%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV156^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:41:33 EDT 2024
% Result : Theorem 1.87s 0.60s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 55
% Syntax : Number of formulae : 391 ( 30 unt; 36 typ; 0 def)
% Number of atoms : 4105 ( 331 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 14047 ( 524 ~; 803 |; 762 &;8883 @)
% ( 18 <=>;1121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 1140 (1140 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 49 con; 0-2 aty)
% (1936 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2260 (2003 ^ 256 !; 0 ?;2260 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: a > a > $o ).
thf(func_def_21,type,
sK3: a ).
thf(func_def_22,type,
sK4: a ).
thf(func_def_23,type,
sK5: a > a > $o ).
thf(func_def_24,type,
sK6: a > a > $o ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a ).
thf(func_def_27,type,
sK9: a > a > $o ).
thf(func_def_28,type,
sK10: a ).
thf(func_def_29,type,
sK11: a ).
thf(func_def_30,type,
sK12: a ).
thf(func_def_31,type,
sK13: a ).
thf(func_def_32,type,
sK14: a ).
thf(func_def_33,type,
sK15: a ).
thf(func_def_34,type,
sK16: a > a > $o ).
thf(func_def_35,type,
sK17: a ).
thf(func_def_36,type,
sK18: a ).
thf(func_def_37,type,
sK19: a ).
thf(func_def_38,type,
sK20: a ).
thf(func_def_39,type,
sK21: a ).
thf(func_def_40,type,
sK22: a ).
thf(func_def_41,type,
sK23: a ).
thf(func_def_42,type,
sK24: a ).
thf(func_def_43,type,
sK25: a ).
thf(func_def_44,type,
sK26: a ).
thf(func_def_45,type,
sK27: a ).
thf(func_def_46,type,
sK28: a ).
thf(func_def_47,type,
sK29: a ).
thf(func_def_48,type,
sK30: a ).
thf(func_def_49,type,
sK31: a ).
thf(func_def_50,type,
sK32: a ).
thf(func_def_51,type,
sK33: a ).
thf(func_def_52,type,
sK34: a ).
thf(f1840,plain,
$false,
inference(avatar_sat_refutation,[],[f29,f41,f110,f230,f359,f593,f740,f778,f785,f989,f1057,f1186,f1192,f1198,f1246,f1483,f1530,f1657,f1837]) ).
thf(f1837,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f1836]) ).
thf(f1836,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f1835]) ).
thf(f1835,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1817,f1690]) ).
thf(f1690,plain,
( ( ( sK9 @ sK33 @ sK34 )
= $false )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1687]) ).
thf(f1687,plain,
( ( ( ( sK2 @ sK33 @ sK34 )
=> ( sK9 @ sK33 @ sK34 ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1686]) ).
thf(f1686,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK33 @ Y0 )
=> ( sK9 @ sK33 @ Y0 ) )
@ sK34 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f1683]) ).
thf(f1683,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK33 @ Y0 )
=> ( sK9 @ sK33 @ Y0 ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f1682]) ).
thf(f1682,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ sK33 )
= $false )
| ~ spl0_8 ),
inference(sigma_clausification,[],[f358]) ).
thf(f358,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f357]) ).
thf(f357,plain,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f1817,plain,
( ( ( sK9 @ sK33 @ sK34 )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1816]) ).
thf(f1816,plain,
( ( ( $true
=> ( sK9 @ sK33 @ sK34 ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1813]) ).
thf(f1813,plain,
( ( ( ( $true
| ( sK5 @ sK33 @ sK34 ) )
=> ( sK9 @ sK33 @ sK34 ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f1795,f1691]) ).
thf(f1691,plain,
( ( ( sK2 @ sK33 @ sK34 )
= $true )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f1687]) ).
thf(f1795,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X1 @ X2 )
| ( sK5 @ X1 @ X2 ) )
=> ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1794]) ).
thf(f1794,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f1790]) ).
thf(f1790,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1789]) ).
thf(f1789,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f1679]) ).
thf(f1679,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1675]) ).
thf(f1675,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f1662]) ).
thf(f1662,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK9 @ sK7 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f1661]) ).
thf(f1661,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ sK9 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f1660]) ).
thf(f1660,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1659]) ).
thf(f1659,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f1658]) ).
thf(f1658,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f1264,f106]) ).
thf(f106,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f105]) ).
thf(f105,plain,
( spl0_5
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f1264,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f1263]) ).
thf(f1263,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f1256]) ).
thf(f1256,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f1255]) ).
thf(f1255,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f37]) ).
thf(f37,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f36,plain,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f1657,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1656]) ).
thf(f1656,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f1655]) ).
thf(f1655,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1648,f1576]) ).
thf(f1576,plain,
( ( ( sK9 @ sK31 @ sK32 )
= $false )
| ~ spl0_26 ),
inference(binary_proxy_clausification,[],[f1560]) ).
thf(f1560,plain,
( ( ( ( ( sK9 @ sK30 @ sK32 )
& ( sK9 @ sK31 @ sK30 ) )
=> ( sK9 @ sK31 @ sK32 ) )
= $false )
| ~ spl0_26 ),
inference(beta_eta_normalization,[],[f1559]) ).
thf(f1559,plain,
( ( ( ^ [Y0: a] :
( ( ( sK9 @ sK30 @ Y0 )
& ( sK9 @ sK31 @ sK30 ) )
=> ( sK9 @ sK31 @ Y0 ) )
@ sK32 )
= $false )
| ~ spl0_26 ),
inference(sigma_clausification,[],[f1551]) ).
thf(f1551,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ sK30 @ Y0 )
& ( sK9 @ sK31 @ sK30 ) )
=> ( sK9 @ sK31 @ Y0 ) ) )
= $false )
| ~ spl0_26 ),
inference(beta_eta_normalization,[],[f1550]) ).
thf(f1550,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ sK30 @ Y1 )
& ( sK9 @ Y0 @ sK30 ) )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ sK31 ) )
| ~ spl0_26 ),
inference(sigma_clausification,[],[f1540]) ).
thf(f1540,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ sK30 @ Y1 )
& ( sK9 @ Y0 @ sK30 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_26 ),
inference(beta_eta_normalization,[],[f1536]) ).
thf(f1536,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) )
@ sK30 )
= $false )
| ~ spl0_26 ),
inference(sigma_clausification,[],[f1479]) ).
thf(f1479,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
= $false )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1478]) ).
thf(f1478,plain,
( spl0_26
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f1648,plain,
( ( ( sK9 @ sK31 @ sK32 )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_26 ),
inference(boolean_simplification,[],[f1647]) ).
thf(f1647,plain,
( ( $true
= ( $true
=> ( sK9 @ sK31 @ sK32 ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_26 ),
inference(superposition,[],[f1602,f1592]) ).
thf(f1592,plain,
( ( ( sK9 @ sK31 @ sK30 )
= $true )
| ~ spl0_26 ),
inference(binary_proxy_clausification,[],[f1577]) ).
thf(f1577,plain,
( ( ( ( sK9 @ sK30 @ sK32 )
& ( sK9 @ sK31 @ sK30 ) )
= $true )
| ~ spl0_26 ),
inference(binary_proxy_clausification,[],[f1560]) ).
thf(f1602,plain,
( ! [X0: a] :
( ( ( sK9 @ X0 @ sK30 )
=> ( sK9 @ X0 @ sK32 ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_26 ),
inference(boolean_simplification,[],[f1597]) ).
thf(f1597,plain,
( ! [X0: a] :
( ( ( ( sK9 @ X0 @ sK30 )
& $true )
=> ( sK9 @ X0 @ sK32 ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_26 ),
inference(superposition,[],[f1412,f1595]) ).
thf(f1595,plain,
( ( ( sK9 @ sK30 @ sK32 )
= $true )
| ~ spl0_26 ),
inference(boolean_simplification,[],[f1594]) ).
thf(f1594,plain,
( ( ( ( sK9 @ sK30 @ sK32 )
& $true )
= $true )
| ~ spl0_26 ),
inference(backward_demodulation,[],[f1577,f1592]) ).
thf(f1412,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK9 @ X3 @ X2 )
& ( sK9 @ X2 @ X1 ) )
=> ( sK9 @ X3 @ X1 ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1411]) ).
thf(f1411,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK9 @ Y0 @ X2 )
& ( sK9 @ X2 @ X1 ) )
=> ( sK9 @ Y0 @ X1 ) )
@ X3 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f1404]) ).
thf(f1404,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ Y0 @ X2 )
& ( sK9 @ X2 @ X1 ) )
=> ( sK9 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1403]) ).
thf(f1403,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ X1 ) )
=> ( sK9 @ Y1 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f1399]) ).
thf(f1399,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ X1 ) )
=> ( sK9 @ Y1 @ X1 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1398]) ).
thf(f1398,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f1289]) ).
thf(f1289,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1284]) ).
thf(f1284,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1277]) ).
thf(f1277,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK9 @ sK7 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1276]) ).
thf(f1276,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ sK9 )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[],[f1267]) ).
thf(f1267,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1266]) ).
thf(f1266,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1265]) ).
thf(f1265,plain,
( ( ( ( $true
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1264,f109]) ).
thf(f109,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f108]) ).
thf(f108,plain,
( spl0_6
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f1530,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1529]) ).
thf(f1529,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f1528]) ).
thf(f1528,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_27 ),
inference(boolean_simplification,[],[f1527]) ).
thf(f1527,plain,
( ( ~ $true = $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_27 ),
inference(boolean_simplification,[],[f1526]) ).
thf(f1526,plain,
( ( ( ~ ( ( sK2 @ sK28 @ sK29 )
| $true ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1520,f1511]) ).
thf(f1511,plain,
( ( ( sK5 @ sK28 @ sK29 )
= $true )
| ~ spl0_27 ),
inference(binary_proxy_clausification,[],[f1509]) ).
thf(f1509,plain,
( ( $false
= ( ( sK5 @ sK28 @ sK29 )
=> ( sK9 @ sK28 @ sK29 ) ) )
| ~ spl0_27 ),
inference(beta_eta_normalization,[],[f1508]) ).
thf(f1508,plain,
( ( ( ^ [Y0: a] :
( ( sK5 @ sK28 @ Y0 )
=> ( sK9 @ sK28 @ Y0 ) )
@ sK29 )
= $false )
| ~ spl0_27 ),
inference(sigma_clausification,[],[f1502]) ).
thf(f1502,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK5 @ sK28 @ Y0 )
=> ( sK9 @ sK28 @ Y0 ) ) )
= $false )
| ~ spl0_27 ),
inference(beta_eta_normalization,[],[f1500]) ).
thf(f1500,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ sK28 )
= $false )
| ~ spl0_27 ),
inference(sigma_clausification,[],[f1482]) ).
thf(f1482,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f1481]) ).
thf(f1481,plain,
( spl0_27
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
thf(f1520,plain,
( ( ( ~ ( ( sK2 @ sK28 @ sK29 )
| ( sK5 @ sK28 @ sK29 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_27 ),
inference(boolean_simplification,[],[f1519]) ).
thf(f1519,plain,
( ( ( ( ( sK2 @ sK28 @ sK29 )
| ( sK5 @ sK28 @ sK29 ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_27 ),
inference(superposition,[],[f1308,f1510]) ).
thf(f1510,plain,
( ( ( sK9 @ sK28 @ sK29 )
= $false )
| ~ spl0_27 ),
inference(binary_proxy_clausification,[],[f1509]) ).
thf(f1308,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X1 @ X2 )
| ( sK5 @ X1 @ X2 ) )
=> ( sK9 @ X1 @ X2 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1307]) ).
thf(f1307,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f1301]) ).
thf(f1301,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK5 @ X1 @ Y0 ) )
=> ( sK9 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1300]) ).
thf(f1300,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(pi_clausification,[],[f1292]) ).
thf(f1292,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1291]) ).
thf(f1291,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& $true )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[],[f1284,f1289]) ).
thf(f1483,plain,
( spl0_26
| spl0_27
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f1474,f108,f36,f1481,f1478]) ).
thf(f1474,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1468]) ).
thf(f1468,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(not_proxy_clausification,[],[f1353]) ).
thf(f1353,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1350]) ).
thf(f1350,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y2 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y1 @ Y2 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f1338,f1283]) ).
thf(f1283,plain,
( ( ( sK9 @ sK7 @ sK8 )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1277]) ).
thf(f1338,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK5 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK7 @ sK8 ) )
= $true )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1337]) ).
thf(f1337,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ X1 )
= $true )
| ~ spl0_6 ),
inference(pi_clausification,[],[f109]) ).
thf(f1246,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1245]) ).
thf(f1245,plain,
( $false
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f1244]) ).
thf(f1244,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(backward_demodulation,[],[f1222,f1243]) ).
thf(f1243,plain,
( ( ( sK16 @ sK22 @ sK21 )
= $false )
| ~ spl0_12
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1242]) ).
thf(f1242,plain,
( ( ( $true
=> ( sK16 @ sK22 @ sK21 ) )
= $false )
| ~ spl0_12
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1241]) ).
thf(f1241,plain,
( ( ( ( $true
| ( sK5 @ sK22 @ sK21 ) )
=> ( sK16 @ sK22 @ sK21 ) )
= $false )
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1240,f774]) ).
thf(f774,plain,
( ( ( sK2 @ sK22 @ sK21 )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f773]) ).
thf(f773,plain,
( spl0_13
<=> ( ( sK2 @ sK22 @ sK21 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f1240,plain,
( ( ( ( ( sK2 @ sK22 @ sK21 )
| ( sK5 @ sK22 @ sK21 ) )
=> ( sK16 @ sK22 @ sK21 ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f1239]) ).
thf(f1239,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK21 )
| ( sK5 @ Y0 @ sK21 ) )
=> ( sK16 @ Y0 @ sK21 ) )
@ sK22 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f1226]) ).
thf(f1226,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK21 )
| ( sK5 @ Y0 @ sK21 ) )
=> ( sK16 @ Y0 @ sK21 ) ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f1223]) ).
thf(f1223,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK16 @ Y1 @ Y0 ) ) )
@ sK21 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f739]) ).
thf(f739,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK16 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f738]) ).
thf(f738,plain,
( spl0_12
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK16 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f1222,plain,
( ( ( sK16 @ sK22 @ sK21 )
= $true )
| ~ spl0_1
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1221]) ).
thf(f1221,plain,
( ( ( $true
=> ( sK16 @ sK22 @ sK21 ) )
= $true )
| ~ spl0_1
| ~ spl0_13 ),
inference(boolean_simplification,[],[f1214]) ).
thf(f1214,plain,
( ( ( ( ( sK5 @ sK22 @ sK21 )
| $true )
=> ( sK16 @ sK22 @ sK21 ) )
= $true )
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[],[f642,f774]) ).
thf(f642,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK5 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
=> ( sK16 @ X1 @ X2 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f641]) ).
thf(f641,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK16 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f638]) ).
thf(f638,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK5 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK16 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f637]) ).
thf(f637,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f630]) ).
thf(f630,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f611]) ).
thf(f611,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y0 @ Y1 )
& ( sK16 @ Y2 @ Y0 ) )
=> ( sK16 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f609]) ).
thf(f609,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y0 @ Y1 )
& ( sK16 @ Y2 @ Y0 ) )
=> ( sK16 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK16 @ sK13 @ sK14 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f608]) ).
thf(f608,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) )
@ sK16 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f605]) ).
thf(f605,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f604]) ).
thf(f604,plain,
( ( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f601,f603]) ).
thf(f603,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK15 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f601]) ).
thf(f601,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK15 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK15 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK13 @ sK14 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f600]) ).
thf(f600,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK13 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK13 @ sK14 ) ) ) )
@ sK15 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f599]) ).
thf(f599,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK13 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK5 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK13 @ sK14 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f598]) ).
thf(f598,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 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK13 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ sK13 @ Y0 ) ) ) ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f597]) ).
thf(f597,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 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK5 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK13 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK5 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ sK13 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f596]) ).
thf(f596,plain,
( ( $false
= ( ^ [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 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) )
@ sK13 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f25]) ).
thf(f25,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 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f24,plain,
( spl0_1
<=> ( $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 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f1198,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1197]) ).
thf(f1197,plain,
( $false
| ~ spl0_1
| ~ spl0_16
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f1196]) ).
thf(f1196,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_23 ),
inference(boolean_simplification,[],[f1195]) ).
thf(f1195,plain,
( ( ~ $true = $true )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_23 ),
inference(boolean_simplification,[],[f1194]) ).
thf(f1194,plain,
( ( ( ~ ( $true
| ( sK2 @ sK26 @ sK27 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_23 ),
inference(backward_demodulation,[],[f1174,f1185]) ).
thf(f1185,plain,
( ( ( sK5 @ sK26 @ sK27 )
= $true )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1184]) ).
thf(f1184,plain,
( spl0_23
<=> ( ( sK5 @ sK26 @ sK27 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f1174,plain,
( ( ( ~ ( ( sK5 @ sK26 @ sK27 )
| ( sK2 @ sK26 @ sK27 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(boolean_simplification,[],[f1172]) ).
thf(f1172,plain,
( ( ( ( ( sK5 @ sK26 @ sK27 )
| ( sK2 @ sK26 @ sK27 ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(superposition,[],[f642,f1163]) ).
thf(f1163,plain,
( ( ( sK16 @ sK26 @ sK27 )
= $false )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f1159]) ).
thf(f1159,plain,
( ( ( ( ( sK2 @ sK26 @ sK27 )
| ( sK5 @ sK26 @ sK27 ) )
=> ( sK16 @ sK26 @ sK27 ) )
= $false )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f1158]) ).
thf(f1158,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK26 @ Y0 )
| ( sK5 @ sK26 @ Y0 ) )
=> ( sK16 @ sK26 @ Y0 ) )
@ sK27 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f1135]) ).
thf(f1135,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK26 @ Y0 )
| ( sK5 @ sK26 @ Y0 ) )
=> ( sK16 @ sK26 @ Y0 ) ) )
= $false )
| ~ spl0_16 ),
inference(beta_eta_normalization,[],[f1132]) ).
thf(f1132,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) )
@ sK26 )
= $false )
| ~ spl0_16 ),
inference(sigma_clausification,[],[f985]) ).
thf(f985,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f984]) ).
thf(f984,plain,
( spl0_16
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f1192,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1191]) ).
thf(f1191,plain,
( $false
| ~ spl0_1
| ~ spl0_16
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f1190]) ).
thf(f1190,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1189]) ).
thf(f1189,plain,
( ( ~ $true = $true )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_22 ),
inference(boolean_simplification,[],[f1187]) ).
thf(f1187,plain,
( ( ( ~ ( ( sK5 @ sK26 @ sK27 )
| $true ) )
= $true )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_22 ),
inference(backward_demodulation,[],[f1174,f1182]) ).
thf(f1182,plain,
( ( ( sK2 @ sK26 @ sK27 )
= $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1181]) ).
thf(f1181,plain,
( spl0_22
<=> ( ( sK2 @ sK26 @ sK27 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f1186,plain,
( spl0_22
| spl0_23
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f1179,f984,f1184,f1181]) ).
thf(f1179,plain,
( ( ( sK5 @ sK26 @ sK27 )
= $true )
| ( ( sK2 @ sK26 @ sK27 )
= $true )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f1164]) ).
thf(f1164,plain,
( ( ( ( sK2 @ sK26 @ sK27 )
| ( sK5 @ sK26 @ sK27 ) )
= $true )
| ~ spl0_16 ),
inference(binary_proxy_clausification,[],[f1159]) ).
thf(f1057,plain,
( ~ spl0_1
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1056]) ).
thf(f1056,plain,
( $false
| ~ spl0_1
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f1052]) ).
thf(f1052,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_17 ),
inference(superposition,[],[f1034,f680]) ).
thf(f680,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK16 @ X1 @ X2 )
& ( sK16 @ X3 @ X1 ) )
=> ( sK16 @ X3 @ X2 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f679]) ).
thf(f679,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK16 @ X1 @ X2 )
& ( sK16 @ Y0 @ X1 ) )
=> ( sK16 @ Y0 @ X2 ) )
@ X3 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f670]) ).
thf(f670,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK16 @ X1 @ X2 )
& ( sK16 @ Y0 @ X1 ) )
=> ( sK16 @ Y0 @ X2 ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f669]) ).
thf(f669,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK16 @ X1 @ Y0 )
& ( sK16 @ Y1 @ X1 ) )
=> ( sK16 @ Y1 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f662]) ).
thf(f662,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK16 @ X1 @ Y0 )
& ( sK16 @ Y1 @ X1 ) )
=> ( sK16 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f660]) ).
thf(f660,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y0 @ Y1 )
& ( sK16 @ Y2 @ Y0 ) )
=> ( sK16 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f632]) ).
thf(f632,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y0 @ Y1 )
& ( sK16 @ Y2 @ Y0 ) )
=> ( sK16 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f631]) ).
thf(f631,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y0 @ Y1 )
& ( sK16 @ Y2 @ Y0 ) )
=> ( sK16 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f611,f630]) ).
thf(f1034,plain,
( ( ( ( ( sK16 @ sK25 @ sK24 )
& ( sK16 @ sK23 @ sK25 ) )
=> ( sK16 @ sK23 @ sK24 ) )
= $false )
| ~ spl0_17 ),
inference(beta_eta_normalization,[],[f1033]) ).
thf(f1033,plain,
( ( ( ^ [Y0: a] :
( ( ( sK16 @ Y0 @ sK24 )
& ( sK16 @ sK23 @ Y0 ) )
=> ( sK16 @ sK23 @ sK24 ) )
@ sK25 )
= $false )
| ~ spl0_17 ),
inference(sigma_clausification,[],[f1018]) ).
thf(f1018,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK16 @ Y0 @ sK24 )
& ( sK16 @ sK23 @ Y0 ) )
=> ( sK16 @ sK23 @ sK24 ) ) )
= $false )
| ~ spl0_17 ),
inference(beta_eta_normalization,[],[f1017]) ).
thf(f1017,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK16 @ Y1 @ Y0 )
& ( sK16 @ sK23 @ Y1 ) )
=> ( sK16 @ sK23 @ Y0 ) ) )
@ sK24 )
= $false )
| ~ spl0_17 ),
inference(sigma_clausification,[],[f1000]) ).
thf(f1000,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK16 @ Y1 @ Y0 )
& ( sK16 @ sK23 @ Y1 ) )
=> ( sK16 @ sK23 @ Y0 ) ) ) )
= $false )
| ~ spl0_17 ),
inference(beta_eta_normalization,[],[f995]) ).
thf(f995,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y2 @ Y1 )
& ( sK16 @ Y0 @ Y2 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) )
@ sK23 )
= $false )
| ~ spl0_17 ),
inference(sigma_clausification,[],[f988]) ).
thf(f988,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y2 @ Y1 )
& ( sK16 @ Y0 @ Y2 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f987]) ).
thf(f987,plain,
( spl0_17
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y2 @ Y1 )
& ( sK16 @ Y0 @ Y2 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f989,plain,
( spl0_16
| spl0_17
| ~ spl0_1
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f978,f735,f24,f987,f984]) ).
thf(f735,plain,
( spl0_11
<=> ( ( sK16 @ sK13 @ sK17 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f978,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y2 @ Y1 )
& ( sK16 @ Y0 @ Y2 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_11 ),
inference(binary_proxy_clausification,[],[f972]) ).
thf(f972,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y2 @ Y1 )
& ( sK16 @ Y0 @ Y2 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_11 ),
inference(not_proxy_clausification,[],[f828]) ).
thf(f828,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y2 @ Y1 )
& ( sK16 @ Y0 @ Y2 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_11 ),
inference(boolean_simplification,[],[f820]) ).
thf(f820,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK16 @ Y2 @ Y1 )
& ( sK16 @ Y0 @ Y2 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK16 @ Y0 @ Y1 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_11 ),
inference(superposition,[],[f711,f799]) ).
thf(f799,plain,
( ( ( sK16 @ sK17 @ sK14 )
= $false )
| ~ spl0_1
| ~ spl0_11 ),
inference(boolean_simplification,[],[f788]) ).
thf(f788,plain,
( ( ( ( sK16 @ sK17 @ sK14 )
& $true )
= $false )
| ~ spl0_1
| ~ spl0_11 ),
inference(superposition,[],[f712,f736]) ).
thf(f736,plain,
( ( ( sK16 @ sK13 @ sK17 )
= $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f735]) ).
thf(f712,plain,
( ! [X0: a] :
( $false
= ( ( sK16 @ X0 @ sK14 )
& ( sK16 @ sK13 @ X0 ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f695]) ).
thf(f695,plain,
( ! [X0: a] :
( ( ~ ( ( sK16 @ X0 @ sK14 )
& ( sK16 @ sK13 @ X0 ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f692]) ).
thf(f692,plain,
( ! [X0: a] :
( ( ( ( sK16 @ X0 @ sK14 )
& ( sK16 @ sK13 @ X0 ) )
=> $false )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f680,f610]) ).
thf(f610,plain,
( ( ( sK16 @ sK13 @ sK14 )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f609]) ).
thf(f711,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK17 @ sK14 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f710]) ).
thf(f710,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK14 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f634]) ).
thf(f634,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK14 ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f626]) ).
thf(f626,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK17 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f625]) ).
thf(f625,plain,
( ( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK17 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK17 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f624]) ).
thf(f624,plain,
( ( ( ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK13 @ Y0 ) ) ) )
@ sK17 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f607]) ).
thf(f607,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK13 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f606]) ).
thf(f606,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK14 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK5 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK13 @ Y0 ) ) ) )
=> $false ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f599,f605]) ).
thf(f785,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f784]) ).
thf(f784,plain,
( $false
| ~ spl0_1
| ~ spl0_12
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f783]) ).
thf(f783,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_14 ),
inference(boolean_simplification,[],[f782]) ).
thf(f782,plain,
( ( ~ $true = $true )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_14 ),
inference(boolean_simplification,[],[f779]) ).
thf(f779,plain,
( ( ( ~ ( $true
| ( sK2 @ sK22 @ sK21 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_14 ),
inference(backward_demodulation,[],[f765,f777]) ).
thf(f777,plain,
( ( ( sK5 @ sK22 @ sK21 )
= $true )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f776]) ).
thf(f776,plain,
( spl0_14
<=> ( ( sK5 @ sK22 @ sK21 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f765,plain,
( ( ( ~ ( ( sK5 @ sK22 @ sK21 )
| ( sK2 @ sK22 @ sK21 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[],[f762]) ).
thf(f762,plain,
( ( ( ( ( sK5 @ sK22 @ sK21 )
| ( sK2 @ sK22 @ sK21 ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f642,f753]) ).
thf(f753,plain,
( ( ( sK16 @ sK22 @ sK21 )
= $false )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f752]) ).
thf(f752,plain,
( ( ( ( ( sK2 @ sK22 @ sK21 )
| ( sK5 @ sK22 @ sK21 ) )
=> ( sK16 @ sK22 @ sK21 ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f751]) ).
thf(f751,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK21 )
| ( sK5 @ Y0 @ sK21 ) )
=> ( sK16 @ Y0 @ sK21 ) )
@ sK22 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f747]) ).
thf(f747,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK21 )
| ( sK5 @ Y0 @ sK21 ) )
=> ( sK16 @ Y0 @ sK21 ) ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f745]) ).
thf(f745,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK16 @ Y1 @ Y0 ) ) )
@ sK21 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f739]) ).
thf(f778,plain,
( spl0_13
| spl0_14
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f771,f738,f776,f773]) ).
thf(f771,plain,
( ( ( sK5 @ sK22 @ sK21 )
= $true )
| ( ( sK2 @ sK22 @ sK21 )
= $true )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f754]) ).
thf(f754,plain,
( ( ( ( sK2 @ sK22 @ sK21 )
| ( sK5 @ sK22 @ sK21 ) )
= $true )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f752]) ).
thf(f740,plain,
( spl0_11
| spl0_12
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f733,f24,f738,f735]) ).
thf(f733,plain,
( ( ( sK16 @ sK13 @ sK17 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK16 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f663]) ).
thf(f663,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK16 @ Y1 @ Y0 ) ) ) )
=> ( sK16 @ sK13 @ sK17 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f661]) ).
thf(f661,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( sK16 @ Y1 @ Y0 ) ) ) ) )
=> ( sK16 @ sK13 @ sK17 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f640,f632]) ).
thf(f640,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK5 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK13 @ sK17 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f639]) ).
thf(f639,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK17 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f636]) ).
thf(f636,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK17 ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f635]) ).
thf(f635,plain,
( ( ( $true
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK5 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 @ sK17 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f626,f634]) ).
thf(f593,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f592]) ).
thf(f592,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f591]) ).
thf(f591,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f590]) ).
thf(f590,plain,
( ( ~ $true = $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f584,f527]) ).
thf(f527,plain,
( ( ( sK9 @ sK20 @ sK18 )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f520]) ).
thf(f520,plain,
( ( ( ( sK9 @ sK18 @ sK19 )
& ( sK9 @ sK20 @ sK18 ) )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f505]) ).
thf(f505,plain,
( ( ( ( ( sK9 @ sK18 @ sK19 )
& ( sK9 @ sK20 @ sK18 ) )
=> ( sK9 @ sK20 @ sK19 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f504]) ).
thf(f504,plain,
( ( ( ^ [Y0: a] :
( ( ( sK9 @ sK18 @ sK19 )
& ( sK9 @ Y0 @ sK18 ) )
=> ( sK9 @ Y0 @ sK19 ) )
@ sK20 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f501]) ).
thf(f501,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ sK18 @ sK19 )
& ( sK9 @ Y0 @ sK18 ) )
=> ( sK9 @ Y0 @ sK19 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f500]) ).
thf(f500,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ sK18 @ Y0 )
& ( sK9 @ Y1 @ sK18 ) )
=> ( sK9 @ Y1 @ Y0 ) ) )
@ sK19 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f494]) ).
thf(f494,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ sK18 @ Y0 )
& ( sK9 @ Y1 @ sK18 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f490]) ).
thf(f490,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y2 @ Y1 ) ) ) )
@ sK18 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f355]) ).
thf(f355,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f354]) ).
thf(f354,plain,
( spl0_7
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y2 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f584,plain,
( ( ( ~ ( sK9 @ sK20 @ sK18 ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f581]) ).
thf(f581,plain,
( ( ( ( sK9 @ sK20 @ sK18 )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f547,f522]) ).
thf(f522,plain,
( ( ( sK9 @ sK20 @ sK19 )
= $false )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f521]) ).
thf(f521,plain,
( ( ( $true
=> ( sK9 @ sK20 @ sK19 ) )
= $false )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f505,f520]) ).
thf(f547,plain,
( ! [X0: a] :
( ( ( sK9 @ X0 @ sK18 )
=> ( sK9 @ X0 @ sK19 ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f539]) ).
thf(f539,plain,
( ! [X0: a] :
( ( ( ( sK9 @ X0 @ sK18 )
& $true )
=> ( sK9 @ X0 @ sK19 ) )
= $true )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f532,f530]) ).
thf(f530,plain,
( ( ( sK9 @ sK18 @ sK19 )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f529]) ).
thf(f529,plain,
( ( ( ( sK9 @ sK18 @ sK19 )
& $true )
= $true )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f520,f527]) ).
thf(f532,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK9 @ X3 @ X2 )
& ( sK9 @ X2 @ X1 ) )
=> ( sK9 @ X3 @ X1 ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f531]) ).
thf(f531,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK9 @ Y0 @ X2 )
& ( sK9 @ X2 @ X1 ) )
=> ( sK9 @ Y0 @ X1 ) )
@ X3 )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f526]) ).
thf(f526,plain,
( ! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK9 @ Y0 @ X2 )
& ( sK9 @ X2 @ X1 ) )
=> ( sK9 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f525]) ).
thf(f525,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ X1 ) )
=> ( sK9 @ Y1 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f524]) ).
thf(f524,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK9 @ Y1 @ Y0 )
& ( sK9 @ Y0 @ X1 ) )
=> ( sK9 @ Y1 @ X1 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f523]) ).
thf(f523,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(pi_clausification,[],[f518]) ).
thf(f518,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f517]) ).
thf(f517,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f507,f516]) ).
thf(f516,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f507]) ).
thf(f507,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f503]) ).
thf(f503,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK9 @ sK7 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f502]) ).
thf(f502,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ sK9 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f499]) ).
thf(f499,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f498]) ).
thf(f498,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f497]) ).
thf(f497,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f496,f106]) ).
thf(f496,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f495]) ).
thf(f495,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f489]) ).
thf(f489,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f488]) ).
thf(f488,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f37]) ).
thf(f359,plain,
( spl0_7
| spl0_8
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f350,f105,f36,f357,f354]) ).
thf(f350,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f253]) ).
thf(f253,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(not_proxy_clausification,[],[f252]) ).
thf(f252,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f251]) ).
thf(f251,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y0 @ Y1 )
& ( sK9 @ Y2 @ Y0 ) )
=> ( sK9 @ Y2 @ Y1 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f236,f245]) ).
thf(f245,plain,
( ( ( sK9 @ sK7 @ sK8 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f244]) ).
thf(f244,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK5 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK9 @ Y2 @ Y1 )
& ( sK9 @ Y1 @ Y0 ) )
=> ( sK9 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK9 @ sK7 @ sK8 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f243]) ).
thf(f243,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ sK9 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(sigma_clausification,[],[f241]) ).
thf(f241,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f240]) ).
thf(f240,plain,
( ( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[],[f239]) ).
thf(f239,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| $true )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f238,f106]) ).
thf(f238,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f237]) ).
thf(f237,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f234]) ).
thf(f234,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f233]) ).
thf(f233,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f37]) ).
thf(f236,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK7 @ sK8 ) )
= $true )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f235]) ).
thf(f235,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ X1 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[],[f106]) ).
thf(f230,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f229]) ).
thf(f229,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f228]) ).
thf(f228,plain,
( ( $false = $true )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f222,f178]) ).
thf(f178,plain,
( ( ( sK6 @ sK12 @ sK10 )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f177]) ).
thf(f177,plain,
( ( ( ( ( sK6 @ sK12 @ sK11 )
& ( sK6 @ sK11 @ sK10 ) )
=> ( sK6 @ sK12 @ sK10 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f176]) ).
thf(f176,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK11 )
& ( sK6 @ sK11 @ sK10 ) )
=> ( sK6 @ Y0 @ sK10 ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f175]) ).
thf(f175,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK11 )
& ( sK6 @ sK11 @ sK10 ) )
=> ( sK6 @ Y0 @ sK10 ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f174]) ).
thf(f174,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ sK10 ) )
=> ( sK6 @ Y1 @ sK10 ) ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f171]) ).
thf(f171,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ sK10 ) )
=> ( sK6 @ Y1 @ sK10 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f169]) ).
thf(f169,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f159]) ).
thf(f159,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f136,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f135]) ).
thf(f135,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f132,f47]) ).
thf(f47,plain,
( ( sK6 @ sK4 @ sK3 )
= $false ),
inference(boolean_simplification,[],[f46]) ).
thf(f46,plain,
( ( $true
=> ( sK6 @ sK4 @ sK3 ) )
= $false ),
inference(backward_demodulation,[],[f33,f45]) ).
thf(f45,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f33,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK4 @ sK3 ) )
= $false ),
inference(beta_eta_normalization,[],[f32]) ).
thf(f32,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f18]) ).
thf(f18,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ 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 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ 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 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ 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 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ sK3 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ 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 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ 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 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK3 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ 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 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ 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 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y7 @ Y8 )
| ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( sK2 @ Y8 @ Y7 )
| ( Y2 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ 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 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ 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 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ 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 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ 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 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
| ( Y3 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y0 @ Y9 @ Y8 )
| ( Y3 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y3 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a,X2: a,X3: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X3 @ X6 @ X5 )
| ( X0 @ X6 @ X5 ) )
=> ( X4 @ X6 @ X5 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
| ( ! [X10: a,X11: a,X12: a] :
( ( ! [X13: a > a > $o] :
( ( ! [X14: a,X15: a] :
( ( ( X0 @ X14 @ X15 )
| ( X3 @ X14 @ X15 ) )
=> ( X13 @ X14 @ X15 ) )
& ! [X16: a,X17: a,X18: a] :
( ( ( X13 @ X16 @ X18 )
& ( X13 @ X18 @ X17 ) )
=> ( X13 @ X16 @ X17 ) ) )
=> ( X13 @ X12 @ X10 ) )
& ! [X19: a > a > $o] :
( ( ! [X20: a,X21: a] :
( ( ( X0 @ X21 @ X20 )
| ( X3 @ X21 @ X20 ) )
=> ( X19 @ X21 @ X20 ) )
& ! [X22: a,X23: a,X24: a] :
( ( ( X19 @ X24 @ X22 )
& ( X19 @ X22 @ X23 ) )
=> ( X19 @ X24 @ X23 ) ) )
=> ( X19 @ X10 @ X11 ) ) )
=> ! [X25: a > a > $o] :
( ( ! [X26: a,X27: a,X28: a] :
( ( ( X25 @ X26 @ X28 )
& ( X25 @ X28 @ X27 ) )
=> ( X25 @ X26 @ X27 ) )
& ! [X29: a,X30: a] :
( ( ( X3 @ X30 @ X29 )
| ( X0 @ X30 @ X29 ) )
=> ( X25 @ X30 @ X29 ) ) )
=> ( X25 @ X12 @ X11 ) ) )
& ! [X31: a,X32: a] :
( ( ! [X33: a > a > $o] :
( ( ! [X34: a,X35: a,X36: a] :
( ( ( X33 @ X34 @ X36 )
& ( X33 @ X36 @ X35 ) )
=> ( X33 @ X34 @ X35 ) )
& ! [X37: a,X38: a] :
( ( X3 @ X38 @ X37 )
=> ( X33 @ X38 @ X37 ) ) )
=> ( X33 @ X32 @ X31 ) )
| ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a,X42: a] :
( ( ( X39 @ X41 @ X42 )
& ( X39 @ X42 @ X40 ) )
=> ( X39 @ X41 @ X40 ) )
& ! [X43: a,X44: a] :
( ( X0 @ X44 @ X43 )
=> ( X39 @ X44 @ X43 ) ) )
=> ( X39 @ X32 @ X31 ) ) )
=> ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a,X48: a] :
( ( ( X45 @ X47 @ X48 )
& ( X45 @ X46 @ X47 ) )
=> ( X45 @ X46 @ X48 ) )
& ! [X49: a,X50: a] :
( ( ( X0 @ X50 @ X49 )
| ( X3 @ X50 @ X49 ) )
=> ( X45 @ X50 @ X49 ) ) )
=> ( X45 @ X32 @ X31 ) ) )
& ~ ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a,X54: a] :
( ( ( X51 @ X53 @ X54 )
& ( X51 @ X52 @ X53 ) )
=> ( X51 @ X52 @ X54 ) )
& ! [X55: a,X56: a] :
( ( ( X3 @ X56 @ X55 )
| ( X0 @ X56 @ X55 ) )
=> ( X51 @ X56 @ X55 ) ) )
=> ( X51 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > $o,X2: a,X3: a,X0: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
| ( ! [X6: a,X7: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X10: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X10: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X10: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X7 ) ) )
& ! [X6: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X7: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ~ ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: a > a > $o,X2: a,X3: a,X0: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
| ( ! [X6: a,X7: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X8: a,X10: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X10: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X10: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X7 ) ) )
& ! [X6: a,X5: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X8: a,X7: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
& ~ ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HqsKVA6tVA/Vampire---4.8_4524',cTHM250H_pme) ).
thf(f132,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) )
=> ( sK6 @ sK4 @ sK3 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f130]) ).
thf(f130,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK6 @ sK4 @ sK3 ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[],[f123,f55]) ).
thf(f55,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f54]) ).
thf(f54,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(backward_demodulation,[],[f45,f53]) ).
thf(f53,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f123,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK5 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK4 @ sK3 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f122]) ).
thf(f122,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f117]) ).
thf(f117,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
= $true )
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f40]) ).
thf(f40,plain,
( ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f39,plain,
( spl0_4
<=> ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f222,plain,
( ( ( sK6 @ sK12 @ sK10 )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f220]) ).
thf(f220,plain,
( ( ( $true
=> ( sK6 @ sK12 @ sK10 ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[],[f203,f194]) ).
thf(f194,plain,
( ( $true
= ( sK6 @ sK11 @ sK10 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f179]) ).
thf(f179,plain,
( ( ( ( sK6 @ sK12 @ sK11 )
& ( sK6 @ sK11 @ sK10 ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f177]) ).
thf(f203,plain,
( ! [X0: a] :
( ( ( sK6 @ sK11 @ X0 )
=> ( sK6 @ sK12 @ X0 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f199]) ).
thf(f199,plain,
( ! [X0: a] :
( ( ( ( sK6 @ sK11 @ X0 )
& $true )
=> ( sK6 @ sK12 @ X0 ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[],[f140,f197]) ).
thf(f197,plain,
( ( ( sK6 @ sK12 @ sK11 )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f196]) ).
thf(f196,plain,
( ( ( ( sK6 @ sK12 @ sK11 )
& $true )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f179,f194]) ).
thf(f140,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK6 @ X1 @ X3 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ X2 @ X3 ) )
= $true ),
inference(beta_eta_normalization,[],[f139]) ).
thf(f139,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f125]) ).
thf(f125,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ X2 @ X1 ) )
=> ( sK6 @ X2 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f124]) ).
thf(f124,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y1 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f121]) ).
thf(f121,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y1 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f120]) ).
thf(f120,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f53]) ).
thf(f110,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f103,f36,f108,f105]) ).
thf(f103,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f57]) ).
thf(f57,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f51]) ).
thf(f51,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK5 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK5 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f50]) ).
thf(f50,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f49]) ).
thf(f49,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK5 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK5 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f48]) ).
thf(f48,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f37]) ).
thf(f41,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f34,f27,f39,f36]) ).
thf(f27,plain,
( spl0_2
<=> ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f34,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f28]) ).
thf(f28,plain,
( ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f22,f27,f24]) ).
thf(f22,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 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ 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 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( ( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK5 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK5 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK5 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ 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 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK5 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK5 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK5 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| $false )
= $false ),
inference(backward_demodulation,[],[f17,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV156^5 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.15 % 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
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 12:05:12 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a TH0_THM_NEQ_NAR problem
% 0.15/0.37 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.HqsKVA6tVA/Vampire---4.8_4524
% 0.15/0.39 % (4810)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39 % (4810)Instruction limit reached!
% 0.15/0.39 % (4810)------------------------------
% 0.15/0.39 % (4810)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (4810)Termination reason: Unknown
% 0.15/0.39 % (4810)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (4810)Memory used [KB]: 1023
% 0.15/0.39 % (4810)Time elapsed: 0.003 s
% 0.15/0.39 % (4810)Instructions burned: 2 (million)
% 0.15/0.39 % (4810)------------------------------
% 0.15/0.39 % (4810)------------------------------
% 0.15/0.39 % (4807)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.39 % (4808)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.15/0.39 % (4809)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on Vampire---4 for (2999ds/27Mi)
% 0.15/0.39 % (4812)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.39 % (4811)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39 % (4813)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.39 % (4811)Instruction limit reached!
% 0.15/0.39 % (4811)------------------------------
% 0.15/0.39 % (4811)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (4811)Termination reason: Unknown
% 0.15/0.39 % (4811)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (4811)Memory used [KB]: 1023
% 0.15/0.39 % (4811)Time elapsed: 0.004 s
% 0.15/0.39 % (4811)Instructions burned: 3 (million)
% 0.15/0.39 % (4811)------------------------------
% 0.15/0.39 % (4811)------------------------------
% 0.15/0.39 % (4808)Instruction limit reached!
% 0.15/0.39 % (4808)------------------------------
% 0.15/0.39 % (4808)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (4808)Termination reason: Unknown
% 0.15/0.39 % (4808)Termination phase: Preprocessing 3
% 0.15/0.39
% 0.15/0.39 % (4808)Memory used [KB]: 1023
% 0.15/0.39 % (4808)Time elapsed: 0.005 s
% 0.15/0.39 % (4808)Instructions burned: 5 (million)
% 0.15/0.39 % (4808)------------------------------
% 0.15/0.39 % (4808)------------------------------
% 0.15/0.39 % (4814)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.39 % (4814)Instruction limit reached!
% 0.15/0.39 % (4814)------------------------------
% 0.15/0.39 % (4814)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (4814)Termination reason: Unknown
% 0.15/0.39 % (4814)Termination phase: Property scanning
% 0.15/0.39
% 0.15/0.39 % (4814)Memory used [KB]: 1023
% 0.15/0.39 % (4814)Time elapsed: 0.003 s
% 0.15/0.39 % (4814)Instructions burned: 3 (million)
% 0.15/0.39 % (4814)------------------------------
% 0.15/0.39 % (4814)------------------------------
% 0.15/0.40 % (4813)Instruction limit reached!
% 0.15/0.40 % (4813)------------------------------
% 0.15/0.40 % (4813)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (4813)Termination reason: Unknown
% 0.15/0.40 % (4813)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (4813)Memory used [KB]: 5756
% 0.15/0.40 % (4813)Time elapsed: 0.013 s
% 0.15/0.40 % (4813)Instructions burned: 19 (million)
% 0.15/0.40 % (4813)------------------------------
% 0.15/0.40 % (4813)------------------------------
% 0.15/0.40 % (4818)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (2999ds/37Mi)
% 0.15/0.40 % (4809)Instruction limit reached!
% 0.15/0.40 % (4809)------------------------------
% 0.15/0.40 % (4809)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (4809)Termination reason: Unknown
% 0.15/0.40 % (4809)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (4809)Memory used [KB]: 5756
% 0.15/0.40 % (4809)Time elapsed: 0.017 s
% 0.15/0.40 % (4809)Instructions burned: 27 (million)
% 0.15/0.40 % (4809)------------------------------
% 0.15/0.40 % (4809)------------------------------
% 0.15/0.40 % (4820)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.15/0.41 % (4822)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.41 % (4823)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.15/0.41 % (4822)Instruction limit reached!
% 0.15/0.41 % (4822)------------------------------
% 0.15/0.41 % (4822)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (4822)Termination reason: Unknown
% 0.15/0.41 % (4822)Termination phase: Naming
% 0.15/0.41
% 0.15/0.41 % (4822)Memory used [KB]: 1023
% 0.15/0.41 % (4822)Time elapsed: 0.004 s
% 0.15/0.41 % (4822)Instructions burned: 4 (million)
% 0.15/0.41 % (4822)------------------------------
% 0.15/0.41 % (4822)------------------------------
% 0.22/0.41 % (4820)Instruction limit reached!
% 0.22/0.41 % (4820)------------------------------
% 0.22/0.41 % (4820)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (4820)Termination reason: Unknown
% 0.22/0.41 % (4820)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (4820)Memory used [KB]: 5756
% 0.22/0.41 % (4820)Time elapsed: 0.011 s
% 0.22/0.41 % (4820)Instructions burned: 15 (million)
% 0.22/0.41 % (4820)------------------------------
% 0.22/0.41 % (4820)------------------------------
% 0.22/0.41 % (4828)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.42 % (4818)Instruction limit reached!
% 0.22/0.42 % (4818)------------------------------
% 0.22/0.42 % (4818)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (4818)Termination reason: Unknown
% 0.22/0.42 % (4818)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (4818)Memory used [KB]: 5628
% 0.22/0.42 % (4818)Time elapsed: 0.018 s
% 0.22/0.42 % (4818)Instructions burned: 37 (million)
% 0.22/0.42 % (4818)------------------------------
% 0.22/0.42 % (4818)------------------------------
% 0.22/0.42 % (4831)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.22/0.42 % (4828)Instruction limit reached!
% 0.22/0.42 % (4828)------------------------------
% 0.22/0.42 % (4828)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (4828)Termination reason: Unknown
% 0.22/0.42 % (4828)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (4828)Memory used [KB]: 1151
% 0.22/0.42 % (4828)Time elapsed: 0.006 s
% 0.22/0.42 % (4828)Instructions burned: 7 (million)
% 0.22/0.42 % (4828)------------------------------
% 0.22/0.42 % (4828)------------------------------
% 0.22/0.42 % (4833)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.42 % (4833)Instruction limit reached!
% 0.22/0.42 % (4833)------------------------------
% 0.22/0.42 % (4833)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (4833)Termination reason: Unknown
% 0.22/0.42 % (4833)Termination phase: Preprocessing 2
% 0.22/0.42
% 0.22/0.42 % (4833)Memory used [KB]: 1023
% 0.22/0.42 % (4833)Time elapsed: 0.004 s
% 0.22/0.42 % (4833)Instructions burned: 3 (million)
% 0.22/0.42 % (4833)------------------------------
% 0.22/0.42 % (4833)------------------------------
% 0.22/0.43 % (4831)Instruction limit reached!
% 0.22/0.43 % (4831)------------------------------
% 0.22/0.43 % (4831)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (4831)Termination reason: Unknown
% 0.22/0.43 % (4831)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (4831)Memory used [KB]: 1151
% 0.22/0.43 % (4831)Time elapsed: 0.010 s
% 0.22/0.43 % (4831)Instructions burned: 16 (million)
% 0.22/0.43 % (4831)------------------------------
% 0.22/0.43 % (4831)------------------------------
% 0.22/0.43 % (4837)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.43 % (4837)Instruction limit reached!
% 0.22/0.43 % (4837)------------------------------
% 0.22/0.43 % (4837)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (4837)Termination reason: Unknown
% 0.22/0.43 % (4837)Termination phase: Naming
% 0.22/0.43
% 0.22/0.43 % (4837)Memory used [KB]: 1023
% 0.22/0.43 % (4837)Time elapsed: 0.004 s
% 0.22/0.43 % (4837)Instructions burned: 4 (million)
% 0.22/0.43 % (4837)------------------------------
% 0.22/0.43 % (4837)------------------------------
% 0.22/0.43 % (4839)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.43 % (4840)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.43 % (4840)Instruction limit reached!
% 0.22/0.43 % (4840)------------------------------
% 0.22/0.43 % (4840)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (4840)Termination reason: Unknown
% 0.22/0.43 % (4840)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (4840)Memory used [KB]: 1023
% 0.22/0.43 % (4840)Time elapsed: 0.004 s
% 0.22/0.43 % (4840)Instructions burned: 4 (million)
% 0.22/0.43 % (4840)------------------------------
% 0.22/0.43 % (4840)------------------------------
% 0.22/0.44 % (4839)Instruction limit reached!
% 0.22/0.44 % (4839)------------------------------
% 0.22/0.44 % (4839)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (4839)Termination reason: Unknown
% 0.22/0.44 % (4839)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (4839)Memory used [KB]: 1151
% 0.22/0.44 % (4839)Time elapsed: 0.006 s
% 0.22/0.44 % (4839)Instructions burned: 8 (million)
% 0.22/0.44 % (4839)------------------------------
% 0.22/0.44 % (4839)------------------------------
% 0.22/0.44 % (4842)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.22/0.44 % (4843)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.22/0.44 % (4842)Instruction limit reached!
% 0.22/0.44 % (4842)------------------------------
% 0.22/0.44 % (4842)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (4842)Termination reason: Unknown
% 0.22/0.44 % (4842)Termination phase: Naming
% 0.22/0.44
% 0.22/0.44 % (4842)Memory used [KB]: 1023
% 0.22/0.44 % (4842)Time elapsed: 0.004 s
% 0.22/0.44 % (4842)Instructions burned: 4 (million)
% 0.22/0.44 % (4842)------------------------------
% 0.22/0.44 % (4842)------------------------------
% 0.22/0.44 % (4845)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.22/0.45 % (4849)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on Vampire---4 for (2999ds/902Mi)
% 0.22/0.45 % (4848)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.45 % (4843)Instruction limit reached!
% 0.22/0.45 % (4843)------------------------------
% 0.22/0.45 % (4843)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (4843)Termination reason: Unknown
% 0.22/0.45 % (4843)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (4843)Memory used [KB]: 5628
% 0.22/0.45 % (4843)Time elapsed: 0.012 s
% 0.22/0.45 % (4843)Instructions burned: 18 (million)
% 0.22/0.45 % (4843)------------------------------
% 0.22/0.45 % (4843)------------------------------
% 0.22/0.45 % (4848)Instruction limit reached!
% 0.22/0.45 % (4848)------------------------------
% 0.22/0.45 % (4848)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (4848)Termination reason: Unknown
% 0.22/0.45 % (4848)Termination phase: Property scanning
% 0.22/0.45
% 0.22/0.45 % (4848)Memory used [KB]: 1151
% 0.22/0.45 % (4848)Time elapsed: 0.006 s
% 0.22/0.45 % (4848)Instructions burned: 7 (million)
% 0.22/0.45 % (4848)------------------------------
% 0.22/0.45 % (4848)------------------------------
% 0.22/0.46 % (4854)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (2999ds/21Mi)
% 0.22/0.46 % (4865)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.22/0.47 % (4854)Instruction limit reached!
% 0.22/0.47 % (4854)------------------------------
% 0.22/0.47 % (4854)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (4854)Termination reason: Unknown
% 0.22/0.47 % (4854)Termination phase: Saturation
% 0.22/0.47
% 0.22/0.47 % (4854)Memory used [KB]: 5756
% 0.22/0.47 % (4854)Time elapsed: 0.014 s
% 0.22/0.47 % (4854)Instructions burned: 21 (million)
% 0.22/0.47 % (4854)------------------------------
% 0.22/0.47 % (4854)------------------------------
% 0.22/0.47 % (4865)Instruction limit reached!
% 0.22/0.47 % (4865)------------------------------
% 0.22/0.47 % (4865)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (4865)Termination reason: Unknown
% 0.22/0.47 % (4865)Termination phase: Property scanning
% 0.22/0.47
% 0.22/0.47 % (4865)Memory used [KB]: 1023
% 0.22/0.47 % (4865)Time elapsed: 0.005 s
% 0.22/0.47 % (4865)Instructions burned: 6 (million)
% 0.22/0.47 % (4865)------------------------------
% 0.22/0.47 % (4865)------------------------------
% 0.22/0.47 % (4867)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.47 % (4867)Instruction limit reached!
% 0.22/0.47 % (4867)------------------------------
% 0.22/0.47 % (4867)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (4867)Termination reason: Unknown
% 0.22/0.47 % (4867)Termination phase: SInE selection
% 0.22/0.47
% 0.22/0.47 % (4867)Memory used [KB]: 1023
% 0.22/0.47 % (4867)Time elapsed: 0.005 s
% 0.22/0.47 % (4867)Instructions burned: 6 (million)
% 0.22/0.47 % (4867)------------------------------
% 0.22/0.47 % (4867)------------------------------
% 0.22/0.48 % (4875)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.22/0.48 % (4876)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on Vampire---4 for (2999ds/779Mi)
% 0.22/0.48 % (4879)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (2999ds/19Mi)
% 0.22/0.49 % (4807)Instruction limit reached!
% 0.22/0.49 % (4807)------------------------------
% 0.22/0.49 % (4807)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (4807)Termination reason: Unknown
% 0.22/0.49 % (4807)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (4807)Memory used [KB]: 6140
% 0.22/0.49 % (4807)Time elapsed: 0.104 s
% 0.22/0.49 % (4807)Instructions burned: 183 (million)
% 0.22/0.49 % (4807)------------------------------
% 0.22/0.49 % (4807)------------------------------
% 0.22/0.49 % (4879)Instruction limit reached!
% 0.22/0.49 % (4879)------------------------------
% 0.22/0.49 % (4879)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (4879)Termination reason: Unknown
% 0.22/0.49 % (4879)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (4879)Memory used [KB]: 5500
% 0.22/0.49 % (4879)Time elapsed: 0.009 s
% 0.22/0.49 % (4879)Instructions burned: 20 (million)
% 0.22/0.49 % (4879)------------------------------
% 0.22/0.49 % (4879)------------------------------
% 0.22/0.50 % (4894)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2998ds/879Mi)
% 0.22/0.50 % (4896)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.22/0.51 % (4896)Instruction limit reached!
% 0.22/0.51 % (4896)------------------------------
% 0.22/0.51 % (4896)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (4896)Termination reason: Unknown
% 0.22/0.51 % (4896)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (4896)Memory used [KB]: 5756
% 0.22/0.51 % (4896)Time elapsed: 0.009 s
% 0.22/0.51 % (4896)Instructions burned: 19 (million)
% 0.22/0.51 % (4896)------------------------------
% 0.22/0.51 % (4896)------------------------------
% 0.22/0.52 % (4912)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.22/0.52 % (4812)Instruction limit reached!
% 0.22/0.52 % (4812)------------------------------
% 0.22/0.52 % (4812)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (4812)Termination reason: Unknown
% 0.22/0.52 % (4812)Termination phase: Saturation
% 0.22/0.52
% 0.22/0.52 % (4812)Memory used [KB]: 6396
% 0.22/0.52 % (4812)Time elapsed: 0.133 s
% 0.22/0.52 % (4812)Instructions burned: 276 (million)
% 0.22/0.52 % (4812)------------------------------
% 0.22/0.52 % (4812)------------------------------
% 0.22/0.52 % (4912)Instruction limit reached!
% 0.22/0.52 % (4912)------------------------------
% 0.22/0.52 % (4912)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (4912)Termination reason: Unknown
% 0.22/0.52 % (4912)Termination phase: Property scanning
% 0.22/0.52
% 0.22/0.52 % (4912)Memory used [KB]: 1023
% 0.22/0.52 % (4912)Time elapsed: 0.002 s
% 0.22/0.52 % (4912)Instructions burned: 3 (million)
% 0.22/0.52 % (4912)------------------------------
% 0.22/0.52 % (4912)------------------------------
% 0.22/0.53 % (4918)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2998ds/30Mi)
% 0.22/0.53 % (4919)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2998ds/127Mi)
% 0.22/0.54 % (4918)Instruction limit reached!
% 0.22/0.54 % (4918)------------------------------
% 0.22/0.54 % (4918)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.54 % (4918)Termination reason: Unknown
% 0.22/0.54 % (4918)Termination phase: Saturation
% 0.22/0.54
% 0.22/0.54 % (4918)Memory used [KB]: 5756
% 0.22/0.54 % (4918)Time elapsed: 0.011 s
% 0.22/0.54 % (4918)Instructions burned: 30 (million)
% 0.22/0.54 % (4918)------------------------------
% 0.22/0.54 % (4918)------------------------------
% 0.22/0.55 % (4926)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on Vampire---4 for (2998ds/100Mi)
% 0.22/0.57 % (4919)Instruction limit reached!
% 0.22/0.57 % (4919)------------------------------
% 0.22/0.57 % (4919)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.57 % (4919)Termination reason: Unknown
% 0.22/0.57 % (4919)Termination phase: Saturation
% 0.22/0.57
% 0.22/0.57 % (4919)Memory used [KB]: 6268
% 0.22/0.57 % (4919)Time elapsed: 0.042 s
% 0.22/0.57 % (4919)Instructions burned: 127 (million)
% 0.22/0.57 % (4919)------------------------------
% 0.22/0.57 % (4919)------------------------------
% 1.67/0.58 % (4944)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 1.67/0.58 % (4944)Instruction limit reached!
% 1.67/0.58 % (4944)------------------------------
% 1.67/0.58 % (4944)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.67/0.58 % (4944)Termination reason: Unknown
% 1.67/0.58 % (4944)Termination phase: shuffling
% 1.67/0.58
% 1.67/0.58 % (4944)Memory used [KB]: 1023
% 1.67/0.58 % (4944)Time elapsed: 0.002 s
% 1.67/0.58 % (4944)Instructions burned: 3 (million)
% 1.67/0.58 % (4944)------------------------------
% 1.67/0.58 % (4944)------------------------------
% 1.67/0.58 % (4926)Instruction limit reached!
% 1.67/0.58 % (4926)------------------------------
% 1.67/0.58 % (4926)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.67/0.58 % (4926)Termination reason: Unknown
% 1.67/0.58 % (4926)Termination phase: Saturation
% 1.67/0.58
% 1.67/0.58 % (4926)Memory used [KB]: 6012
% 1.67/0.58 % (4926)Time elapsed: 0.036 s
% 1.67/0.58 % (4926)Instructions burned: 101 (million)
% 1.67/0.58 % (4926)------------------------------
% 1.67/0.58 % (4926)------------------------------
% 1.67/0.58 % (4823)First to succeed.
% 1.67/0.59 % (4948)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on Vampire---4 for (2997ds/20Mi)
% 1.67/0.59 % (4949)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on Vampire---4 for (2997ds/86Mi)
% 1.87/0.60 % (4948)Instruction limit reached!
% 1.87/0.60 % (4948)------------------------------
% 1.87/0.60 % (4948)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.87/0.60 % (4948)Termination reason: Unknown
% 1.87/0.60 % (4948)Termination phase: Saturation
% 1.87/0.60
% 1.87/0.60 % (4948)Memory used [KB]: 5756
% 1.87/0.60 % (4948)Time elapsed: 0.008 s
% 1.87/0.60 % (4948)Instructions burned: 22 (million)
% 1.87/0.60 % (4948)------------------------------
% 1.87/0.60 % (4948)------------------------------
% 1.87/0.60 % (4823)Refutation found. Thanks to Tanya!
% 1.87/0.60 % SZS status Theorem for Vampire---4
% 1.87/0.60 % SZS output start Proof for Vampire---4
% See solution above
% 1.87/0.60 % (4823)------------------------------
% 1.87/0.60 % (4823)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.87/0.60 % (4823)Termination reason: Refutation
% 1.87/0.60
% 1.87/0.60 % (4823)Memory used [KB]: 7036
% 1.87/0.60 % (4823)Time elapsed: 0.215 s
% 1.87/0.60 % (4823)Instructions burned: 392 (million)
% 1.87/0.60 % (4823)------------------------------
% 1.87/0.60 % (4823)------------------------------
% 1.87/0.60 % (4805)Success in time 0.222 s
% 1.87/0.60 % Vampire---4.8 exiting
%------------------------------------------------------------------------------