------------------
% 0.14/0.43 % (7316)Instruction limit reached!
% 0.14/0.43 % (7316)------------------------------
% 0.14/0.43 % (7316)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.43 % (7316)Termination reason: Unknown
% 0.14/0.43 % (7316)Termination phase: Preprocessing 2
% 0.14/0.43
% 0.14/0.43 % (7316)Memory used [KB]: 1023
% 0.14/0.43 % (7316)Time elapsed: 0.004 s
% 0.14/0.43 % (7316)Instructions burned: 4 (million)
% 0.14/0.43 % (7316)------------------------------
% 0.14/0.43 % (7316)------------------------------
% 0.14/0.45 % (7318)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.14/0.46 % (7317)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.14/0.48 % (7317)Instruction limit reached!
% 0.14/0.48 % (7317)------------------------------
% 0.14/0.48 % (7317)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.48 % (7317)Termination reason: Unknown
% 0.14/0.48 % (7317)Termination phase: Saturation
% 0.14/0.48
% 0.14/0.48 % (7317)Memory used [KB]: 5756
% 0.14/0.48 % (7317)Time elapsed: 0.060 s
% 0.14/0.48 % (7317)Instructions burned: 32 (million)
% 0.14/0.48 % (7317)------------------------------
% 0.14/0.48 % (7317)------------------------------
% 0.14/0.49 % (7318)Instruction limit reached!
% 0.14/0.49 % (7318)------------------------------
% 0.14/0.49 % (7318)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.49 % (7318)Termination reason: Unknown
% 0.14/0.49 % (7318)Termination phase: Saturation
% 0.14/0.49
% 0.14/0.49 % (7318)Memory used [KB]: 6268
% 0.14/0.49 % (7318)Time elapsed: 0.069 s
% 0.14/0.49 % (7318)Instructions burned: 128 (million)
% 0.14/0.49 % (7318)------------------------------
% 0.14/0.49 % (7318)------------------------------
% 0.14/0.49 % (7319)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.14/0.50 % (7320)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.14/0.50 % (7320)Instruction limit reached!
% 0.14/0.50 % (7320)------------------------------
% 0.14/0.50 % (7320)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.50 % (7320)Termination reason: Unknown
% 0.14/0.50 % (7320)Termination phase: Property scanning
% 0.14/0.50
% 0.14/0.50 % (7320)Memory used [KB]: 1023
% 0.14/0.50 % (7320)Time elapsed: 0.003 s
% 0.14/0.50 % (7320)Instructions burned: 4 (million)
% 0.14/0.50 % (7320)------------------------------
% 0.14/0.50 % (7320)------------------------------
% 0.14/0.52 % (7321)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 0.14/0.52 % (7319)Instruction limit reached!
% 0.14/0.52 % (7319)------------------------------
% 0.14/0.52 % (7319)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.52 % (7319)Termination reason: Unknown
% 0.14/0.52 % (7319)Termination phase: Saturation
% 0.14/0.52
% 0.14/0.52 % (7319)Memory used [KB]: 6012
% 0.14/0.52 % (7319)Time elapsed: 0.057 s
% 0.14/0.52 % (7319)Instructions burned: 100 (million)
% 0.14/0.52 % (7319)------------------------------
% 0.14/0.52 % (7319)------------------------------
% 0.14/0.52 % (7321)Instruction limit reached!
% 0.14/0.52 % (7321)------------------------------
% 0.14/0.52 % (7321)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.52 % (7321)Termination reason: Unknown
% 0.14/0.52 % (7321)Termination phase: Saturation
% 0.14/0.52
% 0.14/0.52 % (7321)Memory used [KB]: 5628
% 0.14/0.52 % (7321)Time elapsed: 0.011 s
% 0.14/0.52 % (7321)Instructions burned: 20 (million)
% 0.14/0.53 % (7321)------------------------------
% 0.14/0.53 % (7321)------------------------------
% 0.14/0.53 % (7322)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2997ds/86Mi)
% 0.14/0.54 % (7296)First to succeed.
% 0.14/0.54 % (7323)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2997ds/107Mi)
% 0.14/0.56 % (7322)Instruction limit reached!
% 0.14/0.56 % (7322)------------------------------
% 0.14/0.56 % (7322)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.56 % (7322)Termination reason: Unknown
% 0.14/0.56 % (7322)Termination phase: Saturation
% 0.14/0.56
% 0.14/0.56 % (7322)Memory used [KB]: 6012
% 0.14/0.56 % (7322)Time elapsed: 0.058 s
% 0.14/0.56 % (7322)Instructions burned: 87 (million)
% 0.14/0.56 % (7322)------------------------------
% 0.14/0.56 % (7322)------------------------------
% 0.14/0.56 % (7311)Refutation not found, non-redundant clauses discarded% (7311)------------------------------
% 0.14/0.56 % (7311)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.56 % (7311)Termination reason: Refutation not found, non-redundant clauses discarded
% 0.14/0.56
% 0.14/0.56 % (7311)Memory used [KB]: 6012
% 0.14/0.56 % (7311)Time elapsed: 0.184 s
% 0.14/0.56 % (7311)Instructions burned: 353 (million)
% 0.14/0.56 % (7311)------------------------------
% 0.14/0.56 % (7311)------------------------------
% 0.14/0.56 % (7296)Refutation found. Thanks to Tanya!
% 0.14/0.56 % SZS status Theorem for theBenchmark
% 0.14/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.56 % (7296)------------------------------
% 0.14/0.56 % (7296)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.56 % (7296)Termination reason: Refutation
% 0.14/0.56
% 0.14/0.56 % (7296)Memory used [KB]: 7164
% 0.14/0.56 % (7296)Time elapsed: 0.225 s
% 0.14/0.56 % (7296)Instructions burned: 402 (million)
% 0.14/0.56 % (7296)------------------------------
% 0.14/0.56 % (7296)------------------------------
% 0.14/0.56 % (7283)Success in time 0.267 s
% 0.14/0.56 % Vampire---4.8 exiting
%------------------------------------------------------------------------------