TSTP Solution File: SEV125^5 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV125^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n028.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 : Mon Jun 24 16:01:54 EDT 2024
% Result : Theorem 2.89s 0.82s
% Output : Refutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 25
% Syntax : Number of formulae : 448 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 6356 (1458 equ; 0 cnn)
% Maximal formula atoms : 14 ( 14 avg)
% Number of connectives : 10275 ( 954 ~;1961 |; 447 &;5681 @)
% ( 23 <=>; 429 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 2170 (2170 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 53 usr; 29 con; 0-5 aty)
% ( 569 !!; 211 ??; 0 @@+; 0 @@-)
% Number of variables : 1701 (1085 ^ 603 !; 13 ?;1701 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_14,type,
sK0: ( a > a > $o ) > $o ).
thf(func_def_15,type,
sK1: ( a > a > $o ) > $o ).
thf(func_def_18,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK4: a ).
thf(func_def_20,type,
sK5: a ).
thf(func_def_21,type,
sK6: a > a > $o ).
thf(func_def_22,type,
sK7: a > a > $o ).
thf(func_def_23,type,
sK8: ( a > a > $o ) > a ).
thf(func_def_24,type,
sK9: ( a > a > $o ) > a ).
thf(func_def_25,type,
sK10: ( a > a > $o ) > a > a > $o ).
thf(func_def_26,type,
sK11: ( a > a > $o ) > a ).
thf(func_def_27,type,
sK12: ( a > a > $o ) > a ).
thf(func_def_28,type,
sK13: ( a > a > $o ) > a > a > $o ).
thf(func_def_29,type,
sK14: ( a > a > $o ) > a > a > $o ).
thf(func_def_30,type,
sK15: ( a > a > $o ) > a ).
thf(func_def_31,type,
sK16: ( a > a > $o ) > a ).
thf(func_def_32,type,
sK17: ( a > a > $o ) > a > a > $o ).
thf(func_def_33,type,
sK18: ( a > a > $o ) > a ).
thf(func_def_34,type,
sK19: ( a > a > $o ) > a ).
thf(func_def_35,type,
sK20: ( a > a > $o ) > a > a > $o ).
thf(func_def_36,type,
sK21: ( a > a > $o ) > a ).
thf(func_def_37,type,
sK22: ( a > a > $o ) > a ).
thf(func_def_38,type,
sK23: ( a > a > $o ) > a > a > $o ).
thf(func_def_39,type,
sK24: a > ( a > a > $o ) > a > a > a > $o ).
thf(func_def_40,type,
sK25: a > ( a > a > $o ) > a > a > a > $o ).
thf(func_def_41,type,
sK26: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_42,type,
sK27: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_43,type,
sK28: a > ( a > a > $o ) > a > a > a > $o ).
thf(func_def_44,type,
sK29: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_45,type,
sK30: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(f2691,plain,
$false,
inference(avatar_sat_refutation,[],[f164,f168,f172,f179,f183,f187,f194,f198,f202,f209,f213,f217,f226,f230,f235,f240,f244,f245,f246,f247,f248,f395,f544,f608,f797,f886,f1012,f1042,f2606,f2629,f2663,f2690]) ).
thf(f2690,plain,
( ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(avatar_contradiction_clause,[],[f2689]) ).
thf(f2689,plain,
( $false
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2688]) ).
thf(f2688,plain,
( ( $true = $false )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(forward_demodulation,[],[f2687,f221]) ).
thf(f221,plain,
( ( ( sK6 @ sK4 @ sK5 )
= $false )
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f219,plain,
( spl2_17
<=> ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
thf(f2687,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(subsumption_resolution,[],[f2681,f400]) ).
thf(f400,plain,
( ( ( sK1 @ sK6 )
!= $false )
| spl2_30 ),
inference(avatar_component_clause,[],[f399]) ).
thf(f399,plain,
( spl2_30
<=> ( ( sK1 @ sK6 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
thf(f2681,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2679]) ).
thf(f2679,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(superposition,[],[f2677,f182]) ).
thf(f182,plain,
( ! [X2: a > a > $o] :
( ( $true
= ( sK0 @ ( sK20 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) )
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f181,plain,
( spl2_7
<=> ! [X2: a > a > $o] :
( ( $true
= ( sK0 @ ( sK20 @ X2 ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
thf(f2677,plain,
( ( ( sK0 @ ( sK20 @ sK6 ) )
= $false )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2676]) ).
thf(f2676,plain,
( ( ( sK0 @ ( sK20 @ sK6 ) )
= $false )
| ( $true = $false )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(forward_demodulation,[],[f2675,f221]) ).
thf(f2675,plain,
( ( ( sK0 @ ( sK20 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(subsumption_resolution,[],[f2673,f400]) ).
thf(f2673,plain,
( ( ( sK0 @ ( sK20 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f2668]) ).
thf(f2668,plain,
( ( ( sK0 @ ( sK20 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(superposition,[],[f186,f1059]) ).
thf(f1059,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK19 @ sK6 ) @ ( sK18 @ sK6 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_5
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f1058]) ).
thf(f1058,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK19 @ sK6 ) @ ( sK18 @ sK6 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl2_5
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f1057,f221]) ).
thf(f1057,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK19 @ sK6 ) @ ( sK18 @ sK6 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) ) )
| ~ spl2_5
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f1056]) ).
thf(f1056,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( $true = $false )
| ( ( X0 @ ( sK19 @ sK6 ) @ ( sK18 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) ) )
| ~ spl2_5
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f710,f234]) ).
thf(f234,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f232,plain,
( spl2_20
<=> ( $true
= ( sK1 @ sK6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
thf(f710,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( X0 @ ( sK19 @ sK6 ) @ ( sK18 @ sK6 ) )
= $false ) )
| ~ spl2_5
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f689]) ).
thf(f689,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( ( X0 @ ( sK19 @ sK6 ) @ ( sK18 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_5
| ~ spl2_19 ),
inference(superposition,[],[f229,f175]) ).
thf(f175,plain,
( ! [X2: a > a > $o] :
( ( ( X2 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f174]) ).
thf(f174,plain,
( spl2_5
<=> ! [X2: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( X2 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
thf(f229,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X3 )
= $false ) )
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f228,plain,
( spl2_19
<=> ! [X2: a,X1: a,X3: a > a > $o] :
( ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X3 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
thf(f186,plain,
( ! [X2: a > a > $o] :
( ( $true
= ( sK20 @ X2 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f185,plain,
( spl2_8
<=> ! [X2: a > a > $o] :
( ( $true
= ( sK20 @ X2 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
thf(f2663,plain,
( ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(avatar_contradiction_clause,[],[f2662]) ).
thf(f2662,plain,
( $false
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2661]) ).
thf(f2661,plain,
( ( $true = $false )
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(forward_demodulation,[],[f2660,f221]) ).
thf(f2660,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(subsumption_resolution,[],[f2654,f400]) ).
thf(f2654,plain,
( ( ( sK1 @ sK6 )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2653]) ).
thf(f2653,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ( $true = $false )
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(superposition,[],[f197,f2651]) ).
thf(f2651,plain,
( ( ( sK0 @ ( sK17 @ sK6 ) )
= $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2650]) ).
thf(f2650,plain,
( ( $true = $false )
| ( ( sK0 @ ( sK17 @ sK6 ) )
= $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(forward_demodulation,[],[f2649,f221]) ).
thf(f2649,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK0 @ ( sK17 @ sK6 ) )
= $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(subsumption_resolution,[],[f2648,f400]) ).
thf(f2648,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK0 @ ( sK17 @ sK6 ) )
= $false )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f2644]) ).
thf(f2644,plain,
( ( ( sK1 @ sK6 )
= $false )
| ( $true = $false )
| ( ( sK0 @ ( sK17 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(superposition,[],[f1067,f201]) ).
thf(f201,plain,
( ! [X2: a > a > $o] :
( ( ( sK17 @ X2 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
= $true )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) )
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f200,plain,
( spl2_12
<=> ! [X2: a > a > $o] :
( ( ( sK17 @ X2 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
= $true )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
thf(f1067,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK16 @ sK6 ) @ ( sK15 @ sK6 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_10
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f1066]) ).
thf(f1066,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK16 @ sK6 ) @ ( sK15 @ sK6 ) )
= $false )
| ( $true = $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_10
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f1065,f234]) ).
thf(f1065,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK6 )
= $false )
| ( ( X0 @ ( sK16 @ sK6 ) @ ( sK15 @ sK6 ) )
= $false ) )
| ~ spl2_10
| ~ spl2_17
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f1064]) ).
thf(f1064,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK6 )
= $false )
| ( ( X0 @ ( sK16 @ sK6 ) @ ( sK15 @ sK6 ) )
= $false ) )
| ~ spl2_10
| ~ spl2_17
| ~ spl2_19 ),
inference(forward_demodulation,[],[f924,f221]) ).
thf(f924,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK16 @ sK6 ) @ ( sK15 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_10
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f903]) ).
thf(f903,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK6 )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( X0 @ ( sK16 @ sK6 ) @ ( sK15 @ sK6 ) )
= $false )
| ( $true = $false ) )
| ~ spl2_10
| ~ spl2_19 ),
inference(superposition,[],[f229,f193]) ).
thf(f193,plain,
( ! [X2: a > a > $o] :
( ( ( X2 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f192]) ).
thf(f192,plain,
( spl2_10
<=> ! [X2: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( ( X2 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
thf(f197,plain,
( ! [X2: a > a > $o] :
( ( $true
= ( sK0 @ ( sK17 @ X2 ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) )
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f196,plain,
( spl2_11
<=> ! [X2: a > a > $o] :
( ( $true
= ( sK0 @ ( sK17 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
thf(f2629,plain,
( ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(avatar_contradiction_clause,[],[f2628]) ).
thf(f2628,plain,
( $false
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2627]) ).
thf(f2627,plain,
( ( $true = $false )
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(forward_demodulation,[],[f2626,f221]) ).
thf(f2626,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(subsumption_resolution,[],[f2620,f400]) ).
thf(f2620,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2619]) ).
thf(f2619,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(superposition,[],[f212,f2617]) ).
thf(f2617,plain,
( ( ( sK0 @ ( sK13 @ sK6 ) )
= $false )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2616]) ).
thf(f2616,plain,
( ( $true = $false )
| ( ( sK0 @ ( sK13 @ sK6 ) )
= $false )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(forward_demodulation,[],[f2615,f221]) ).
thf(f2615,plain,
( ( ( sK0 @ ( sK13 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20
| spl2_30 ),
inference(subsumption_resolution,[],[f2612,f400]) ).
thf(f2612,plain,
( ( ( sK0 @ ( sK13 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f2608]) ).
thf(f2608,plain,
( ( $true = $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK0 @ ( sK13 @ sK6 ) )
= $false )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(superposition,[],[f216,f1063]) ).
thf(f1063,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK12 @ sK6 ) @ ( sK11 @ sK6 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_14
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f1062]) ).
thf(f1062,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( $true = $false )
| ( ( X0 @ ( sK12 @ sK6 ) @ ( sK11 @ sK6 ) )
= $false ) )
| ~ spl2_14
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f1061,f221]) ).
thf(f1061,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( X0 @ ( sK12 @ sK6 ) @ ( sK11 @ sK6 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_14
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f1060]) ).
thf(f1060,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( ( X0 @ ( sK12 @ sK6 ) @ ( sK11 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_14
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f816,f234]) ).
thf(f816,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ sK6 )
= $false )
| ( ( X0 @ ( sK12 @ sK6 ) @ ( sK11 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_14
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f806]) ).
thf(f806,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( ( X0 @ ( sK12 @ sK6 ) @ ( sK11 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK6 )
= $false ) )
| ~ spl2_14
| ~ spl2_19 ),
inference(superposition,[],[f229,f208]) ).
thf(f208,plain,
( ! [X2: a > a > $o] :
( ( ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) )
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f207]) ).
thf(f207,plain,
( spl2_14
<=> ! [X2: a > a > $o] :
( ( ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
thf(f216,plain,
( ! [X2: a > a > $o] :
( ( $true
= ( sK13 @ X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) )
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f215,plain,
( spl2_16
<=> ! [X2: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( sK13 @ X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
thf(f212,plain,
( ! [X2: a > a > $o] :
( ( $true
= ( sK0 @ ( sK13 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f211,plain,
( spl2_15
<=> ! [X2: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK13 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
thf(f2606,plain,
( ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_17
| ~ spl2_19
| spl2_30 ),
inference(avatar_contradiction_clause,[],[f2605]) ).
thf(f2605,plain,
( $false
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_17
| ~ spl2_19
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2604]) ).
thf(f2604,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_17
| ~ spl2_19
| spl2_30 ),
inference(forward_demodulation,[],[f2603,f221]) ).
thf(f2603,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_17
| ~ spl2_19
| spl2_30 ),
inference(subsumption_resolution,[],[f2597,f400]) ).
thf(f2597,plain,
( ( ( sK1 @ sK6 )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_17
| ~ spl2_19
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2595]) ).
thf(f2595,plain,
( ( $true = $false )
| ( ( sK1 @ sK6 )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_17
| ~ spl2_19
| spl2_30 ),
inference(superposition,[],[f2577,f178]) ).
thf(f178,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f177,plain,
( spl2_6
<=> ! [X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
thf(f2577,plain,
( ( ( sK0 @ ( sK14 @ sK6 ) )
= $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_17
| ~ spl2_19
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2576]) ).
thf(f2576,plain,
( ( ( sK0 @ ( sK14 @ sK6 ) )
= $false )
| ( $true = $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_17
| ~ spl2_19
| spl2_30 ),
inference(forward_demodulation,[],[f2575,f221]) ).
thf(f2575,plain,
( ( ( sK0 @ ( sK14 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_19
| spl2_30 ),
inference(subsumption_resolution,[],[f2566,f400]) ).
thf(f2566,plain,
( ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ ( sK14 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_19
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2565]) ).
thf(f2565,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ ( sK14 @ sK6 ) )
= $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_19
| spl2_30 ),
inference(duplicate_literal_removal,[],[f2554]) ).
thf(f2554,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( ( sK1 @ sK6 )
= $false )
| ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ ( sK14 @ sK6 ) )
= $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_19
| spl2_30 ),
inference(superposition,[],[f160,f2502]) ).
thf(f2502,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK6 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) ) )
| ~ spl2_9
| ~ spl2_13
| ~ spl2_19
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2501]) ).
thf(f2501,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK6 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK1 @ X0 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false ) )
| ~ spl2_9
| ~ spl2_13
| ~ spl2_19
| spl2_30 ),
inference(duplicate_literal_removal,[],[f2467]) ).
thf(f2467,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( sK6 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK1 @ X0 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl2_9
| ~ spl2_13
| ~ spl2_19
| spl2_30 ),
inference(superposition,[],[f2282,f205]) ).
thf(f205,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f204]) ).
thf(f204,plain,
( spl2_13
<=> ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
thf(f2282,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK10 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( $true
= ( sK6 @ X1 @ X2 ) )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl2_9
| ~ spl2_19
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2281]) ).
thf(f2281,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $true
= ( sK6 @ X1 @ X2 ) )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK10 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( $false != $false ) )
| ~ spl2_9
| ~ spl2_19
| spl2_30 ),
inference(duplicate_literal_removal,[],[f2266]) ).
thf(f2266,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK10 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK6 @ X1 @ X2 ) )
| ( ( sK1 @ X0 )
= $false )
| ( $false != $false )
| ( $true
= ( sK6 @ X1 @ X2 ) ) )
| ~ spl2_9
| ~ spl2_19
| spl2_30 ),
inference(equality_factoring,[],[f2210]) ).
thf(f2210,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK10 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK6 @ X3 @ X4 ) )
| ( ( sK10 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK6 @ X1 @ X2 ) )
| ( ( sK1 @ X0 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false ) )
| ~ spl2_9
| ~ spl2_19
| spl2_30 ),
inference(subsumption_resolution,[],[f2206,f400]) ).
thf(f2206,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK10 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( $true
= ( sK6 @ X1 @ X2 ) )
| ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( ( sK10 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( $true
= ( sK6 @ X3 @ X4 ) ) )
| ~ spl2_9
| ~ spl2_19
| spl2_30 ),
inference(trivial_inequality_removal,[],[f2205]) ).
thf(f2205,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK1 @ X0 )
= $false )
| ( ( sK10 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( $true
= ( sK6 @ X1 @ X2 ) )
| ( $true = $false )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( $true
= ( sK6 @ X3 @ X4 ) )
| ( ( sK10 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK1 @ sK6 )
= $false ) )
| ~ spl2_9
| ~ spl2_19
| spl2_30 ),
inference(duplicate_literal_removal,[],[f2175]) ).
thf(f2175,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( $true
= ( sK6 @ X1 @ X2 ) )
| ( $true = $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( $true
= ( sK6 @ X3 @ X4 ) )
| ( ( sK1 @ X0 )
= $false )
| ( ( sK10 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK10 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl2_9
| ~ spl2_19
| spl2_30 ),
inference(superposition,[],[f1803,f1381]) ).
thf(f1381,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( $true
= ( sK14 @ X1 @ ( sK29 @ X1 @ X4 ) @ ( sK30 @ X1 @ X4 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK1 @ X4 ) )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl2_9 ),
inference(binary_proxy_clausification,[],[f1379]) ).
thf(f1379,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( ( sK14 @ X1 @ ( sK29 @ X1 @ X4 ) @ ( sK30 @ X1 @ X4 ) )
=> ( X4 @ ( sK29 @ X1 @ X4 ) @ ( sK30 @ X1 @ X4 ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( $false
= ( sK1 @ X4 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_9 ),
inference(beta_eta_normalization,[],[f1378]) ).
thf(f1378,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( $false
= ( sK1 @ X4 ) )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false )
| ( ( ^ [Y0: a] :
( ( sK14 @ X1 @ ( sK29 @ X1 @ X4 ) @ Y0 )
=> ( X4 @ ( sK29 @ X1 @ X4 ) @ Y0 ) )
@ ( sK30 @ X1 @ X4 ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl2_9 ),
inference(sigma_clausification,[],[f1377]) ).
thf(f1377,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK14 @ X1 @ ( sK29 @ X1 @ X4 ) @ Y0 )
=> ( X4 @ ( sK29 @ X1 @ X4 ) @ Y0 ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false )
| ( $false
= ( sK1 @ X4 ) )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_9 ),
inference(beta_eta_normalization,[],[f1376]) ).
thf(f1376,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( X4 @ X2 @ X3 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK1 @ X4 ) )
| ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK14 @ X1 @ Y0 @ Y1 )
=> ( X4 @ Y0 @ Y1 ) ) )
@ ( sK29 @ X1 @ X4 ) ) )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl2_9 ),
inference(sigma_clausification,[],[f1375]) ).
thf(f1375,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( X4 @ X2 @ X3 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK14 @ X1 @ Y0 @ Y1 )
=> ( X4 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK1 @ X4 ) )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false ) )
| ~ spl2_9 ),
inference(binary_proxy_clausification,[],[f1374]) ).
thf(f1374,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK14 @ X1 @ Y0 @ Y1 )
=> ( X4 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ X4 ) )
= $false )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl2_9 ),
inference(binary_proxy_clausification,[],[f1373]) ).
thf(f1373,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK14 @ X1 @ Y0 @ Y1 )
=> ( X4 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) )
= $true ) )
| ~ spl2_9 ),
inference(beta_eta_normalization,[],[f1372]) ).
thf(f1372,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK14 @ X1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ X2 @ X3 ) )
@ X4 ) ) )
| ~ spl2_9 ),
inference(pi_clausification,[],[f1359]) ).
thf(f1359,plain,
( ! [X2: a,X3: a,X1: a > a > $o] :
( ( ( sK10 @ X1 @ X2 @ X3 )
= $false )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK14 @ X1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ X2 @ X3 ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_9 ),
inference(binary_proxy_clausification,[],[f1358]) ).
thf(f1358,plain,
( ! [X2: a,X3: a,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK14 @ X1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ X2 @ X3 ) ) )
= ( sK10 @ X1 @ X2 @ X3 ) ) )
| ~ spl2_9 ),
inference(beta_eta_normalization,[],[f1357]) ).
thf(f1357,plain,
( ! [X2: a,X3: a,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK14 @ X1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK1 @ Y1 ) )
=> ( Y1 @ X2 @ Y0 ) ) )
@ X3 )
= ( sK10 @ X1 @ X2 @ X3 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_9 ),
inference(argument_congruence,[],[f1172]) ).
thf(f1172,plain,
( ! [X2: a,X1: a > a > $o] :
( ( ( sK10 @ X1 @ X2 )
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK14 @ X1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK1 @ Y1 ) )
=> ( Y1 @ X2 @ Y0 ) ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_9 ),
inference(beta_eta_normalization,[],[f1170]) ).
thf(f1170,plain,
( ! [X2: a,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK10 @ X1 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2 ) ) )
| ~ spl2_9 ),
inference(argument_congruence,[],[f190]) ).
thf(f190,plain,
( ! [X1: a > a > $o] :
( ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f189]) ).
thf(f189,plain,
( spl2_9
<=> ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK1 @ X1 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
thf(f1803,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( X1 @ ( sK29 @ X0 @ sK6 ) @ ( sK30 @ X0 @ sK6 ) )
= $false )
| ( ( sK10 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK0 @ X1 )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK6 @ X2 @ X3 )
= $true ) )
| ~ spl2_9
| ~ spl2_19
| spl2_30 ),
inference(subsumption_resolution,[],[f1798,f400]) ).
thf(f1798,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK10 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( ( sK6 @ X2 @ X3 )
= $true )
| ( ( X1 @ ( sK29 @ X0 @ sK6 ) @ ( sK30 @ X0 @ sK6 ) )
= $false )
| ( ( sK0 @ X1 )
= $false )
| ( ( sK1 @ sK6 )
= $false ) )
| ~ spl2_9
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f1770]) ).
thf(f1770,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ sK6 )
= $false )
| ( $true = $false )
| ( ( X1 @ ( sK29 @ X0 @ sK6 ) @ ( sK30 @ X0 @ sK6 ) )
= $false )
| ( ( sK10 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK6 @ X2 @ X3 )
= $true )
| ( ( sK0 @ X1 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl2_9
| ~ spl2_19 ),
inference(superposition,[],[f229,f1380]) ).
thf(f1380,plain,
( ! [X2: a,X3: a,X1: a > a > $o,X4: a > a > $o] :
( ( ( X4 @ ( sK29 @ X1 @ X4 ) @ ( sK30 @ X1 @ X4 ) )
= $false )
| ( ( X4 @ X2 @ X3 )
= $true )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK1 @ X4 ) )
| ( ( sK10 @ X1 @ X2 @ X3 )
= $false ) )
| ~ spl2_9 ),
inference(binary_proxy_clausification,[],[f1379]) ).
thf(f160,plain,
( ! [X1: a > a > $o] :
( ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f159]) ).
thf(f159,plain,
( spl2_1
<=> ! [X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
thf(f1042,plain,
( ~ spl2_20
| ~ spl2_30 ),
inference(avatar_contradiction_clause,[],[f1041]) ).
thf(f1041,plain,
( $false
| ~ spl2_20
| ~ spl2_30 ),
inference(trivial_inequality_removal,[],[f1040]) ).
thf(f1040,plain,
( ( $true = $false )
| ~ spl2_20
| ~ spl2_30 ),
inference(forward_demodulation,[],[f234,f401]) ).
thf(f401,plain,
( ( ( sK1 @ sK6 )
= $false )
| ~ spl2_30 ),
inference(avatar_component_clause,[],[f399]) ).
thf(f1012,plain,
( ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(avatar_contradiction_clause,[],[f1011]) ).
thf(f1011,plain,
( $false
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f1010]) ).
thf(f1010,plain,
( ( $true = $false )
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f1009,f225]) ).
thf(f225,plain,
( ( ( sK7 @ sK4 @ sK5 )
= $false )
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f223,plain,
( spl2_18
<=> ( ( sK7 @ sK4 @ sK5 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
thf(f1009,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f1008]) ).
thf(f1008,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( $true = $false )
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f1001,f239]) ).
thf(f239,plain,
( ( $true
= ( sK1 @ sK7 ) )
| ~ spl2_21 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f237,plain,
( spl2_21
<=> ( $true
= ( sK1 @ sK7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
thf(f1001,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f999]) ).
thf(f999,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( $true = $false )
| ~ spl2_10
| ~ spl2_11
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(superposition,[],[f998,f197]) ).
thf(f998,plain,
( ( ( sK0 @ ( sK17 @ sK7 ) )
= $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f997]) ).
thf(f997,plain,
( ( ( sK0 @ ( sK17 @ sK7 ) )
= $false )
| ( $true = $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f996,f239]) ).
thf(f996,plain,
( ( ( sK0 @ ( sK17 @ sK7 ) )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f995]) ).
thf(f995,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ( ( sK0 @ ( sK17 @ sK7 ) )
= $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f994,f225]) ).
thf(f994,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK0 @ ( sK17 @ sK7 ) )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f992]) ).
thf(f992,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ( ( sK0 @ ( sK17 @ sK7 ) )
= $false )
| ~ spl2_10
| ~ spl2_12
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(superposition,[],[f928,f201]) ).
thf(f928,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK16 @ sK7 ) @ ( sK15 @ sK7 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_10
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f927]) ).
thf(f927,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( $true = $false )
| ( ( X0 @ ( sK16 @ sK7 ) @ ( sK15 @ sK7 ) )
= $false ) )
| ~ spl2_10
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f926,f225]) ).
thf(f926,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( X0 @ ( sK16 @ sK7 ) @ ( sK15 @ sK7 ) )
= $false ) )
| ~ spl2_10
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f925]) ).
thf(f925,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( X0 @ ( sK16 @ sK7 ) @ ( sK15 @ sK7 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_10
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f923,f239]) ).
thf(f923,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( X0 @ ( sK16 @ sK7 ) @ ( sK15 @ sK7 ) )
= $false ) )
| ~ spl2_10
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f905]) ).
thf(f905,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK16 @ sK7 ) @ ( sK15 @ sK7 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( $true = $false ) )
| ~ spl2_10
| ~ spl2_22 ),
inference(superposition,[],[f437,f193]) ).
thf(f437,plain,
( ! [X2: a,X0: a,X1: a > a > $o] :
( ( ( sK7 @ X0 @ X2 )
= $true )
| ( ( X1 @ X0 @ X2 )
= $false )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f436]) ).
thf(f436,plain,
( ! [X2: a,X0: a,X1: a > a > $o] :
( ( $true = $false )
| ( ( sK0 @ X1 )
= $false )
| ( ( sK7 @ X0 @ X2 )
= $true )
| ( ( X1 @ X0 @ X2 )
= $false ) )
| ~ spl2_22 ),
inference(duplicate_literal_removal,[],[f427]) ).
thf(f427,plain,
( ! [X2: a,X0: a,X1: a > a > $o] :
( ( ( X1 @ X0 @ X2 )
= $false )
| ( ( sK0 @ X1 )
= $false )
| ( ( sK7 @ X0 @ X2 )
= $true )
| ( ( sK7 @ X0 @ X2 )
= $true )
| ( $true = $false )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl2_22 ),
inference(superposition,[],[f412,f420]) ).
thf(f420,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
= ( sK24 @ X1 @ X0 @ X2 @ X3 @ X4 ) )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( $false
= ( X0 @ X3 @ X4 ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_22 ),
inference(binary_proxy_clausification,[],[f419]) ).
thf(f419,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK0 @ X0 )
= $false )
| ( $true
= ( ( X0 @ X3 @ X4 )
=> ( sK24 @ X1 @ X0 @ X2 @ X3 @ X4 ) ) )
| ( ( sK7 @ X1 @ X2 )
= $true ) )
| ~ spl2_22 ),
inference(beta_eta_normalization,[],[f418]) ).
thf(f418,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
= ( ^ [Y0: a] :
( ( X0 @ X3 @ Y0 )
=> ( sK24 @ X1 @ X0 @ X2 @ X3 @ Y0 ) )
@ X4 ) )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_22 ),
inference(pi_clausification,[],[f417]) ).
thf(f417,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( X0 @ X3 @ Y0 )
=> ( sK24 @ X1 @ X0 @ X2 @ X3 @ Y0 ) ) ) )
| ( ( sK7 @ X1 @ X2 )
= $true ) )
| ~ spl2_22 ),
inference(beta_eta_normalization,[],[f416]) ).
thf(f416,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X0 @ Y0 @ Y1 )
=> ( sK24 @ X1 @ X0 @ X2 @ Y0 @ Y1 ) ) )
@ X3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true ) )
| ~ spl2_22 ),
inference(pi_clausification,[],[f415]) ).
thf(f415,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK7 @ X1 @ X2 )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X0 @ Y0 @ Y1 )
=> ( sK24 @ X1 @ X0 @ X2 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_22 ),
inference(binary_proxy_clausification,[],[f413]) ).
thf(f413,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X0 @ Y0 @ Y1 )
=> ( sK24 @ X1 @ X0 @ X2 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ ( sK24 @ X1 @ X0 @ X2 ) ) ) ) )
| ~ spl2_22 ),
inference(binary_proxy_clausification,[],[f411]) ).
thf(f411,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X0 @ Y0 @ Y1 )
=> ( sK24 @ X1 @ X0 @ X2 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ ( sK24 @ X1 @ X0 @ X2 ) ) )
=> ( sK24 @ X1 @ X0 @ X2 @ X1 @ X2 ) )
= $false ) )
| ~ spl2_22 ),
inference(beta_eta_normalization,[],[f410]) ).
thf(f410,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( X0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ X1 @ X2 ) )
@ ( sK24 @ X1 @ X0 @ X2 ) )
= $false ) )
| ~ spl2_22 ),
inference(sigma_clausification,[],[f409]) ).
thf(f409,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK7 @ X1 @ X2 )
= $true )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( X0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ X1 @ X2 ) ) ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_22 ),
inference(beta_eta_normalization,[],[f408]) ).
thf(f408,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1
@ X2 )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_22 ),
inference(equality_resolution,[],[f243]) ).
thf(f243,plain,
( ! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X3 )
| ( $false
= ( sK0 @ X4 ) )
| ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( sK7 @ X1 @ X2 )
= $true ) )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f242,plain,
( spl2_22
<=> ! [X4: a > a > $o,X3: a > a > $o,X2: a,X1: a] :
( ( ( sK7 @ X1 @ X2 )
= $true )
| ( $false
= ( sK0 @ X4 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X3 )
| ( $false
= ( X3 @ X1 @ X2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
thf(f412,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK24 @ X1 @ X0 @ X2 @ X1 @ X2 )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_22 ),
inference(binary_proxy_clausification,[],[f411]) ).
thf(f886,plain,
( ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(avatar_contradiction_clause,[],[f885]) ).
thf(f885,plain,
( $false
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f884]) ).
thf(f884,plain,
( ( $true = $false )
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(backward_demodulation,[],[f239,f883]) ).
thf(f883,plain,
( ( ( sK1 @ sK7 )
= $false )
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f882]) ).
thf(f882,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f881,f225]) ).
thf(f881,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f879]) ).
thf(f879,plain,
( ( $true = $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(superposition,[],[f212,f877]) ).
thf(f877,plain,
( ( $false
= ( sK0 @ ( sK13 @ sK7 ) ) )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f876]) ).
thf(f876,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ ( sK13 @ sK7 ) ) )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f875,f239]) ).
thf(f875,plain,
( ( $false
= ( sK0 @ ( sK13 @ sK7 ) ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f874]) ).
thf(f874,plain,
( ( $false
= ( sK0 @ ( sK13 @ sK7 ) ) )
| ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f873,f225]) ).
thf(f873,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( $false
= ( sK0 @ ( sK13 @ sK7 ) ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f871]) ).
thf(f871,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( $false
= ( sK0 @ ( sK13 @ sK7 ) ) )
| ( $true = $false )
| ~ spl2_14
| ~ spl2_16
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(superposition,[],[f831,f216]) ).
thf(f831,plain,
( ! [X0: a > a > $o] :
( ( $false
= ( X0 @ ( sK12 @ sK7 ) @ ( sK11 @ sK7 ) ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_14
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f830]) ).
thf(f830,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( $false
= ( X0 @ ( sK12 @ sK7 ) @ ( sK11 @ sK7 ) ) )
| ( $true = $false ) )
| ~ spl2_14
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f829,f239]) ).
thf(f829,plain,
( ! [X0: a > a > $o] :
( ( $false
= ( X0 @ ( sK12 @ sK7 ) @ ( sK11 @ sK7 ) ) )
| ( ( sK1 @ sK7 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_14
| ~ spl2_18
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f828]) ).
thf(f828,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( $false
= ( X0 @ ( sK12 @ sK7 ) @ ( sK11 @ sK7 ) ) )
| ( $true = $false )
| ( ( sK1 @ sK7 )
= $false ) )
| ~ spl2_14
| ~ spl2_18
| ~ spl2_22 ),
inference(forward_demodulation,[],[f822,f225]) ).
thf(f822,plain,
( ! [X0: a > a > $o] :
( ( $false
= ( X0 @ ( sK12 @ sK7 ) @ ( sK11 @ sK7 ) ) )
| ( ( sK1 @ sK7 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) ) )
| ~ spl2_14
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f805]) ).
thf(f805,plain,
( ! [X0: a > a > $o] :
( ( $false
= ( X0 @ ( sK12 @ sK7 ) @ ( sK11 @ sK7 ) ) )
| ( $true = $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK7 )
= $false ) )
| ~ spl2_14
| ~ spl2_22 ),
inference(superposition,[],[f208,f437]) ).
thf(f797,plain,
( ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(avatar_contradiction_clause,[],[f796]) ).
thf(f796,plain,
( $false
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f795]) ).
thf(f795,plain,
( ( $true = $false )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(backward_demodulation,[],[f239,f794]) ).
thf(f794,plain,
( ( ( sK1 @ sK7 )
= $false )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f793]) ).
thf(f793,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f792,f225]) ).
thf(f792,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f789]) ).
thf(f789,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(superposition,[],[f760,f182]) ).
thf(f760,plain,
( ( $false
= ( sK0 @ ( sK20 @ sK7 ) ) )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f759]) ).
thf(f759,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ ( sK20 @ sK7 ) ) )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f758,f239]) ).
thf(f758,plain,
( ( $false
= ( sK0 @ ( sK20 @ sK7 ) ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f757]) ).
thf(f757,plain,
( ( $true = $false )
| ( ( sK1 @ sK7 )
= $false )
| ( $false
= ( sK0 @ ( sK20 @ sK7 ) ) )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f756,f225]) ).
thf(f756,plain,
( ( $false
= ( sK0 @ ( sK20 @ sK7 ) ) )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f754]) ).
thf(f754,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $false
= ( sK0 @ ( sK20 @ sK7 ) ) )
| ( $true = $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ~ spl2_5
| ~ spl2_8
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(superposition,[],[f714,f186]) ).
thf(f714,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK19 @ sK7 ) @ ( sK18 @ sK7 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_5
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f713]) ).
thf(f713,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ ( sK19 @ sK7 ) @ ( sK18 @ sK7 ) )
= $false ) )
| ~ spl2_5
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f712,f239]) ).
thf(f712,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK19 @ sK7 ) @ ( sK18 @ sK7 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK7 )
= $false ) )
| ~ spl2_5
| ~ spl2_18
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f711]) ).
thf(f711,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( ( X0 @ ( sK19 @ sK7 ) @ ( sK18 @ sK7 ) )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_5
| ~ spl2_18
| ~ spl2_22 ),
inference(forward_demodulation,[],[f709,f225]) ).
thf(f709,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ sK7 )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( X0 @ ( sK19 @ sK7 ) @ ( sK18 @ sK7 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_5
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f688]) ).
thf(f688,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ( ( X0 @ ( sK19 @ sK7 ) @ ( sK18 @ sK7 ) )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) ) )
| ~ spl2_5
| ~ spl2_22 ),
inference(superposition,[],[f175,f437]) ).
thf(f608,plain,
( ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(avatar_contradiction_clause,[],[f607]) ).
thf(f607,plain,
( $false
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f606]) ).
thf(f606,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f605,f225]) ).
thf(f605,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f604]) ).
thf(f604,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( $true = $false )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f597,f239]) ).
thf(f597,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f596]) ).
thf(f596,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(superposition,[],[f178,f584]) ).
thf(f584,plain,
( ( ( sK0 @ ( sK14 @ sK7 ) )
= $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f583]) ).
thf(f583,plain,
( ( ( sK0 @ ( sK14 @ sK7 ) )
= $false )
| ( $true = $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f582,f239]) ).
thf(f582,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( ( sK0 @ ( sK14 @ sK7 ) )
= $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f581]) ).
thf(f581,plain,
( ( $true = $false )
| ( ( sK0 @ ( sK14 @ sK7 ) )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_18
| ~ spl2_22 ),
inference(forward_demodulation,[],[f579,f225]) ).
thf(f579,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK0 @ ( sK14 @ sK7 ) )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f578]) ).
thf(f578,plain,
( ( $true = $false )
| ( ( sK0 @ ( sK14 @ sK7 ) )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_22 ),
inference(duplicate_literal_removal,[],[f553]) ).
thf(f553,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ( ( sK0 @ ( sK14 @ sK7 ) )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_1
| ~ spl2_9
| ~ spl2_13
| ~ spl2_22 ),
inference(superposition,[],[f160,f529]) ).
thf(f529,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK7 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) ) )
| ~ spl2_9
| ~ spl2_13
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f528]) ).
thf(f528,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( $true
= ( sK7 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK1 @ X0 )
= $false )
| ( $true = $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) ) )
| ~ spl2_9
| ~ spl2_13
| ~ spl2_22 ),
inference(duplicate_literal_removal,[],[f521]) ).
thf(f521,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ X0 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( $true
= ( sK7 @ ( sK8 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( $true = $false )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl2_9
| ~ spl2_13
| ~ spl2_22 ),
inference(superposition,[],[f438,f205]) ).
thf(f438,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK10 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( $true
= ( X0 @ sK4 @ sK5 ) ) )
| ~ spl2_9
| ~ spl2_22 ),
inference(equality_resolution,[],[f422]) ).
thf(f422,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK10 @ X0 )
!= X1 )
| ( ( sK0 @ ( sK14 @ X0 ) )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( ( X1 @ X2 @ X3 )
= $false )
| ( $true
= ( X0 @ sK4 @ sK5 ) )
| ( $true
= ( sK7 @ X2 @ X3 ) ) )
| ~ spl2_9
| ~ spl2_22 ),
inference(superposition,[],[f243,f190]) ).
thf(f544,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(avatar_contradiction_clause,[],[f543]) ).
thf(f543,plain,
( $false
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f542]) ).
thf(f542,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(backward_demodulation,[],[f239,f541]) ).
thf(f541,plain,
( ( ( sK1 @ sK7 )
= $false )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f540,plain,
( ( $true = $false )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f533,f225]) ).
thf(f533,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f532]) ).
thf(f532,plain,
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false )
| ( $true = $false )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(superposition,[],[f167,f515]) ).
thf(f515,plain,
( ( ( sK0 @ ( sK23 @ sK7 ) )
= $false )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f514]) ).
thf(f514,plain,
( ( ( sK0 @ ( sK23 @ sK7 ) )
= $false )
| ( $true = $false )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f513,f225]) ).
thf(f513,plain,
( ( ( sK0 @ ( sK23 @ sK7 ) )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f512]) ).
thf(f512,plain,
( ( ( sK0 @ ( sK23 @ sK7 ) )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( $true = $false )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f510,f239]) ).
thf(f510,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( ( sK0 @ ( sK23 @ sK7 ) )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f487]) ).
thf(f487,plain,
( ( $true = $false )
| ( ( sK1 @ sK7 )
= $false )
| ( ( sK0 @ ( sK23 @ sK7 ) )
= $false )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(superposition,[],[f455,f171]) ).
thf(f171,plain,
( ! [X2: a > a > $o] :
( ( $true
= ( sK23 @ X2 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f170]) ).
thf(f170,plain,
( spl2_4
<=> ! [X2: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( $true
= ( sK23 @ X2 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
thf(f455,plain,
( ! [X0: a > a > $o] :
( ( $false
= ( X0 @ ( sK22 @ sK7 ) @ ( sK21 @ sK7 ) ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_2
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f454]) ).
thf(f454,plain,
( ! [X0: a > a > $o] :
( ( $false
= ( X0 @ ( sK22 @ sK7 ) @ ( sK21 @ sK7 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl2_2
| ~ spl2_18
| ~ spl2_21
| ~ spl2_22 ),
inference(forward_demodulation,[],[f453,f239]) ).
thf(f453,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ sK7 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( X0 @ ( sK22 @ sK7 ) @ ( sK21 @ sK7 ) ) ) )
| ~ spl2_2
| ~ spl2_18
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f452]) ).
thf(f452,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ sK7 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $true = $false )
| ( $false
= ( X0 @ ( sK22 @ sK7 ) @ ( sK21 @ sK7 ) ) ) )
| ~ spl2_2
| ~ spl2_18
| ~ spl2_22 ),
inference(forward_demodulation,[],[f450,f225]) ).
thf(f450,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK7 )
= $false )
| ( $false
= ( X0 @ ( sK22 @ sK7 ) @ ( sK21 @ sK7 ) ) ) )
| ~ spl2_2
| ~ spl2_22 ),
inference(trivial_inequality_removal,[],[f444]) ).
thf(f444,plain,
( ! [X0: a > a > $o] :
( ( $true = $false )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( X0 @ ( sK22 @ sK7 ) @ ( sK21 @ sK7 ) ) )
| ( $true
= ( sK7 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK7 )
= $false ) )
| ~ spl2_2
| ~ spl2_22 ),
inference(superposition,[],[f163,f437]) ).
thf(f163,plain,
( ! [X2: a > a > $o] :
( ( $false
= ( X2 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f162]) ).
thf(f162,plain,
( spl2_2
<=> ! [X2: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $false
= ( X2 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
thf(f167,plain,
( ! [X2: a > a > $o] :
( ( $true
= ( sK0 @ ( sK23 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f166]) ).
thf(f166,plain,
( spl2_3
<=> ! [X2: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( $true
= ( sK0 @ ( sK23 @ X2 ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
thf(f395,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(avatar_contradiction_clause,[],[f394]) ).
thf(f394,plain,
( $false
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f393]) ).
thf(f393,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f392,f221]) ).
thf(f392,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f391]) ).
thf(f391,plain,
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( $true = $false )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f384,f234]) ).
thf(f384,plain,
( ( ( sK1 @ sK6 )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f382]) ).
thf(f382,plain,
( ( ( sK1 @ sK6 )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( $true = $false )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(superposition,[],[f357,f167]) ).
thf(f357,plain,
( ( ( sK0 @ ( sK23 @ sK6 ) )
= $false )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f356]) ).
thf(f356,plain,
( ( $true = $false )
| ( ( sK0 @ ( sK23 @ sK6 ) )
= $false )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f355,f234]) ).
thf(f355,plain,
( ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ ( sK23 @ sK6 ) )
= $false )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f354]) ).
thf(f354,plain,
( ( ( sK0 @ ( sK23 @ sK6 ) )
= $false )
| ( $true = $false )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f342,f221]) ).
thf(f342,plain,
( ( ( sK0 @ ( sK23 @ sK6 ) )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f328]) ).
thf(f328,plain,
( ( $true = $false )
| ( ( sK1 @ sK6 )
= $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK0 @ ( sK23 @ sK6 ) )
= $false )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(superposition,[],[f301,f171]) ).
thf(f301,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK22 @ sK6 ) @ ( sK21 @ sK6 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_2
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f300,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ ( sK22 @ sK6 ) @ ( sK21 @ sK6 ) )
= $false )
| ( $true = $false ) )
| ~ spl2_2
| ~ spl2_17
| ~ spl2_19
| ~ spl2_20 ),
inference(forward_demodulation,[],[f299,f234]) ).
thf(f299,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK22 @ sK6 ) @ ( sK21 @ sK6 ) )
= $false )
| ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_2
| ~ spl2_17
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f298]) ).
thf(f298,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK22 @ sK6 ) @ ( sK21 @ sK6 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ sK6 )
= $false )
| ( $true = $false ) )
| ~ spl2_2
| ~ spl2_17
| ~ spl2_19 ),
inference(forward_demodulation,[],[f296,f221]) ).
thf(f296,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ ( sK22 @ sK6 ) @ ( sK21 @ sK6 ) )
= $false ) )
| ~ spl2_2
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f292]) ).
thf(f292,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ sK6 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $true = $false )
| ( $true
= ( sK6 @ sK4 @ sK5 ) )
| ( ( X0 @ ( sK22 @ sK6 ) @ ( sK21 @ sK6 ) )
= $false ) )
| ~ spl2_2
| ~ spl2_19 ),
inference(superposition,[],[f163,f229]) ).
thf(f248,plain,
( spl2_22
| spl2_20 ),
inference(avatar_split_clause,[],[f39,f232,f242]) ).
thf(f39,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( $false
= ( X3 @ X1 @ X2 ) )
| ( $true
= ( sK1 @ sK6 ) )
| ( $false
= ( sK0 @ X4 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X3 )
| ( ( sK7 @ X1 @ X2 )
= $true ) ),
inference(equality_proxy_clausification,[],[f38]) ).
thf(f38,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( $true
= ( sK1 @ sK6 ) )
| ( ( X3
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( sK0 @ X4 ) ) ),
inference(binary_proxy_clausification,[],[f37]) ).
thf(f37,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( ( X3
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ( sK0 @ X4 ) )
= $false )
| ( $false
= ( X3 @ X1 @ X2 ) )
| ( $true
= ( sK1 @ sK6 ) )
| ( ( sK7 @ X1 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[],[f36]) ).
thf(f36,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] :
( ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) )
@ X4 )
= $false )
| ( $true
= ( sK1 @ sK6 ) )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( $false
= ( X3 @ X1 @ X2 ) ) ),
inference(pi_clausification,[],[f35]) ).
thf(f35,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK1 @ sK6 ) )
| ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f34]) ).
thf(f34,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK7 @ X1 @ X2 )
= $true )
| ( $true
= ( sK1 @ sK6 ) )
| ( ( ( X3 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f33]) ).
thf(f33,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK1 @ sK6 ) )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_clausification,[],[f32]) ).
thf(f32,plain,
! [X2: a,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) ) )
= $false )
| ( $true
= ( sK1 @ sK6 ) )
| ( ( sK7 @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f31]) ).
thf(f31,plain,
! [X2: a,X1: a] :
( ( $true
= ( sK1 @ sK6 ) )
| ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) ) )
=> ( sK7 @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f30]) ).
thf(f30,plain,
! [X2: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) )
& ( sK0 @ Y2 ) ) ) ) )
=> ( sK7 @ X1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( sK1 @ sK6 ) ) ),
inference(pi_clausification,[],[f29]) ).
thf(f29,plain,
! [X1: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) )
& ( sK0 @ Y2 ) ) ) ) )
=> ( sK7 @ X1 @ Y0 ) ) ) )
| ( $true
= ( sK1 @ sK6 ) ) ),
inference(beta_eta_normalization,[],[f28]) ).
thf(f28,plain,
! [X1: a] :
( ( $true
= ( sK1 @ sK6 ) )
| ( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) )
@ X1 ) ) ),
inference(pi_clausification,[],[f27]) ).
thf(f27,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) ) )
| ( $true
= ( sK1 @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( ( $true
= ( ( sK1 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) ) ) ),
inference(binary_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( ( $false
= ( ( ( sK1 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) ) ) ),
inference(binary_proxy_clausification,[],[f19]) ).
thf(f19,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) )
=> ( sK7 @ sK4 @ sK5 ) )
= $false )
| ( $false
= ( ( ( sK1 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[],[f18]) ).
thf(f18,plain,
( ( $false
= ( ( ( sK1 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) ) )
| ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( sK1 @ Y7 ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) )
& ( sK0 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK7 )
= $false ) ),
inference(sigma_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( sK1 @ Y7 ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) )
& ( sK0 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false )
| ( $false
= ( ( ( sK1 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( sK1 @ Y7 ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) )
& ( sK0 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false )
| ( ( ^ [Y0: a > a > $o] :
( ( ( sK1 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y2 @ Y1 )
& ( sK0 @ Y3 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK6 )
= $false ) ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK1 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y2 @ Y1 )
& ( sK0 @ Y3 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( sK1 @ Y7 ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) )
& ( sK0 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( sK1 @ Y7 ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) )
& ( sK0 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK1 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y2 @ Y1 )
& ( sK0 @ Y3 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK1 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y3 @ Y2 )
& ( sK0 @ Y4 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y4
= ( ^ [Y6: a,Y7: a] :
( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y5 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) )
& ( sK1 @ Y8 ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) ) )
& ( sK0 @ Y5 ) ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK1 @ Y1 ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y4
= ( ^ [Y6: a,Y7: a] :
( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y5 @ Y9 @ Y10 )
=> ( Y8 @ Y9 @ Y10 ) ) ) )
& ( sK1 @ Y8 ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) ) )
& ( sK0 @ Y5 ) ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( sK1 @ Y1 ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK1 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y3 @ Y2 )
& ( sK0 @ Y4 ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) )
& ( sK1 @ Y9 ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) )
& ( sK0 @ Y6 ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y4 @ Y3 )
& ( sK0 @ Y5 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y4 @ Y3 )
& ( sK0 @ Y5 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) )
& ( sK1 @ Y9 ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) )
& ( sK0 @ Y6 ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y4 @ Y3 )
& ( sK0 @ Y5 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) )
& ( sK1 @ Y9 ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) )
& ( sK0 @ Y6 ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) )
& ( X1 @ Y9 ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) )
& ( X0 @ Y6 ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y4 @ Y3 )
& ( X0 @ Y5 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
=> ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y4 @ Y3 )
& ( sK0 @ Y5 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) )
& ( sK1 @ Y9 ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) )
& ( sK0 @ Y6 ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f6,plain,
? [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) )
& ( X1 @ Y9 ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) )
& ( X0 @ Y6 ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y4 @ Y3 )
& ( X0 @ Y5 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y10 @ Y11 )
=> ( Y9 @ Y10 @ Y11 ) ) ) )
& ( X1 @ Y9 ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) )
& ( X0 @ Y6 ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( X1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y4 @ Y3 )
& ( X0 @ Y5 ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ( X1 @ X4 )
& ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( X0 @ X8 )
& ( X7
= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ( X1 @ X11 )
& ! [X12: a,X13: a] :
( ( X8 @ X13 @ X12 )
=> ( X11 @ X13 @ X12 ) ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
& ( X7 @ X6 @ X5 ) )
=> ( X4 @ X6 @ X5 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X14: a,X15: a] :
! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ? [X19: a > a > $o] :
( ( X0 @ X19 )
& ( X19 @ X17 @ X18 ) )
=> ( X16 @ X17 @ X18 ) )
& ( X1 @ X16 ) )
=> ( X16 @ X14 @ X15 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( X1 @ X8 )
& ( X7
= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ( X0 @ X11 )
& ! [X13: a,X12: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ( X0 @ X4 )
& ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( X1 @ X8 )
& ( X7
= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ( X0 @ X11 )
& ! [X13: a,X12: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) ) )
=> ( X11 @ X9 @ X10 ) ) ) ) )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM254_pme) ).
thf(f247,plain,
( spl2_20
| spl2_21 ),
inference(avatar_split_clause,[],[f26,f237,f232]) ).
thf(f26,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ( $true
= ( sK1 @ sK7 ) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f246,plain,
( spl2_22
| spl2_19 ),
inference(avatar_split_clause,[],[f61,f228,f242]) ).
thf(f61,plain,
! [X2: a,X3: a > a > $o,X1: a,X6: a > a > $o,X7: a > a > $o,X4: a,X5: a] :
( ( $true
= ( sK7 @ X4 @ X5 ) )
| ( ( X6 @ X4 @ X5 )
= $false )
| ( ( sK0 @ X3 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X7 )
= $false )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X7 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X6 ) ),
inference(equality_proxy_clausification,[],[f60]) ).
thf(f60,plain,
! [X2: a,X3: a > a > $o,X1: a,X6: a > a > $o,X7: a > a > $o,X4: a,X5: a] :
( ( ( X6
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X7 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( X6 @ X4 @ X5 )
= $false )
| ( ( sK0 @ X7 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( sK0 @ X3 )
= $false )
| ( $true
= ( sK7 @ X4 @ X5 ) )
| ( ( X3 @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f59]) ).
thf(f59,plain,
! [X2: a,X3: a > a > $o,X1: a,X6: a > a > $o,X7: a > a > $o,X4: a,X5: a] :
( ( ( X6 @ X4 @ X5 )
= $false )
| ( $true
= ( sK7 @ X4 @ X5 ) )
| ( $false
= ( ( X6
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X7 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ( sK0 @ X7 ) ) )
| ( ( sK0 @ X3 )
= $false )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f58]) ).
thf(f58,plain,
! [X2: a,X3: a > a > $o,X1: a,X6: a > a > $o,X7: a > a > $o,X4: a,X5: a] :
( ( ( X6 @ X4 @ X5 )
= $false )
| ( ( sK0 @ X3 )
= $false )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( ( ^ [Y0: a > a > $o] :
( ( X6
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) )
@ X7 )
= $false )
| ( $true
= ( sK7 @ X4 @ X5 ) )
| ( $true
= ( sK6 @ X2 @ X1 ) ) ),
inference(pi_clausification,[],[f57]) ).
thf(f57,plain,
! [X2: a,X3: a > a > $o,X1: a,X6: a > a > $o,X4: a,X5: a] :
( ( ( X3 @ X2 @ X1 )
= $false )
| ( ( X6 @ X4 @ X5 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( sK0 @ X3 )
= $false )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( X6
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) ) )
= $false )
| ( $true
= ( sK7 @ X4 @ X5 ) ) ),
inference(binary_proxy_clausification,[],[f56]) ).
thf(f56,plain,
! [X2: a,X3: a > a > $o,X1: a,X6: a > a > $o,X4: a,X5: a] :
( ( ( sK0 @ X3 )
= $false )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( ( X6 @ X4 @ X5 )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( X6
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK7 @ X4 @ X5 ) ) ),
inference(beta_eta_normalization,[],[f55]) ).
thf(f55,plain,
! [X2: a,X3: a > a > $o,X1: a,X6: a > a > $o,X4: a,X5: a] :
( ( $true
= ( sK7 @ X4 @ X5 ) )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ X4 @ X5 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) )
@ X6 )
= $false )
| ( ( sK0 @ X3 )
= $false ) ),
inference(pi_clausification,[],[f54]) ).
thf(f54,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a,X5: a] :
( ( ( sK0 @ X3 )
= $false )
| ( $true
= ( sK7 @ X4 @ X5 ) )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X4 @ X5 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f53]) ).
thf(f53,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a,X5: a] :
( ( ( sK0 @ X3 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X4 @ X5 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) ) )
=> ( sK7 @ X4 @ X5 ) ) )
| ( ( X3 @ X2 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f52]) ).
thf(f52,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a,X5: a] :
( ( ( sK0 @ X3 )
= $false )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X4 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) )
& ( sK0 @ Y2 ) ) ) ) )
=> ( sK7 @ X4 @ Y0 ) )
@ X5 ) ) ),
inference(pi_clausification,[],[f51]) ).
thf(f51,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a] :
( ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X3 )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X4 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) )
& ( sK0 @ Y2 ) ) ) ) )
=> ( sK7 @ X4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f50]) ).
thf(f50,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a] :
( ( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) )
@ X4 ) )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( sK0 @ X3 )
= $false ) ),
inference(pi_clausification,[],[f49]) ).
thf(f49,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( X3 @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK0 @ X3 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f48]) ).
thf(f48,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( ( X3 @ X2 @ X1 )
& ( sK0 @ X3 ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( sK6 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f47]) ).
thf(f47,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK6 @ X2 @ X1 ) )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) ) ),
inference(pi_clausification,[],[f46]) ).
thf(f46,plain,
! [X2: a,X1: a] :
( ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f45,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) ) )
=> ( sK6 @ X2 @ X1 ) ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f43]) ).
thf(f43,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) ) )
| ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) ) )
=> ( sK6 @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f42]) ).
thf(f42,plain,
! [X2: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ X1 )
& ( sK0 @ Y1 ) ) )
=> ( sK6 @ Y0 @ X1 ) )
@ X2 ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) ) ) ),
inference(pi_clausification,[],[f41]) ).
thf(f41,plain,
! [X1: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ X1 )
& ( sK0 @ Y1 ) ) )
=> ( sK6 @ Y0 @ X1 ) ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) ) ) ),
inference(beta_eta_normalization,[],[f40]) ).
thf(f40,plain,
! [X1: a] :
( ( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) ) ) ),
inference(pi_clausification,[],[f24]) ).
thf(f24,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) ) ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f245,plain,
( spl2_21
| spl2_19 ),
inference(avatar_split_clause,[],[f65,f228,f237]) ).
thf(f65,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X3 )
= $false )
| ( $true
= ( sK1 @ sK7 ) ) ),
inference(binary_proxy_clausification,[],[f64]) ).
thf(f64,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK1 @ sK7 ) )
| ( ( ( X3 @ X2 @ X1 )
& ( sK0 @ X3 ) )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f63]) ).
thf(f63,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) )
@ X3 ) )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( $true
= ( sK1 @ sK7 ) ) ),
inference(pi_clausification,[],[f62]) ).
thf(f62,plain,
! [X2: a,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) ) )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( $true
= ( sK1 @ sK7 ) ) ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) ) )
=> ( sK6 @ X2 @ X1 ) ) )
| ( $true
= ( sK1 @ sK7 ) ) ),
inference(binary_proxy_clausification,[],[f43]) ).
thf(f244,plain,
( spl2_22
| spl2_17 ),
inference(avatar_split_clause,[],[f79,f219,f242]) ).
thf(f79,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( sK6 @ sK4 @ sK5 )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( $false
= ( X3 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X4 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X3 ) ),
inference(equality_proxy_clausification,[],[f78]) ).
thf(f78,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( sK6 @ sK4 @ sK5 )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( X3
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( sK0 @ X4 ) ) ),
inference(binary_proxy_clausification,[],[f77]) ).
thf(f77,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( sK7 @ X1 @ X2 )
= $true )
| ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( ( X3
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ( sK0 @ X4 ) )
= $false )
| ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
inference(beta_eta_normalization,[],[f76]) ).
thf(f76,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( ^ [Y0: a > a > $o] :
( ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) )
@ X4 )
= $false )
| ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
inference(pi_clausification,[],[f75]) ).
thf(f75,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( X3 @ X1 @ X2 ) )
| ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[],[f74]) ).
thf(f74,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( ( X3 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) ) ) )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true )
| ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
inference(beta_eta_normalization,[],[f73]) ).
thf(f73,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK7 @ X1 @ X2 )
= $true )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) )
@ X3 ) )
| ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
inference(pi_clausification,[],[f72]) ).
thf(f72,plain,
! [X2: a,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) ) )
= $false )
| ( ( sK6 @ sK4 @ sK5 )
= $false )
| ( ( sK7 @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f71]) ).
thf(f71,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) ) )
=> ( sK7 @ X1 @ X2 ) ) )
| ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
inference(beta_eta_normalization,[],[f70]) ).
thf(f70,plain,
! [X2: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) )
& ( sK0 @ Y2 ) ) ) ) )
=> ( sK7 @ X1 @ Y0 ) )
@ X2 ) )
| ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
inference(pi_clausification,[],[f69]) ).
thf(f69,plain,
! [X1: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) )
& ( sK0 @ Y2 ) ) ) ) )
=> ( sK7 @ X1 @ Y0 ) ) ) )
| ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
! [X1: a] :
( ( ( sK6 @ sK4 @ sK5 )
= $false )
| ( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) )
@ X1 ) ) ),
inference(pi_clausification,[],[f67]) ).
thf(f67,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK6 @ sK4 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[],[f22]) ).
thf(f22,plain,
( ( ( sK6 @ sK4 @ sK5 )
= $false )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ sK7 ) ) ) ),
inference(binary_proxy_clausification,[],[f21]) ).
thf(f240,plain,
( spl2_17
| spl2_21 ),
inference(avatar_split_clause,[],[f66,f237,f219]) ).
thf(f66,plain,
( ( ( sK6 @ sK4 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK7 ) ) ),
inference(binary_proxy_clausification,[],[f22]) ).
thf(f235,plain,
( spl2_20
| spl2_18 ),
inference(avatar_split_clause,[],[f83,f223,f232]) ).
thf(f83,plain,
( ( ( sK7 @ sK4 @ sK5 )
= $false )
| ( $true
= ( sK1 @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f81]) ).
thf(f81,plain,
( ( ( sK7 @ sK4 @ sK5 )
= $false )
| ( $true
= ( ( sK1 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f20]) ).
thf(f20,plain,
( ( $false
= ( ( ( sK1 @ sK6 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) ) )
| ( ( sK7 @ sK4 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[],[f19]) ).
thf(f230,plain,
( spl2_18
| spl2_19 ),
inference(avatar_split_clause,[],[f91,f228,f223]) ).
thf(f91,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( sK0 @ X3 )
= $false )
| ( ( X3 @ X2 @ X1 )
= $false )
| ( ( sK7 @ sK4 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[],[f90]) ).
thf(f90,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK7 @ sK4 @ sK5 )
= $false )
| ( ( ( X3 @ X2 @ X1 )
& ( sK0 @ X3 ) )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f89]) ).
thf(f89,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) )
@ X3 ) )
| ( ( sK7 @ sK4 @ sK5 )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) ) ),
inference(pi_clausification,[],[f88]) ).
thf(f88,plain,
! [X2: a,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) ) )
= $false )
| ( $true
= ( sK6 @ X2 @ X1 ) )
| ( ( sK7 @ sK4 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[],[f87]) ).
thf(f87,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X1 )
& ( sK0 @ Y0 ) ) )
=> ( sK6 @ X2 @ X1 ) ) )
| ( ( sK7 @ sK4 @ sK5 )
= $false ) ),
inference(beta_eta_normalization,[],[f86]) ).
thf(f86,plain,
! [X2: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ X1 )
& ( sK0 @ Y1 ) ) )
=> ( sK6 @ Y0 @ X1 ) )
@ X2 ) )
| ( ( sK7 @ sK4 @ sK5 )
= $false ) ),
inference(pi_clausification,[],[f85]) ).
thf(f85,plain,
! [X1: a] :
( ( ( sK7 @ sK4 @ sK5 )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ X1 )
& ( sK0 @ Y1 ) ) )
=> ( sK6 @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f84]) ).
thf(f84,plain,
! [X1: a] :
( ( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ( ( sK7 @ sK4 @ sK5 )
= $false ) ),
inference(pi_clausification,[],[f82]) ).
thf(f82,plain,
( ( ( sK7 @ sK4 @ sK5 )
= $false )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f81]) ).
thf(f226,plain,
( spl2_17
| spl2_18 ),
inference(avatar_split_clause,[],[f80,f223,f219]) ).
thf(f80,plain,
( ( ( sK6 @ sK4 @ sK5 )
= $false )
| ( ( sK7 @ sK4 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[],[f20]) ).
thf(f217,plain,
( spl2_16
| spl2_13 ),
inference(avatar_split_clause,[],[f119,f204,f215]) ).
thf(f119,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( sK13 @ X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f117]) ).
thf(f117,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( ( sK13 @ X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
& ( sK0 @ ( sK13 @ X2 ) ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ),
inference(beta_eta_normalization,[],[f116]) ).
thf(f116,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
& ( sK0 @ Y0 ) )
@ ( sK13 @ X2 ) ) )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) ),
inference(sigma_clausification,[],[f115]) ).
thf(f115,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
& ( sK0 @ Y0 ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f113]) ).
thf(f113,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
& ( sK0 @ Y0 ) ) )
=> ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f112]) ).
thf(f112,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ ( sK11 @ X2 ) )
& ( sK0 @ Y1 ) ) )
=> ( X2 @ Y0 @ ( sK11 @ X2 ) ) )
@ ( sK12 @ X2 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ),
inference(sigma_clausification,[],[f111]) ).
thf(f111,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ ( sK11 @ X2 ) )
& ( sK0 @ Y1 ) ) )
=> ( X2 @ Y0 @ ( sK11 @ X2 ) ) ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f110]) ).
thf(f110,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) )
@ ( sK11 @ X2 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) ) ),
inference(sigma_clausification,[],[f109]) ).
thf(f109,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[],[f108]) ).
thf(f108,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[],[f106]) ).
thf(f106,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK10 @ X1 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) ) ) )
= $true )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ),
inference(beta_eta_normalization,[],[f105]) ).
thf(f105,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) )
@ ( sK10 @ X1 ) ) ) ),
inference(sigma_clausification,[],[f104]) ).
thf(f104,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f102]) ).
thf(f102,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( sK1 @ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ( sK0 @ Y1 ) ) ) ) )
=> ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
= $false )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ),
inference(beta_eta_normalization,[],[f101]) ).
thf(f101,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ ( sK8 @ X1 ) @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) )
& ( sK0 @ Y2 ) ) ) ) )
=> ( X1 @ ( sK8 @ X1 ) @ Y0 ) )
@ ( sK9 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[],[f100]) ).
thf(f100,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ ( sK8 @ X1 ) @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( sK1 @ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) )
& ( sK0 @ Y2 ) ) ) ) )
=> ( X1 @ ( sK8 @ X1 ) @ Y0 ) ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f99]) ).
thf(f99,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) )
@ ( sK8 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[],[f98]) ).
thf(f98,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
= $false )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f97]) ).
thf(f97,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ X1 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f96]) ).
thf(f96,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
=> ( X2 @ sK4 @ sK5 ) ) )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f95]) ).
thf(f95,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ X1 ) )
=> ( X1 @ sK4 @ sK5 ) ) )
| ( $true
= ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
=> ( X2 @ sK4 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[],[f94]) ).
thf(f94,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ X1 ) )
=> ( X1 @ sK4 @ sK5 ) ) )
| ( ( ^ [Y0: a > a > $o] :
( ( ( sK1 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y2 @ Y1 )
& ( sK0 @ Y3 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[],[f93]) ).
thf(f93,plain,
! [X1: a > a > $o] :
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK1 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y2 @ Y1 )
& ( sK0 @ Y3 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( sK1 @ Y6 ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) )
& ( sK0 @ Y3 ) ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( sK1 @ X1 ) )
=> ( X1 @ sK4 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[],[f92]) ).
thf(f92,plain,
! [X1: a > a > $o] :
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK1 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y2 @ Y1 )
& ( sK0 @ Y3 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( sK1 @ Y7 ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) )
& ( sK0 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 ) ) ),
inference(pi_clausification,[],[f14]) ).
thf(f14,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( sK1 @ Y7 ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) )
& ( sK0 @ Y4 ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sK1 @ Y0 ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK1 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y2 @ Y1 )
& ( sK0 @ Y3 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f13]) ).
thf(f213,plain,
( spl2_13
| spl2_15 ),
inference(avatar_split_clause,[],[f118,f211,f204]) ).
thf(f118,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( sK0 @ ( sK13 @ X2 ) ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f117]) ).
thf(f209,plain,
( spl2_13
| spl2_14 ),
inference(avatar_split_clause,[],[f114,f207,f204]) ).
thf(f114,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( sK10 @ X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f113]) ).
thf(f202,plain,
( spl2_12
| spl2_9 ),
inference(avatar_split_clause,[],[f135,f189,f200]) ).
thf(f135,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK17 @ X2 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f133]) ).
thf(f133,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( ( sK17 @ X2 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
& ( sK0 @ ( sK17 @ X2 ) ) ) )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f132]) ).
thf(f132,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
& ( sK0 @ Y0 ) )
@ ( sK17 @ X2 ) ) ) ),
inference(sigma_clausification,[],[f131]) ).
thf(f131,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
& ( sK0 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f129]) ).
thf(f129,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
& ( sK0 @ Y0 ) ) )
=> ( X2 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f128]) ).
thf(f128,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ ( sK15 @ X2 ) )
& ( sK0 @ Y1 ) ) )
=> ( X2 @ Y0 @ ( sK15 @ X2 ) ) )
@ ( sK16 @ X2 ) )
= $false )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ),
inference(sigma_clausification,[],[f127]) ).
thf(f127,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ ( sK15 @ X2 ) )
& ( sK0 @ Y1 ) ) )
=> ( X2 @ Y0 @ ( sK15 @ X2 ) ) ) )
= $false )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ),
inference(beta_eta_normalization,[],[f126]) ).
thf(f126,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) )
@ ( sK15 @ X2 ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) ),
inference(sigma_clausification,[],[f125]) ).
thf(f125,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) )
= $false )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f124]) ).
thf(f124,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f123]) ).
thf(f123,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f121]) ).
thf(f121,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ( sK0 @ ( sK14 @ X1 ) ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ),
inference(beta_eta_normalization,[],[f120]) ).
thf(f120,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( ( sK10 @ X1 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) )
@ ( sK14 @ X1 ) ) )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(sigma_clausification,[],[f107]) ).
thf(f107,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK10 @ X1 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( sK1 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( sK0 @ Y0 ) ) ) )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f106]) ).
thf(f198,plain,
( spl2_11
| spl2_9 ),
inference(avatar_split_clause,[],[f134,f189,f196]) ).
thf(f134,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK0 @ ( sK17 @ X2 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f133]) ).
thf(f194,plain,
( spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f130,f192,f189]) ).
thf(f130,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( X2 @ ( sK16 @ X2 ) @ ( sK15 @ X2 ) )
= $false )
| ( ( sK10 @ X1 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK14 @ X1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( sK1 @ Y2 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f129]) ).
thf(f187,plain,
( spl2_8
| spl2_6 ),
inference(avatar_split_clause,[],[f146,f177,f185]) ).
thf(f146,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK20 @ X2 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[],[f144]) ).
thf(f144,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( ( sK20 @ X2 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) )
& ( sK0 @ ( sK20 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[],[f143]) ).
thf(f143,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) )
& ( sK0 @ Y0 ) )
@ ( sK20 @ X2 ) ) ) ),
inference(sigma_clausification,[],[f142]) ).
thf(f142,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) )
& ( sK0 @ Y0 ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f140]) ).
thf(f140,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) )
& ( sK0 @ Y0 ) ) )
=> ( X2 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f139]) ).
thf(f139,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ ( sK18 @ X2 ) )
& ( sK0 @ Y1 ) ) )
=> ( X2 @ Y0 @ ( sK18 @ X2 ) ) )
@ ( sK19 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[],[f138]) ).
thf(f138,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ ( sK18 @ X2 ) )
& ( sK0 @ Y1 ) ) )
=> ( X2 @ Y0 @ ( sK18 @ X2 ) ) ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ),
inference(beta_eta_normalization,[],[f137]) ).
thf(f137,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) )
@ ( sK18 @ X2 ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) ) ),
inference(sigma_clausification,[],[f136]) ).
thf(f136,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[],[f122]) ).
thf(f122,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f121]) ).
thf(f183,plain,
( spl2_7
| spl2_6 ),
inference(avatar_split_clause,[],[f145,f177,f181]) ).
thf(f145,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK20 @ X2 ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f144]) ).
thf(f179,plain,
( spl2_5
| spl2_6 ),
inference(avatar_split_clause,[],[f141,f177,f174]) ).
thf(f141,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( X2 @ ( sK19 @ X2 ) @ ( sK18 @ X2 ) )
= $false )
| ( $true
= ( sK0 @ ( sK14 @ X1 ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f140]) ).
thf(f172,plain,
( spl2_4
| spl2_1 ),
inference(avatar_split_clause,[],[f157,f159,f170]) ).
thf(f157,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( sK23 @ X2 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f155]) ).
thf(f155,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( $true
= ( ( sK23 @ X2 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) )
& ( sK0 @ ( sK23 @ X2 ) ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[],[f154]) ).
thf(f154,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) )
& ( sK0 @ Y0 ) )
@ ( sK23 @ X2 ) ) )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false ) ),
inference(sigma_clausification,[],[f153]) ).
thf(f153,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) )
& ( sK0 @ Y0 ) ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f151]) ).
thf(f151,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $false
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) )
& ( sK0 @ Y0 ) ) )
=> ( X2 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) ) ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f150]) ).
thf(f150,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ ( sK21 @ X2 ) )
& ( sK0 @ Y1 ) ) )
=> ( X2 @ Y0 @ ( sK21 @ X2 ) ) )
@ ( sK22 @ X2 ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[],[f149]) ).
thf(f149,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ Y0 @ ( sK21 @ X2 ) )
& ( sK0 @ Y1 ) ) )
=> ( X2 @ Y0 @ ( sK21 @ X2 ) ) ) ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f148]) ).
thf(f148,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) )
@ ( sK21 @ X2 ) ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) ) ),
inference(sigma_clausification,[],[f147]) ).
thf(f147,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f103]) ).
thf(f103,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y1 @ Y0 )
& ( sK0 @ Y2 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f102]) ).
thf(f168,plain,
( spl2_3
| spl2_1 ),
inference(avatar_split_clause,[],[f156,f159,f166]) ).
thf(f156,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $true
= ( X1 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ ( sK23 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[],[f155]) ).
thf(f164,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f152,f162,f159]) ).
thf(f152,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK4 @ sK5 ) )
| ( $false
= ( X2 @ ( sK22 @ X2 ) @ ( sK21 @ X2 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) @ ( sK9 @ X1 ) )
= $false )
| ( ( sK1 @ X2 )
= $false )
| ( $true
= ( X1 @ sK4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[],[f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV125^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 18:50:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.20/0.37 % (24932)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.20/0.37 % (24934)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (24933)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (24931)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.37 % (24935)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.20/0.37 % (24936)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % (24930)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.37 % (24933)Instruction limit reached!
% 0.20/0.37 % (24933)------------------------------
% 0.20/0.37 % (24933)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (24933)Termination reason: Unknown
% 0.20/0.37 % (24934)Instruction limit reached!
% 0.20/0.37 % (24934)------------------------------
% 0.20/0.37 % (24934)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (24934)Termination reason: Unknown
% 0.20/0.37 % (24934)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (24934)Memory used [KB]: 1023
% 0.20/0.37 % (24934)Time elapsed: 0.004 s
% 0.20/0.37 % (24934)Instructions burned: 2 (million)
% 0.20/0.37 % (24934)------------------------------
% 0.20/0.37 % (24934)------------------------------
% 0.20/0.37 % (24933)Termination phase: Preprocessing 3
% 0.20/0.37
% 0.20/0.37 % (24933)Memory used [KB]: 1023
% 0.20/0.37 % (24933)Time elapsed: 0.003 s
% 0.20/0.37 % (24933)Instructions burned: 2 (million)
% 0.20/0.37 % (24933)------------------------------
% 0.20/0.37 % (24933)------------------------------
% 0.20/0.38 % (24931)Instruction limit reached!
% 0.20/0.38 % (24931)------------------------------
% 0.20/0.38 % (24931)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (24931)Termination reason: Unknown
% 0.20/0.38 % (24931)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (24931)Memory used [KB]: 5500
% 0.20/0.38 % (24931)Time elapsed: 0.005 s
% 0.20/0.38 % (24931)Instructions burned: 5 (million)
% 0.20/0.38 % (24931)------------------------------
% 0.20/0.38 % (24931)------------------------------
% 0.20/0.38 % (24936)Instruction limit reached!
% 0.20/0.38 % (24936)------------------------------
% 0.20/0.38 % (24936)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (24936)Termination reason: Unknown
% 0.20/0.38 % (24936)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (24936)Memory used [KB]: 5500
% 0.20/0.38 % (24936)Time elapsed: 0.012 s
% 0.20/0.38 % (24936)Instructions burned: 18 (million)
% 0.20/0.38 % (24936)------------------------------
% 0.20/0.38 % (24936)------------------------------
% 0.20/0.39 % (24932)Instruction limit reached!
% 0.20/0.39 % (24932)------------------------------
% 0.20/0.39 % (24932)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (24932)Termination reason: Unknown
% 0.20/0.39 % (24932)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (24932)Memory used [KB]: 5628
% 0.20/0.39 % (24932)Time elapsed: 0.019 s
% 0.20/0.39 % (24932)Instructions burned: 27 (million)
% 0.20/0.39 % (24932)------------------------------
% 0.20/0.39 % (24932)------------------------------
% 0.20/0.39 % (24945)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.39 % (24944)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.39 % (24944)Instruction limit reached!
% 0.20/0.39 % (24944)------------------------------
% 0.20/0.39 % (24944)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (24944)Termination reason: Unknown
% 0.20/0.39 % (24944)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (24944)Memory used [KB]: 5500
% 0.20/0.39 % (24944)Time elapsed: 0.004 s
% 0.20/0.39 % (24944)Instructions burned: 3 (million)
% 0.20/0.39 % (24944)------------------------------
% 0.20/0.39 % (24944)------------------------------
% 0.20/0.39 % (24946)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.40 % (24949)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.40 % (24949)Instruction limit reached!
% 0.20/0.40 % (24949)------------------------------
% 0.20/0.40 % (24949)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.40 % (24949)Termination reason: Unknown
% 0.20/0.40 % (24949)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (24949)Memory used [KB]: 1023
% 0.20/0.40 % (24949)Time elapsed: 0.004 s
% 0.20/0.40 % (24949)Instructions burned: 3 (million)
% 0.20/0.40 % (24949)------------------------------
% 0.20/0.40 % (24949)------------------------------
% 0.20/0.40 % (24946)Instruction limit reached!
% 0.20/0.40 % (24946)------------------------------
% 0.20/0.40 % (24946)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.40 % (24946)Termination reason: Unknown
% 0.20/0.40 % (24946)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (24946)Memory used [KB]: 5756
% 0.20/0.40 % (24946)Time elapsed: 0.012 s
% 0.20/0.40 % (24946)Instructions burned: 16 (million)
% 0.20/0.40 % (24946)------------------------------
% 0.20/0.40 % (24946)------------------------------
% 0.20/0.41 % (24952)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.20/0.41 % (24955)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.41 % (24945)Instruction limit reached!
% 0.20/0.41 % (24945)------------------------------
% 0.20/0.41 % (24945)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (24945)Termination reason: Unknown
% 0.20/0.41 % (24945)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (24945)Memory used [KB]: 5628
% 0.20/0.41 % (24945)Time elapsed: 0.025 s
% 0.20/0.41 % (24945)Instructions burned: 38 (million)
% 0.20/0.41 % (24945)------------------------------
% 0.20/0.41 % (24945)------------------------------
% 0.20/0.41 % (24955)Instruction limit reached!
% 0.20/0.41 % (24955)------------------------------
% 0.20/0.41 % (24955)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (24955)Termination reason: Unknown
% 0.20/0.41 % (24955)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (24955)Memory used [KB]: 1023
% 0.20/0.41 % (24955)Time elapsed: 0.007 s
% 0.20/0.41 % (24955)Instructions burned: 8 (million)
% 0.20/0.41 % (24955)------------------------------
% 0.20/0.41 % (24955)------------------------------
% 0.20/0.42 % (24956)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.42 % (24957)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.42 % (24957)Instruction limit reached!
% 0.20/0.42 % (24957)------------------------------
% 0.20/0.42 % (24957)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (24957)Termination reason: Unknown
% 0.20/0.42 % (24957)Termination phase: Twee Goal Transformation
% 0.20/0.42
% 0.20/0.42 % (24957)Memory used [KB]: 1023
% 0.20/0.42 % (24957)Time elapsed: 0.004 s
% 0.20/0.42 % (24957)Instructions burned: 3 (million)
% 0.20/0.42 % (24957)------------------------------
% 0.20/0.42 % (24957)------------------------------
% 0.20/0.43 % (24956)Instruction limit reached!
% 0.20/0.43 % (24956)------------------------------
% 0.20/0.43 % (24956)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (24956)Termination reason: Unknown
% 0.20/0.43 % (24956)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (24956)Memory used [KB]: 5756
% 0.20/0.43 % (24956)Time elapsed: 0.014 s
% 0.20/0.43 % (24956)Instructions burned: 17 (million)
% 0.20/0.43 % (24956)------------------------------
% 0.20/0.43 % (24956)------------------------------
% 0.20/0.43 % (24958)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.43 % (24959)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.43 % (24958)Instruction limit reached!
% 0.20/0.43 % (24958)------------------------------
% 0.20/0.43 % (24958)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (24958)Termination reason: Unknown
% 0.20/0.43 % (24958)Termination phase: Property scanning
% 0.20/0.43
% 0.20/0.43 % (24958)Memory used [KB]: 1023
% 0.20/0.43 % (24958)Time elapsed: 0.004 s
% 0.20/0.43 % (24958)Instructions burned: 3 (million)
% 0.20/0.43 % (24958)------------------------------
% 0.20/0.43 % (24958)------------------------------
% 0.20/0.43 % (24959)Instruction limit reached!
% 0.20/0.43 % (24959)------------------------------
% 0.20/0.43 % (24959)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (24959)Termination reason: Unknown
% 0.20/0.43 % (24959)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (24959)Memory used [KB]: 5500
% 0.20/0.43 % (24959)Time elapsed: 0.007 s
% 0.20/0.43 % (24959)Instructions burned: 8 (million)
% 0.20/0.43 % (24959)------------------------------
% 0.20/0.43 % (24959)------------------------------
% 0.20/0.44 % (24960)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.44 % (24960)Instruction limit reached!
% 0.20/0.44 % (24960)------------------------------
% 0.20/0.44 % (24960)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.44 % (24960)Termination reason: Unknown
% 0.20/0.44 % (24960)Termination phase: Saturation
% 0.20/0.44
% 0.20/0.44 % (24960)Memory used [KB]: 5500
% 0.20/0.44 % (24960)Time elapsed: 0.004 s
% 0.20/0.44 % (24960)Instructions burned: 3 (million)
% 0.20/0.44 % (24960)------------------------------
% 0.20/0.44 % (24960)------------------------------
% 0.20/0.44 % (24961)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.45 % (24962)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.45 % (24961)Instruction limit reached!
% 0.20/0.45 % (24961)------------------------------
% 0.20/0.45 % (24961)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.45 % (24961)Termination reason: Unknown
% 0.20/0.45 % (24961)Termination phase: Saturation
% 0.20/0.45
% 0.20/0.45 % (24961)Memory used [KB]: 5500
% 0.20/0.45 % (24961)Time elapsed: 0.005 s
% 0.20/0.45 % (24961)Instructions burned: 4 (million)
% 0.20/0.45 % (24961)------------------------------
% 0.20/0.45 % (24961)------------------------------
% 0.20/0.45 % (24963)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.45 % (24964)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.46 % (24962)Instruction limit reached!
% 0.20/0.46 % (24962)------------------------------
% 0.20/0.46 % (24962)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.46 % (24962)Termination reason: Unknown
% 0.20/0.46 % (24962)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (24962)Memory used [KB]: 5500
% 0.20/0.46 % (24962)Time elapsed: 0.013 s
% 0.20/0.46 % (24962)Instructions burned: 19 (million)
% 0.20/0.46 % (24962)------------------------------
% 0.20/0.46 % (24962)------------------------------
% 0.20/0.46 % (24964)Instruction limit reached!
% 0.20/0.46 % (24964)------------------------------
% 0.20/0.46 % (24964)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.46 % (24964)Termination reason: Unknown
% 0.20/0.46 % (24964)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (24964)Memory used [KB]: 5500
% 0.20/0.46 % (24964)Time elapsed: 0.006 s
% 0.20/0.46 % (24964)Instructions burned: 6 (million)
% 0.20/0.46 % (24964)------------------------------
% 0.20/0.46 % (24964)------------------------------
% 0.20/0.46 % (24965)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.20/0.47 % (24930)Instruction limit reached!
% 0.20/0.47 % (24930)------------------------------
% 0.20/0.47 % (24930)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.47 % (24930)Termination reason: Unknown
% 0.20/0.47 % (24930)Termination phase: Saturation
% 0.20/0.47
% 0.20/0.47 % (24930)Memory used [KB]: 8187
% 0.20/0.47 % (24930)Time elapsed: 0.097 s
% 0.20/0.47 % (24930)Instructions burned: 183 (million)
% 0.20/0.47 % (24930)------------------------------
% 0.20/0.47 % (24930)------------------------------
% 0.20/0.47 % (24966)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.20/0.47 % (24967)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.48 % (24967)Instruction limit reached!
% 0.20/0.48 % (24967)------------------------------
% 0.20/0.48 % (24967)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.48 % (24967)Termination reason: Unknown
% 0.20/0.48 % (24967)Termination phase: Saturation
% 0.20/0.48
% 0.20/0.48 % (24967)Memory used [KB]: 5500
% 0.20/0.48 % (24967)Time elapsed: 0.006 s
% 0.20/0.48 % (24967)Instructions burned: 6 (million)
% 0.20/0.48 % (24967)------------------------------
% 0.20/0.48 % (24967)------------------------------
% 0.20/0.48 % (24968)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.49 % (24968)Instruction limit reached!
% 0.20/0.49 % (24968)------------------------------
% 0.20/0.49 % (24968)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.49 % (24968)Termination reason: Unknown
% 0.20/0.49 % (24968)Termination phase: Saturation
% 0.20/0.49
% 0.20/0.49 % (24968)Memory used [KB]: 5500
% 0.20/0.49 % (24968)Time elapsed: 0.006 s
% 0.20/0.49 % (24968)Instructions burned: 7 (million)
% 0.20/0.49 % (24968)------------------------------
% 0.20/0.49 % (24968)------------------------------
% 0.20/0.49 % (24966)Instruction limit reached!
% 0.20/0.49 % (24966)------------------------------
% 0.20/0.49 % (24966)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.49 % (24966)Termination reason: Unknown
% 0.20/0.49 % (24966)Termination phase: Saturation
% 0.20/0.49
% 0.20/0.49 % (24966)Memory used [KB]: 5628
% 0.20/0.49 % (24966)Time elapsed: 0.017 s
% 0.20/0.49 % (24966)Instructions burned: 21 (million)
% 0.20/0.49 % (24966)------------------------------
% 0.20/0.49 % (24966)------------------------------
% 0.20/0.49 % (24969)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.20/0.50 % (24970)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2998ds/779Mi)
% 0.20/0.50 % (24971)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.20/0.51 % (24971)Instruction limit reached!
% 0.20/0.51 % (24971)------------------------------
% 0.20/0.51 % (24971)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.51 % (24971)Termination reason: Unknown
% 0.20/0.51 % (24971)Termination phase: Saturation
% 0.20/0.51
% 0.20/0.51 % (24971)Memory used [KB]: 5500
% 0.20/0.51 % (24971)Time elapsed: 0.013 s
% 0.20/0.51 % (24971)Instructions burned: 19 (million)
% 0.20/0.51 % (24971)------------------------------
% 0.20/0.51 % (24971)------------------------------
% 0.20/0.53 % (24972)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 1.41/0.55 % (24935)Instruction limit reached!
% 1.41/0.55 % (24935)------------------------------
% 1.41/0.55 % (24935)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.41/0.55 % (24935)Termination reason: Unknown
% 1.41/0.55 % (24935)Termination phase: Saturation
% 1.41/0.55
% 1.41/0.55 % (24935)Memory used [KB]: 6652
% 1.41/0.55 % (24935)Time elapsed: 0.173 s
% 1.41/0.55 % (24935)Instructions burned: 275 (million)
% 1.41/0.55 % (24935)------------------------------
% 1.41/0.55 % (24935)------------------------------
% 1.41/0.56 % (24973)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 1.54/0.56 % (24973)Instruction limit reached!
% 1.54/0.56 % (24973)------------------------------
% 1.54/0.56 % (24973)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.54/0.56 % (24973)Termination reason: Unknown
% 1.54/0.56 % (24973)Termination phase: Saturation
% 1.54/0.56
% 1.54/0.56 % (24973)Memory used [KB]: 5756
% 1.54/0.56 % (24973)Time elapsed: 0.007 s
% 1.54/0.56 % (24973)Instructions burned: 18 (million)
% 1.54/0.56 % (24973)------------------------------
% 1.54/0.56 % (24973)------------------------------
% 1.54/0.57 % (24980)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 1.54/0.57 % (24980)Instruction limit reached!
% 1.54/0.57 % (24980)------------------------------
% 1.54/0.57 % (24980)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.54/0.57 % (24980)Termination reason: Unknown
% 1.54/0.57 % (24980)Termination phase: Saturation
% 1.54/0.57
% 1.54/0.57 % (24980)Memory used [KB]: 1023
% 1.54/0.57 % (24980)Time elapsed: 0.003 s
% 1.54/0.57 % (24980)Instructions burned: 4 (million)
% 1.54/0.57 % (24980)------------------------------
% 1.54/0.57 % (24980)------------------------------
% 1.54/0.58 % (24981)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 1.54/0.58 % (24981)Refutation not found, incomplete strategy
% 1.54/0.58 % (24981)------------------------------
% 1.54/0.58 % (24981)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.54/0.58 % (24981)Termination reason: Refutation not found, incomplete strategy
% 1.54/0.58
% 1.54/0.58
% 1.54/0.58 % (24981)Memory used [KB]: 5500
% 1.54/0.58 % (24981)Time elapsed: 0.004 s
% 1.54/0.58 % (24981)Instructions burned: 7 (million)
% 1.54/0.58 % (24981)------------------------------
% 1.54/0.58 % (24981)------------------------------
% 1.54/0.59 % (24982)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2997ds/127Mi)
% 1.96/0.63 % (24982)Instruction limit reached!
% 1.96/0.63 % (24982)------------------------------
% 1.96/0.63 % (24982)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.96/0.63 % (24982)Termination reason: Unknown
% 1.96/0.63 % (24982)Termination phase: Saturation
% 1.96/0.63
% 1.96/0.63 % (24982)Memory used [KB]: 6268
% 1.96/0.63 % (24982)Time elapsed: 0.066 s
% 1.96/0.63 % (24982)Instructions burned: 128 (million)
% 1.96/0.63 % (24982)------------------------------
% 1.96/0.63 % (24982)------------------------------
% 1.96/0.63 % (24969)Instruction limit reached!
% 1.96/0.63 % (24969)------------------------------
% 1.96/0.63 % (24969)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.96/0.63 % (24969)Termination reason: Unknown
% 1.96/0.63 % (24969)Termination phase: Saturation
% 1.96/0.63
% 1.96/0.63 % (24969)Memory used [KB]: 6908
% 1.96/0.63 % (24969)Time elapsed: 0.143 s
% 1.96/0.63 % (24969)Instructions burned: 379 (million)
% 1.96/0.63 % (24969)------------------------------
% 1.96/0.63 % (24969)------------------------------
% 1.96/0.64 % (24995)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2997ds/100Mi)
% 1.96/0.64 % (24997)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2997ds/3Mi)
% 1.96/0.65 % (24997)Instruction limit reached!
% 1.96/0.65 % (24997)------------------------------
% 1.96/0.65 % (24997)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.96/0.65 % (24997)Termination reason: Unknown
% 1.96/0.65 % (24997)Termination phase: Saturation
% 1.96/0.65
% 1.96/0.65 % (24997)Memory used [KB]: 5500
% 1.96/0.65 % (24997)Time elapsed: 0.003 s
% 1.96/0.65 % (24997)Instructions burned: 3 (million)
% 1.96/0.65 % (24997)------------------------------
% 1.96/0.65 % (24997)------------------------------
% 1.96/0.65 % (25002)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2997ds/20Mi)
% 1.96/0.66 % (25002)Refutation not found, incomplete strategy
% 1.96/0.66 % (25002)------------------------------
% 1.96/0.66 % (25002)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.96/0.66 % (25002)Termination reason: Refutation not found, incomplete strategy
% 1.96/0.66
% 1.96/0.66
% 1.96/0.66 % (25002)Memory used [KB]: 5500
% 1.96/0.66 % (25002)Time elapsed: 0.003 s
% 1.96/0.66 % (25002)Instructions burned: 4 (million)
% 1.96/0.66 % (25002)------------------------------
% 1.96/0.66 % (25002)------------------------------
% 2.23/0.67 % (25008)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2996ds/86Mi)
% 2.23/0.68 % (24995)Instruction limit reached!
% 2.23/0.68 % (24995)------------------------------
% 2.23/0.68 % (24995)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.23/0.68 % (24995)Termination reason: Unknown
% 2.23/0.68 % (24995)Termination phase: Saturation
% 2.23/0.68
% 2.23/0.68 % (24995)Memory used [KB]: 6012
% 2.23/0.68 % (24995)Time elapsed: 0.037 s
% 2.23/0.68 % (24995)Instructions burned: 101 (million)
% 2.23/0.68 % (24995)------------------------------
% 2.23/0.68 % (24995)------------------------------
% 2.23/0.69 % (25020)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2996ds/107Mi)
% 2.23/0.69 % (25008)Instruction limit reached!
% 2.23/0.69 % (25008)------------------------------
% 2.23/0.69 % (25008)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.23/0.69 % (25008)Termination reason: Unknown
% 2.23/0.69 % (25008)Termination phase: Saturation
% 2.23/0.69
% 2.23/0.69 % (25008)Memory used [KB]: 6268
% 2.23/0.69 % (25008)Time elapsed: 0.030 s
% 2.23/0.69 % (25008)Instructions burned: 88 (million)
% 2.23/0.69 % (25008)------------------------------
% 2.23/0.69 % (25008)------------------------------
% 2.23/0.70 % (24963)Instruction limit reached!
% 2.23/0.70 % (24963)------------------------------
% 2.23/0.70 % (24963)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.23/0.70 % (24963)Termination reason: Unknown
% 2.23/0.70 % (24963)Termination phase: Saturation
% 2.23/0.70
% 2.23/0.70 % (24963)Memory used [KB]: 8059
% 2.23/0.70 % (24963)Time elapsed: 0.251 s
% 2.23/0.70 % (24963)Instructions burned: 710 (million)
% 2.23/0.70 % (24963)------------------------------
% 2.23/0.70 % (24963)------------------------------
% 2.23/0.70 % (25027)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2996ds/39Mi)
% 2.23/0.71 % (25029)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on theBenchmark for (2996ds/448Mi)
% 2.23/0.72 % (25027)Instruction limit reached!
% 2.23/0.72 % (25027)------------------------------
% 2.23/0.72 % (25027)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.23/0.72 % (25027)Termination reason: Unknown
% 2.23/0.72 % (25027)Termination phase: Saturation
% 2.23/0.72
% 2.23/0.72 % (25027)Memory used [KB]: 6012
% 2.23/0.72 % (25027)Time elapsed: 0.015 s
% 2.23/0.72 % (25027)Instructions burned: 41 (million)
% 2.23/0.72 % (25027)------------------------------
% 2.23/0.72 % (25027)------------------------------
% 2.23/0.72 % (25020)Instruction limit reached!
% 2.23/0.72 % (25020)------------------------------
% 2.23/0.72 % (25020)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.23/0.72 % (25020)Termination reason: Unknown
% 2.23/0.72 % (25020)Termination phase: Saturation
% 2.23/0.72
% 2.23/0.72 % (25020)Memory used [KB]: 6012
% 2.23/0.72 % (25020)Time elapsed: 0.039 s
% 2.23/0.72 % (25020)Instructions burned: 108 (million)
% 2.23/0.72 % (25020)------------------------------
% 2.23/0.72 % (25020)------------------------------
% 2.23/0.73 % (25037)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2996ds/46Mi)
% 2.71/0.73 % (25042)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on theBenchmark for (2996ds/98Mi)
% 2.71/0.74 % (25037)Instruction limit reached!
% 2.71/0.74 % (25037)------------------------------
% 2.71/0.74 % (25037)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.71/0.74 % (25037)Termination reason: Unknown
% 2.71/0.74 % (25037)Termination phase: Saturation
% 2.71/0.74
% 2.71/0.74 % (25037)Memory used [KB]: 5756
% 2.71/0.74 % (25037)Time elapsed: 0.020 s
% 2.71/0.74 % (25037)Instructions burned: 48 (million)
% 2.71/0.74 % (25037)------------------------------
% 2.71/0.74 % (25037)------------------------------
% 2.71/0.75 % (25049)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on theBenchmark for (2996ds/507Mi)
% 2.71/0.76 % (24970)Instruction limit reached!
% 2.71/0.76 % (24970)------------------------------
% 2.71/0.76 % (24970)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.71/0.76 % (24970)Termination reason: Unknown
% 2.71/0.76 % (24970)Termination phase: Saturation
% 2.71/0.76
% 2.71/0.76 % (24970)Memory used [KB]: 8187
% 2.71/0.76 % (24970)Time elapsed: 0.285 s
% 2.71/0.76 % (24970)Instructions burned: 780 (million)
% 2.71/0.76 % (24970)------------------------------
% 2.71/0.76 % (24970)------------------------------
% 2.89/0.77 % (25042)Instruction limit reached!
% 2.89/0.77 % (25042)------------------------------
% 2.89/0.77 % (25042)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.89/0.77 % (25042)Termination reason: Unknown
% 2.89/0.77 % (25042)Termination phase: Saturation
% 2.89/0.77
% 2.89/0.77 % (25042)Memory used [KB]: 1279
% 2.89/0.77 % (25042)Time elapsed: 0.036 s
% 2.89/0.77 % (25042)Instructions burned: 100 (million)
% 2.89/0.77 % (25042)------------------------------
% 2.89/0.77 % (25042)------------------------------
% 2.89/0.77 % (25058)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on theBenchmark for (2995ds/149Mi)
% 2.89/0.78 % (25067)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2995ds/39Mi)
% 2.89/0.79 % (25067)Instruction limit reached!
% 2.89/0.79 % (25067)------------------------------
% 2.89/0.79 % (25067)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.89/0.79 % (25067)Termination reason: Unknown
% 2.89/0.79 % (25067)Termination phase: Saturation
% 2.89/0.79
% 2.89/0.79 % (25067)Memory used [KB]: 5756
% 2.89/0.79 % (25067)Time elapsed: 0.015 s
% 2.89/0.79 % (25067)Instructions burned: 39 (million)
% 2.89/0.79 % (25067)------------------------------
% 2.89/0.79 % (25067)------------------------------
% 2.89/0.80 % (24965)Instruction limit reached!
% 2.89/0.80 % (24965)------------------------------
% 2.89/0.80 % (24965)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.89/0.80 % (24965)Termination reason: Unknown
% 2.89/0.80 % (24965)Termination phase: Saturation
% 2.89/0.80
% 2.89/0.80 % (24965)Memory used [KB]: 7419
% 2.89/0.80 % (24965)Time elapsed: 0.335 s
% 2.89/0.80 % (24965)Instructions burned: 904 (million)
% 2.89/0.80 % (24965)------------------------------
% 2.89/0.80 % (24965)------------------------------
% 2.89/0.80 % (25082)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2995ds/6Mi)
% 2.89/0.80 % (25082)Instruction limit reached!
% 2.89/0.80 % (25082)------------------------------
% 2.89/0.80 % (25082)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.89/0.80 % (25082)Termination reason: Unknown
% 2.89/0.80 % (25082)Termination phase: Saturation
% 2.89/0.80
% 2.89/0.80 % (25082)Memory used [KB]: 9978
% 2.89/0.80 % (25082)Time elapsed: 0.005 s
% 2.89/0.80 % (25082)Instructions burned: 8 (million)
% 2.89/0.80 % (25082)------------------------------
% 2.89/0.80 % (25082)------------------------------
% 2.89/0.81 % (25088)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on theBenchmark for (2995ds/1087Mi)
% 2.89/0.81 % (24972)First to succeed.
% 2.89/0.81 % (25094)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2995ds/47Mi)
% 2.89/0.82 % (25058)Instruction limit reached!
% 2.89/0.82 % (25058)------------------------------
% 2.89/0.82 % (25058)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.89/0.82 % (25058)Termination reason: Unknown
% 2.89/0.82 % (25058)Termination phase: Saturation
% 2.89/0.82
% 2.89/0.82 % (25058)Memory used [KB]: 5884
% 2.89/0.82 % (25058)Time elapsed: 0.052 s
% 2.89/0.82 % (25058)Instructions burned: 149 (million)
% 2.89/0.82 % (25058)------------------------------
% 2.89/0.82 % (25058)------------------------------
% 2.89/0.82 % (24972)Refutation found. Thanks to Tanya!
% 2.89/0.82 % SZS status Theorem for theBenchmark
% 2.89/0.82 % SZS output start Proof for theBenchmark
% See solution above
% 2.89/0.83 % (24972)------------------------------
% 2.89/0.83 % (24972)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.89/0.83 % (24972)Termination reason: Refutation
% 2.89/0.83
% 2.89/0.83 % (24972)Memory used [KB]: 7931
% 2.89/0.83 % (24972)Time elapsed: 0.317 s
% 2.89/0.83 % (24972)Instructions burned: 722 (million)
% 2.89/0.83 % (24972)------------------------------
% 2.89/0.83 % (24972)------------------------------
% 2.89/0.83 % (24927)Success in time 0.465 s
%------------------------------------------------------------------------------