TSTP Solution File: ALG272^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n026.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 May 20 18:20:46 EDT 2024
% Result : Theorem 0.17s 0.37s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 50
% Syntax : Number of formulae : 226 ( 37 unt; 28 typ; 0 def)
% Number of atoms : 1657 ( 811 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 4125 ( 240 ~; 372 |; 191 &;2914 @)
% ( 16 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 39 usr; 28 con; 0-2 aty)
% ( 317 !!; 74 ??; 0 @@+; 0 @@-)
% Number of variables : 695 ( 495 ^ 192 !; 8 ?; 695 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(func_def_3,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_4,type,
cGRP_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_6,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_7,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_20,type,
sK0: g ).
thf(func_def_21,type,
sK1: g > g > g ).
thf(func_def_23,type,
sK3: g ).
thf(func_def_24,type,
sK4: g ).
thf(func_def_25,type,
sK5: g ).
thf(func_def_26,type,
sK6: g ).
thf(func_def_27,type,
sK7: g ).
thf(func_def_28,type,
sK8: g ).
thf(func_def_29,type,
sK9: g ).
thf(func_def_30,type,
sK10: g ).
thf(func_def_31,type,
sK11: g ).
thf(func_def_32,type,
sK12: g ).
thf(func_def_33,type,
sK13: g > g ).
thf(func_def_34,type,
sK14: g > g ).
thf(func_def_35,type,
sK15: g > g ).
thf(func_def_36,type,
sK16: g > g ).
thf(func_def_37,type,
sK17: g > g ).
thf(func_def_38,type,
sK18: g > g ).
thf(func_def_39,type,
sK19: g > g ).
thf(f577,plain,
$false,
inference(avatar_sat_refutation,[],[f220,f230,f238,f242,f281,f283,f285,f287,f340,f372,f376,f378,f410,f422,f430,f530,f575]) ).
thf(f575,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_5
| ~ spl2_9
| ~ spl2_18 ),
inference(avatar_contradiction_clause,[],[f574]) ).
thf(f574,plain,
( $false
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5
| ~ spl2_9
| ~ spl2_18 ),
inference(subsumption_resolution,[],[f571,f237]) ).
thf(f237,plain,
( ! [X1: g] :
( sK0
= ( sK1 @ ( sK17 @ X1 ) @ X1 ) )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f236]) ).
thf(f236,plain,
( spl2_9
<=> ! [X1: g] :
( sK0
= ( sK1 @ ( sK17 @ X1 ) @ X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
thf(f571,plain,
( ( sK0
!= ( sK1 @ ( sK17 @ sK12 ) @ sK12 ) )
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5
| ~ spl2_9
| ~ spl2_18 ),
inference(trivial_inequality_removal,[],[f570]) ).
thf(f570,plain,
( ( sK0
!= ( sK1 @ ( sK17 @ sK12 ) @ sK12 ) )
| ( sK0 != sK0 )
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5
| ~ spl2_9
| ~ spl2_18 ),
inference(superposition,[],[f273,f542]) ).
thf(f542,plain,
( ! [X0: g] :
( sK0
= ( sK1 @ X0 @ ( sK17 @ X0 ) ) )
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5
| ~ spl2_9 ),
inference(superposition,[],[f237,f533]) ).
thf(f533,plain,
( ! [X0: g] :
( ( sK17 @ ( sK17 @ X0 ) )
= X0 )
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5
| ~ spl2_9 ),
inference(superposition,[],[f214,f442]) ).
thf(f442,plain,
( ! [X0: g] :
( ( sK1 @ ( sK17 @ ( sK17 @ X0 ) ) @ sK0 )
= X0 )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_9 ),
inference(superposition,[],[f431,f237]) ).
thf(f431,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ ( sK17 @ X0 ) @ ( sK1 @ X0 @ X1 ) )
= X1 )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_9 ),
inference(forward_demodulation,[],[f426,f218]) ).
thf(f218,plain,
( ! [X4: g] :
( ( sK1 @ sK0 @ X4 )
= X4 )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f217]) ).
thf(f217,plain,
( spl2_5
<=> ! [X4: g] :
( ( sK1 @ sK0 @ X4 )
= X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
thf(f426,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ sK0 @ X1 )
= ( sK1 @ ( sK17 @ X0 ) @ ( sK1 @ X0 @ X1 ) ) )
| ~ spl2_1
| ~ spl2_9 ),
inference(superposition,[],[f203,f237]) ).
thf(f203,plain,
( ! [X3: g,X1: g,X4: g] :
( ( sK1 @ ( sK1 @ X4 @ X1 ) @ X3 )
= ( sK1 @ X4 @ ( sK1 @ X1 @ X3 ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f202,plain,
( spl2_1
<=> ! [X4: g,X1: g,X3: g] :
( ( sK1 @ ( sK1 @ X4 @ X1 ) @ X3 )
= ( sK1 @ X4 @ ( sK1 @ X1 @ X3 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
thf(f214,plain,
( ! [X4: g] :
( ( sK1 @ X4 @ sK0 )
= X4 )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f213,plain,
( spl2_4
<=> ! [X4: g] :
( ( sK1 @ X4 @ sK0 )
= X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
thf(f273,plain,
( ! [X2: g] :
( ( sK0
!= ( sK1 @ sK12 @ X2 ) )
| ( sK0
!= ( sK1 @ X2 @ sK12 ) ) )
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f272,plain,
( spl2_18
<=> ! [X2: g] :
( ( sK0
!= ( sK1 @ sK12 @ X2 ) )
| ( sK0
!= ( sK1 @ X2 @ sK12 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
thf(f530,plain,
( spl2_10
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f529,f233,f217,f213,f202,f240]) ).
thf(f240,plain,
( spl2_10
<=> ! [X2: g] :
( sK0
= ( sK1 @ ( sK16 @ X2 ) @ X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
thf(f233,plain,
( spl2_8
<=> ! [X2: g] :
( sK0
= ( sK1 @ X2 @ ( sK16 @ X2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
thf(f529,plain,
( ! [X0: g] :
( ( sK1 @ ( sK16 @ X0 ) @ X0 )
= sK0 )
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5
| ~ spl2_8 ),
inference(superposition,[],[f234,f452]) ).
thf(f452,plain,
( ! [X0: g] :
( ( sK16 @ ( sK16 @ X0 ) )
= X0 )
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5
| ~ spl2_8 ),
inference(superposition,[],[f358,f214]) ).
thf(f358,plain,
( ! [X0: g] :
( ( sK16 @ ( sK16 @ X0 ) )
= ( sK1 @ X0 @ sK0 ) )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_8 ),
inference(superposition,[],[f350,f234]) ).
thf(f350,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ ( sK16 @ X0 ) @ X1 ) )
= X1 )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_8 ),
inference(forward_demodulation,[],[f346,f218]) ).
thf(f346,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ ( sK16 @ X0 ) @ X1 ) )
= ( sK1 @ sK0 @ X1 ) )
| ~ spl2_1
| ~ spl2_8 ),
inference(superposition,[],[f203,f234]) ).
thf(f234,plain,
( ! [X2: g] :
( sK0
= ( sK1 @ X2 @ ( sK16 @ X2 ) ) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f430,plain,
( ~ spl2_9
| ~ spl2_19 ),
inference(avatar_contradiction_clause,[],[f429]) ).
thf(f429,plain,
( $false
| ~ spl2_9
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f428,plain,
( ( sK0 != sK0 )
| ~ spl2_9
| ~ spl2_19 ),
inference(superposition,[],[f276,f237]) ).
thf(f276,plain,
( ! [X1: g] :
( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f275]) ).
thf(f275,plain,
( spl2_19
<=> ! [X1: g] :
( sK0
!= ( sK1 @ X1 @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
thf(f422,plain,
( ~ spl2_10
| ~ spl2_19 ),
inference(avatar_contradiction_clause,[],[f421]) ).
thf(f421,plain,
( $false
| ~ spl2_10
| ~ spl2_19 ),
inference(trivial_inequality_removal,[],[f417]) ).
thf(f417,plain,
( ( sK0 != sK0 )
| ~ spl2_10
| ~ spl2_19 ),
inference(superposition,[],[f276,f241]) ).
thf(f241,plain,
( ! [X2: g] :
( sK0
= ( sK1 @ ( sK16 @ X2 ) @ X2 ) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f240]) ).
thf(f410,plain,
( ~ spl2_8
| ~ spl2_10
| ~ spl2_18 ),
inference(avatar_contradiction_clause,[],[f409]) ).
thf(f409,plain,
( $false
| ~ spl2_8
| ~ spl2_10
| ~ spl2_18 ),
inference(subsumption_resolution,[],[f398,f241]) ).
thf(f398,plain,
( ( sK0
!= ( sK1 @ ( sK16 @ sK12 ) @ sK12 ) )
| ~ spl2_8
| ~ spl2_18 ),
inference(trivial_inequality_removal,[],[f395]) ).
thf(f395,plain,
( ( sK0
!= ( sK1 @ ( sK16 @ sK12 ) @ sK12 ) )
| ( sK0 != sK0 )
| ~ spl2_8
| ~ spl2_18 ),
inference(superposition,[],[f273,f234]) ).
thf(f378,plain,
( ~ spl2_5
| spl2_17 ),
inference(avatar_contradiction_clause,[],[f377]) ).
thf(f377,plain,
( $false
| ~ spl2_5
| spl2_17 ),
inference(subsumption_resolution,[],[f270,f218]) ).
thf(f270,plain,
( ( ( sK1 @ sK0 @ sK6 )
!= sK6 )
| spl2_17 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f268,plain,
( spl2_17
<=> ( ( sK1 @ sK0 @ sK6 )
= sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
thf(f376,plain,
( ~ spl2_1
| spl2_16 ),
inference(avatar_contradiction_clause,[],[f375]) ).
thf(f375,plain,
( $false
| ~ spl2_1
| spl2_16 ),
inference(subsumption_resolution,[],[f266,f203]) ).
thf(f266,plain,
( ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| spl2_16 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f264,plain,
( spl2_16
<=> ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
thf(f372,plain,
( spl2_4
| ~ spl2_1
| ~ spl2_5
| ~ spl2_8
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f357,f240,f233,f217,f202,f213]) ).
thf(f357,plain,
( ! [X0: g] :
( ( sK1 @ X0 @ sK0 )
= X0 )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_8
| ~ spl2_10 ),
inference(superposition,[],[f350,f241]) ).
thf(f340,plain,
( spl2_4
| ~ spl2_1
| ~ spl2_5
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f335,f236,f217,f202,f213]) ).
thf(f335,plain,
( ! [X0: g] :
( ( sK1 @ X0 @ sK0 )
= X0 )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_9 ),
inference(superposition,[],[f297,f299]) ).
thf(f299,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ ( sK17 @ ( sK17 @ X0 ) ) @ X1 )
= ( sK1 @ X0 @ X1 ) )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_9 ),
inference(superposition,[],[f293,f293]) ).
thf(f293,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ ( sK17 @ X0 ) @ ( sK1 @ X0 @ X1 ) )
= X1 )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_9 ),
inference(forward_demodulation,[],[f292,f218]) ).
thf(f292,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ sK0 @ X1 )
= ( sK1 @ ( sK17 @ X0 ) @ ( sK1 @ X0 @ X1 ) ) )
| ~ spl2_1
| ~ spl2_9 ),
inference(superposition,[],[f203,f237]) ).
thf(f297,plain,
( ! [X0: g] :
( ( sK1 @ ( sK17 @ ( sK17 @ X0 ) ) @ sK0 )
= X0 )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_9 ),
inference(superposition,[],[f293,f237]) ).
thf(f287,plain,
( ~ spl2_4
| spl2_15 ),
inference(avatar_contradiction_clause,[],[f286]) ).
thf(f286,plain,
( $false
| ~ spl2_4
| spl2_15 ),
inference(subsumption_resolution,[],[f262,f214]) ).
thf(f262,plain,
( ( ( sK1 @ sK6 @ sK0 )
!= sK6 )
| spl2_15 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f260,plain,
( spl2_15
<=> ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
thf(f285,plain,
( ~ spl2_5
| spl2_14 ),
inference(avatar_contradiction_clause,[],[f284]) ).
thf(f284,plain,
( $false
| ~ spl2_5
| spl2_14 ),
inference(subsumption_resolution,[],[f258,f218]) ).
thf(f258,plain,
( ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| spl2_14 ),
inference(avatar_component_clause,[],[f256]) ).
thf(f256,plain,
( spl2_14
<=> ( sK3
= ( sK1 @ sK0 @ sK3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
thf(f283,plain,
( ~ spl2_1
| spl2_20 ),
inference(avatar_contradiction_clause,[],[f282]) ).
thf(f282,plain,
( $false
| ~ spl2_1
| spl2_20 ),
inference(subsumption_resolution,[],[f280,f203]) ).
thf(f280,plain,
( ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| spl2_20 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f278,plain,
( spl2_20
<=> ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
thf(f281,plain,
( ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| ~ spl2_17
| spl2_18
| spl2_19
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f81,f278,f275,f272,f268,f264,f260,f256]) ).
thf(f81,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK0 @ sK6 )
!= sK6 )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( ( sK1 @ sK6 @ sK0 )
!= sK6 )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( sK0
!= ( sK1 @ sK12 @ X2 ) )
| ( sK0
!= ( sK1 @ X2 @ sK12 ) ) ),
inference(equality_proxy_clausification,[],[f80]) ).
thf(f80,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK6 @ sK0 )
!= sK6 )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( sK0
!= ( sK1 @ X2 @ sK12 ) )
| ( ( sK1 @ sK0 @ sK6 )
!= sK6 )
| ( $false
= ( ( sK1 @ sK12 @ X2 )
= sK0 ) )
| ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f79]) ).
thf(f79,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK0 @ sK6 )
!= sK6 )
| ( ( sK1 @ sK6 @ sK0 )
!= sK6 )
| ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| ( ( ( sK1 @ X2 @ sK12 )
= sK0 )
= $false )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( $false
= ( ( sK1 @ sK12 @ X2 )
= sK0 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) ) ),
inference(binary_proxy_clausification,[],[f78]) ).
thf(f78,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( $false
= ( ( ( sK1 @ X2 @ sK12 )
= sK0 )
& ( ( sK1 @ sK12 @ X2 )
= sK0 ) ) )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( ( sK1 @ sK0 @ sK6 )
!= sK6 )
| ( ( sK1 @ sK6 @ sK0 )
!= sK6 )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f77]) ).
thf(f77,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK1 @ sK6 @ sK0 )
= sK6 ) )
| ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ X2 @ sK12 )
= sK0 )
& ( ( sK1 @ sK12 @ X2 )
= sK0 ) ) )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( ( sK1 @ sK0 @ sK6 )
!= sK6 ) ),
inference(beta_eta_normalization,[],[f76]) ).
thf(f76,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK1 @ Y0 @ sK12 )
= sK0 )
& ( ( sK1 @ sK12 @ Y0 )
= sK0 ) )
@ X2 ) )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| ( $false
= ( ( sK1 @ sK6 @ sK0 )
= sK6 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( ( sK1 @ sK0 @ sK6 )
!= sK6 ) ),
inference(pi_clausification,[],[f75]) ).
thf(f75,plain,
! [X1: g] :
( ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ Y0 @ sK12 )
= sK0 )
& ( ( sK1 @ sK12 @ Y0 )
= sK0 ) ) ) )
| ( $false
= ( ( sK1 @ sK6 @ sK0 )
= sK6 ) )
| ( ( sK1 @ sK0 @ sK6 )
!= sK6 )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f74]) ).
thf(f74,plain,
! [X1: g] :
( ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( $false
= ( ( sK1 @ sK0 @ sK6 )
= sK6 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ Y0 @ sK12 )
= sK0 )
& ( ( sK1 @ sK12 @ Y0 )
= sK0 ) ) ) )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) ),
inference(binary_proxy_clausification,[],[f73]) ).
thf(f73,plain,
! [X1: g] :
( ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ Y0 @ sK12 )
= sK0 )
& ( ( sK1 @ sK12 @ Y0 )
= sK0 ) ) ) )
| ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
!= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f72]) ).
thf(f72,plain,
! [X1: g] :
( ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
= $false )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ Y0 @ sK12 )
= sK0 )
& ( ( sK1 @ sK12 @ Y0 )
= sK0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f71]) ).
thf(f71,plain,
! [X1: g] :
( ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
= $false )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) )
@ sK12 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) ) ),
inference(sigma_clausification,[],[f70]) ).
thf(f70,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( ( ( sK1 @ sK11 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ sK11 @ sK5 ) @ sK9 ) )
= $false )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) ) ),
inference(beta_eta_normalization,[],[f69]) ).
thf(f69,plain,
! [X1: g] :
( ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK5 ) @ sK9 ) )
@ sK11 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) ) ),
inference(sigma_clausification,[],[f68]) ).
thf(f68,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK5 ) @ sK9 ) ) ) )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( sK0
!= ( sK1 @ X1 @ sK4 ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f67]) ).
thf(f67,plain,
! [X1: g] :
( ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 )
!= ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK5 ) @ sK9 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f66]) ).
thf(f66,plain,
! [X1: g] :
( ( $false
= ( ( sK1 @ sK10 @ ( sK1 @ sK7 @ sK8 ) )
= ( sK1 @ ( sK1 @ sK10 @ sK7 ) @ sK8 ) ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK5 ) @ sK9 ) ) ) ) ),
inference(beta_eta_normalization,[],[f65]) ).
thf(f65,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK5 ) @ sK9 ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK7 @ sK8 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK7 ) @ sK8 ) )
@ sK10 ) ) ),
inference(sigma_clausification,[],[f64]) ).
thf(f64,plain,
! [X1: g] :
( ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK7 @ sK8 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK7 ) @ sK8 ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK5 @ sK9 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK5 ) @ sK9 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false ) ),
inference(beta_eta_normalization,[],[f63]) ).
thf(f63,plain,
! [X1: g] :
( ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK5 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK5 ) @ Y0 ) ) )
@ sK9 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK7 @ sK8 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK7 ) @ sK8 ) ) )
= $false ) ),
inference(sigma_clausification,[],[f62]) ).
thf(f62,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK5 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK5 ) @ Y0 ) ) ) ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ sK7 @ sK8 ) )
= ( sK1 @ ( sK1 @ Y0 @ sK7 ) @ sK8 ) ) )
= $false )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false ) ),
inference(beta_eta_normalization,[],[f61]) ).
thf(f61,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK7 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK7 ) @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK5 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK5 ) @ Y0 ) ) ) ) ) ),
inference(sigma_clausification,[],[f60]) ).
thf(f60,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK7 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK7 ) @ Y0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK5 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK5 ) @ Y0 ) ) ) ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) ) ),
inference(beta_eta_normalization,[],[f59]) ).
thf(f59,plain,
! [X1: g] :
( ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK5 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK5 ) @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) )
@ sK7 ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) ) ),
inference(sigma_clausification,[],[f58]) ).
thf(f58,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK0 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK0 )
= sK6 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK5 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK5 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f57]) ).
thf(f57,plain,
! [X1: g] :
( ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK5 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK5 ) @ Y0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) )
@ sK6 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false ) ),
inference(sigma_clausification,[],[f56]) ).
thf(f56,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK5 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK5 ) @ Y0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false ) ),
inference(binary_proxy_clausification,[],[f55]) ).
thf(f55,plain,
! [X1: g] :
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ sK5 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ sK5 ) @ Y0 ) ) ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false ) ),
inference(beta_eta_normalization,[],[f54]) ).
thf(f54,plain,
! [X1: g] :
( ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) )
@ sK5 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(sigma_clausification,[],[f53]) ).
thf(f53,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( ( ( sK1 @ X1 @ sK4 )
= sK0 )
= $false )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) ) ),
inference(beta_eta_normalization,[],[f52]) ).
thf(f52,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK4 )
= sK0 )
@ X1 ) ) ),
inference(pi_clausification,[],[f51]) ).
thf(f51,plain,
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK4 )
= sK0 ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f50]) ).
thf(f50,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) )
@ sK4 ) ) ),
inference(sigma_clausification,[],[f49]) ).
thf(f49,plain,
( ( sK3
!= ( sK1 @ sK0 @ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f48]) ).
thf(f48,plain,
( ( ( ( sK1 @ sK0 @ sK3 )
= sK3 )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f47]) ).
thf(f47,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( ( ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 )
@ sK3 )
= $false ) ),
inference(sigma_clausification,[],[f46]) ).
thf(f46,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f45]) ).
thf(f45,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f43]) ).
thf(f43,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f41,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
!= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y5 @ Y4 )
= Y3 )
& ( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) ) )
@ Y0
@ Y1 ) )
@ sK1
@ sK0 )
!= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 ) ) ) ) )
@ Y0 ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[],[f37,f39,f38]) ).
thf(f38,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y5 @ Y4 )
= Y3 )
& ( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f33,f32,f31,f35]) ).
thf(f35,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y3 @ Y2 )
= Y1 )
& ( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y3 @ Y2 )
= Y1 )
& ( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,plain,
( cGRP_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( ( X0 @ X2 @ X3 )
= X1 )
& ( ( X0 @ X3 @ X2 )
= X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( cGRP_INVERSE
= ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( ( X0 @ X1 @ X2 )
= X4 )
& ( ( X0 @ X2 @ X1 )
= X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_INVERSE_def) ).
thf(f31,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f26,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f25,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( ( X0 @ X2 @ X1 )
= X2 )
& ( ( X0 @ X1 @ X2 )
= X2 ) ) )
= cGRP_UNIT ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( ( X0 @ X1 @ X4 )
= X1 )
& ( ( X0 @ X4 @ X1 )
= X1 ) ) )
= cGRP_UNIT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_UNIT_def) ).
thf(f32,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ ( Y0 @ Y1 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ ( Y0 @ Y1 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f15,plain,
( ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ X1 @ ( X0 @ X3 @ X2 ) )
= ( X0 @ ( X0 @ X1 @ X3 ) @ X2 ) ) )
= cGRP_ASSOC ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: g > g > g] :
! [X1: g,X3: g,X2: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) )
= cGRP_ASSOC ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(f33,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f21,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_INVERSE @ X0 @ X1 )
& ( cGRP_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) )
= cGROUP1 ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
( ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_INVERSE @ X0 @ X4 )
& ( cGRP_UNIT @ X0 @ X4 )
& ( cGRP_ASSOC @ X0 ) ) )
= cGROUP1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP1_def) ).
thf(f39,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ ( Y2 @ Y3 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y5 @ Y3 ) @ Y4 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f30,f34,f36,f32]) ).
thf(f36,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f19,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) )
= cGRP_LEFT_UNIT ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( X0 @ X4 @ X1 )
= X1 ) )
= cGRP_LEFT_UNIT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_LEFT_UNIT_def) ).
thf(f34,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f18,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f17,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X3 @ X2 )
= X1 ) )
= cGRP_LEFT_INVERSE ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( X0 @ X2 @ X1 )
= X4 ) )
= cGRP_LEFT_INVERSE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_LEFT_INVERSE_def) ).
thf(f30,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_INVERSE @ Y0 @ Y1 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_INVERSE @ Y0 @ Y1 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_UNIT @ X0 @ X1 )
& ( cGRP_LEFT_INVERSE @ X0 @ X1 ) ) )
= cGROUP2 ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_UNIT @ X0 @ X4 )
& ( cGRP_LEFT_INVERSE @ X0 @ X4 ) ) )
= cGROUP2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP2_def) ).
thf(f37,plain,
( ( cGROUP2 @ sK1 @ sK0 )
!= ( cGROUP1 @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f29,plain,
( ( cGROUP2 @ sK1 @ sK0 )
!= ( cGROUP1 @ sK1 @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f28]) ).
thf(f28,plain,
( ? [X0: g,X1: g > g > g] :
( ( cGROUP2 @ X1 @ X0 )
!= ( cGROUP1 @ X1 @ X0 ) )
=> ( ( cGROUP2 @ sK1 @ sK0 )
!= ( cGROUP1 @ sK1 @ sK0 ) ) ),
introduced(choice_axiom,[]) ).
thf(f27,plain,
? [X0: g,X1: g > g > g] :
( ( cGROUP2 @ X1 @ X0 )
!= ( cGROUP1 @ X1 @ X0 ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f24,plain,
~ ! [X0: g,X1: g > g > g] :
( ( cGROUP2 @ X1 @ X0 )
= ( cGROUP1 @ X1 @ X0 ) ),
inference(fool_elimination,[],[f23]) ).
thf(f23,plain,
~ ! [X0: g,X1: g > g > g] :
( ( cGROUP1 @ X1 @ X0 )
<=> ( cGROUP2 @ X1 @ X0 ) ),
inference(rectify,[],[f9]) ).
thf(f9,negated_conjecture,
~ ! [X4: g,X0: g > g > g] :
( ( cGROUP1 @ X0 @ X4 )
<=> ( cGROUP2 @ X0 @ X4 ) ),
inference(negated_conjecture,[],[f8]) ).
thf(f8,conjecture,
! [X4: g,X0: g > g > g] :
( ( cGROUP1 @ X0 @ X4 )
<=> ( cGROUP2 @ X0 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_01_02) ).
thf(f242,plain,
( spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f129,f240,f236]) ).
thf(f129,plain,
! [X2: g,X1: g] :
( ( sK0
= ( sK1 @ ( sK17 @ X1 ) @ X1 ) )
| ( sK0
= ( sK1 @ ( sK16 @ X2 ) @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f128]) ).
thf(f128,plain,
! [X2: g,X1: g] :
( ( sK0
= ( sK1 @ ( sK17 @ X1 ) @ X1 ) )
| ( $true
= ( ( sK1 @ ( sK16 @ X2 ) @ X2 )
= sK0 ) ) ),
inference(binary_proxy_clausification,[],[f126]) ).
thf(f126,plain,
! [X2: g,X1: g] :
( ( sK0
= ( sK1 @ ( sK17 @ X1 ) @ X1 ) )
| ( ( ( ( sK1 @ ( sK16 @ X2 ) @ X2 )
= sK0 )
& ( ( sK1 @ X2 @ ( sK16 @ X2 ) )
= sK0 ) )
= $true ) ),
inference(equality_proxy_clausification,[],[f125]) ).
thf(f125,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK1 @ ( sK17 @ X1 ) @ X1 )
= sK0 ) )
| ( ( ( ( sK1 @ ( sK16 @ X2 ) @ X2 )
= sK0 )
& ( ( sK1 @ X2 @ ( sK16 @ X2 ) )
= sK0 ) )
= $true ) ),
inference(beta_eta_normalization,[],[f124]) ).
thf(f124,plain,
! [X2: g,X1: g] :
( ( ( ( ( sK1 @ ( sK16 @ X2 ) @ X2 )
= sK0 )
& ( ( sK1 @ X2 @ ( sK16 @ X2 ) )
= sK0 ) )
= $true )
| ( $true
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= sK0 )
@ ( sK17 @ X1 ) ) ) ),
inference(sigma_clausification,[],[f123]) ).
thf(f123,plain,
! [X2: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= sK0 ) ) )
| ( ( ( ( sK1 @ ( sK16 @ X2 ) @ X2 )
= sK0 )
& ( ( sK1 @ X2 @ ( sK16 @ X2 ) )
= sK0 ) )
= $true ) ),
inference(beta_eta_normalization,[],[f122]) ).
thf(f122,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK1 @ Y0 @ X2 )
= sK0 )
& ( ( sK1 @ X2 @ Y0 )
= sK0 ) )
@ ( sK16 @ X2 ) ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= sK0 ) ) ) ),
inference(sigma_clausification,[],[f121]) ).
thf(f121,plain,
! [X2: g,X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ Y0 @ X2 )
= sK0 )
& ( ( sK1 @ X2 @ Y0 )
= sK0 ) ) )
= $true )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= sK0 ) ) ) ),
inference(beta_eta_normalization,[],[f120]) ).
thf(f120,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) )
@ X2 ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= sK0 ) ) ) ),
inference(pi_clausification,[],[f119]) ).
thf(f119,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= sK0 ) ) ) ),
inference(beta_eta_normalization,[],[f118]) ).
thf(f118,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) )
@ X1 )
= $true )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) ) ),
inference(pi_clausification,[],[f86]) ).
thf(f86,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) )
= $true )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f85]) ).
thf(f85,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f83]) ).
thf(f83,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f42]) ).
thf(f42,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= sK0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f238,plain,
( spl2_8
| spl2_9 ),
inference(avatar_split_clause,[],[f130,f236,f233]) ).
thf(f130,plain,
! [X2: g,X1: g] :
( ( sK0
= ( sK1 @ ( sK17 @ X1 ) @ X1 ) )
| ( sK0
= ( sK1 @ X2 @ ( sK16 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f127]) ).
thf(f127,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK1 @ X2 @ ( sK16 @ X2 ) )
= sK0 ) )
| ( sK0
= ( sK1 @ ( sK17 @ X1 ) @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f126]) ).
thf(f230,plain,
( spl2_5
| spl2_5 ),
inference(avatar_split_clause,[],[f150,f217,f217]) ).
thf(f150,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK0 @ X1 )
= X1 )
| ( ( sK1 @ sK0 @ X2 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f149]) ).
thf(f149,plain,
! [X2: g,X1: g] :
( ( ( ( sK1 @ sK0 @ X2 )
= X2 )
= $true )
| ( ( sK1 @ sK0 @ X1 )
= X1 ) ),
inference(binary_proxy_clausification,[],[f147]) ).
thf(f147,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK0 @ X1 )
= X1 )
| ( ( ( ( sK1 @ sK0 @ X2 )
= X2 )
& ( ( sK1 @ X2 @ sK0 )
= X2 ) )
= $true ) ),
inference(beta_eta_normalization,[],[f146]) ).
thf(f146,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK0 @ X1 )
= X1 )
| ( ( ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[],[f145]) ).
thf(f145,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
= $true )
| ( ( sK1 @ sK0 @ X1 )
= X1 ) ),
inference(equality_proxy_clausification,[],[f135]) ).
thf(f135,plain,
! [X1: g] :
( ( $true
= ( ( sK1 @ sK0 @ X1 )
= X1 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f134]) ).
thf(f134,plain,
! [X1: g] :
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK0 @ X1 )
= X1 ) ) ),
inference(beta_eta_normalization,[],[f133]) ).
thf(f133,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 )
@ X1 )
= $true )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(pi_clausification,[],[f132]) ).
thf(f132,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 ) )
= $true )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f84]) ).
thf(f84,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ sK0 @ Y0 )
= Y0 ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f83]) ).
thf(f220,plain,
( spl2_1
| spl2_1 ),
inference(avatar_split_clause,[],[f180,f202,f202]) ).
thf(f180,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK1 @ X6 @ ( sK1 @ X4 @ X5 ) )
= ( sK1 @ ( sK1 @ X6 @ X4 ) @ X5 ) )
| ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f179]) ).
thf(f179,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( $true
= ( ( sK1 @ X6 @ ( sK1 @ X4 @ X5 ) )
= ( sK1 @ ( sK1 @ X6 @ X4 ) @ X5 ) ) )
| ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) ) ),
inference(beta_eta_normalization,[],[f178]) ).
thf(f178,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ X4 @ X5 ) )
= ( sK1 @ ( sK1 @ Y0 @ X4 ) @ X5 ) )
@ X6 ) )
| ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) ) ),
inference(pi_clausification,[],[f177]) ).
thf(f177,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ X4 @ X5 ) )
= ( sK1 @ ( sK1 @ Y0 @ X4 ) @ X5 ) ) )
= $true )
| ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) ) ),
inference(beta_eta_normalization,[],[f176]) ).
thf(f176,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ X4 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ X4 ) @ Y0 ) ) )
@ X5 )
= $true )
| ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) ) ),
inference(pi_clausification,[],[f175]) ).
thf(f175,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ X4 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ X4 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f174]) ).
thf(f174,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) )
| ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) )
@ X4 ) ) ),
inference(pi_clausification,[],[f173]) ).
thf(f173,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f171]) ).
thf(f171,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f170]) ).
thf(f170,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ( sK1 @ X3 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ X3 @ X1 ) @ X2 ) )
= $true )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f169]) ).
thf(f169,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ Y0 @ X1 ) @ X2 ) )
@ X3 ) ) ),
inference(pi_clausification,[],[f168]) ).
thf(f168,plain,
! [X2: g,X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ ( sK1 @ Y0 @ X1 ) @ X2 ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f167]) ).
thf(f167,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ X1 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ X1 ) @ Y0 ) ) )
@ X2 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(pi_clausification,[],[f166]) ).
thf(f166,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ X1 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ X1 ) @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f164]) ).
thf(f164,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
= $true )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ ( sK1 @ X1 @ Y0 ) )
= ( sK1 @ ( sK1 @ Y1 @ X1 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f163]) ).
thf(f163,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) )
@ X1 )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
= $true ) ),
inference(pi_clausification,[],[f82]) ).
thf(f82,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ ( sK1 @ Y0 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK0 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y1 @ Y0 )
= sK0 )
& ( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.05/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat May 18 22:36:52 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 This is a TH0_THM_EQU_NAR problem
% 0.10/0.32 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.33 % (12239)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)
% 0.10/0.33 % (12240)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.10/0.33 % (12241)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)
% 0.10/0.33 % (12234)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.10/0.33 % (12237)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.10/0.33 % (12235)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)
% 0.10/0.33 % (12238)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)
% 0.10/0.33 % (12236)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)
% 0.10/0.34 % (12237)Instruction limit reached!
% 0.10/0.34 % (12237)------------------------------
% 0.10/0.34 % (12237)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.34 % (12237)Termination reason: Unknown
% 0.10/0.34 % (12237)Termination phase: Function definition elimination
% 0.10/0.34 % (12238)Instruction limit reached!
% 0.10/0.34 % (12238)------------------------------
% 0.10/0.34 % (12238)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.34 % (12238)Termination reason: Unknown
% 0.10/0.34 % (12238)Termination phase: Function definition elimination
% 0.10/0.34
% 0.10/0.34 % (12238)Memory used [KB]: 1023
% 0.10/0.34 % (12238)Time elapsed: 0.003 s
% 0.10/0.34 % (12238)Instructions burned: 3 (million)
% 0.10/0.34 % (12238)------------------------------
% 0.10/0.34 % (12238)------------------------------
% 0.10/0.34
% 0.10/0.34 % (12237)Memory used [KB]: 1023
% 0.10/0.34 % (12237)Time elapsed: 0.003 s
% 0.10/0.34 % (12237)Instructions burned: 3 (million)
% 0.10/0.34 % (12237)------------------------------
% 0.10/0.34 % (12237)------------------------------
% 0.10/0.34 % (12241)Instruction limit reached!
% 0.10/0.34 % (12241)------------------------------
% 0.10/0.34 % (12241)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.34 % (12241)Termination reason: Unknown
% 0.10/0.34 % (12241)Termination phase: Saturation
% 0.10/0.34
% 0.10/0.34 % (12241)Memory used [KB]: 5500
% 0.10/0.34 % (12241)Time elapsed: 0.003 s
% 0.10/0.34 % (12241)Instructions burned: 4 (million)
% 0.10/0.34 % (12241)------------------------------
% 0.10/0.34 % (12241)------------------------------
% 0.10/0.34 % (12235)Instruction limit reached!
% 0.10/0.34 % (12235)------------------------------
% 0.10/0.34 % (12235)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.34 % (12235)Termination reason: Unknown
% 0.10/0.34 % (12235)Termination phase: Saturation
% 0.10/0.34
% 0.10/0.34 % (12235)Memory used [KB]: 5500
% 0.10/0.34 % (12235)Time elapsed: 0.004 s
% 0.10/0.34 % (12235)Instructions burned: 4 (million)
% 0.10/0.34 % (12235)------------------------------
% 0.10/0.34 % (12235)------------------------------
% 0.10/0.34 % (12240)Instruction limit reached!
% 0.10/0.34 % (12240)------------------------------
% 0.10/0.34 % (12240)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.34 % (12240)Termination reason: Unknown
% 0.10/0.34 % (12240)Termination phase: Saturation
% 0.10/0.34
% 0.10/0.34 % (12240)Memory used [KB]: 5628
% 0.10/0.34 % (12240)Time elapsed: 0.011 s
% 0.10/0.34 % (12240)Instructions burned: 19 (million)
% 0.10/0.34 % (12240)------------------------------
% 0.10/0.34 % (12240)------------------------------
% 0.10/0.35 % (12236)Instruction limit reached!
% 0.10/0.35 % (12236)------------------------------
% 0.10/0.35 % (12236)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.35 % (12236)Termination reason: Unknown
% 0.10/0.35 % (12236)Termination phase: Saturation
% 0.10/0.35
% 0.10/0.35 % (12236)Memory used [KB]: 5756
% 0.10/0.35 % (12236)Time elapsed: 0.015 s
% 0.10/0.35 % (12236)Instructions burned: 27 (million)
% 0.10/0.35 % (12236)------------------------------
% 0.10/0.35 % (12236)------------------------------
% 0.10/0.35 % (12243)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)
% 0.10/0.35 % (12242)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)
% 0.10/0.35 % (12244)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)
% 0.10/0.35 % (12245)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)
% 0.10/0.35 % (12244)Instruction limit reached!
% 0.10/0.35 % (12244)------------------------------
% 0.10/0.35 % (12244)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.35 % (12244)Termination reason: Unknown
% 0.10/0.35 % (12244)Termination phase: Property scanning
% 0.10/0.35
% 0.10/0.35 % (12244)Memory used [KB]: 1023
% 0.10/0.35 % (12244)Time elapsed: 0.003 s
% 0.10/0.35 % (12244)Instructions burned: 4 (million)
% 0.10/0.35 % (12244)------------------------------
% 0.10/0.35 % (12244)------------------------------
% 0.10/0.36 % (12243)Instruction limit reached!
% 0.10/0.36 % (12243)------------------------------
% 0.10/0.36 % (12243)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.36 % (12243)Termination reason: Unknown
% 0.10/0.36 % (12243)Termination phase: Saturation
% 0.10/0.36
% 0.10/0.36 % (12243)Memory used [KB]: 5500
% 0.10/0.36 % (12243)Time elapsed: 0.009 s
% 0.10/0.36 % (12243)Instructions burned: 16 (million)
% 0.10/0.36 % (12243)------------------------------
% 0.10/0.36 % (12243)------------------------------
% 0.10/0.36 % (12246)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.10/0.36 % (12246)Instruction limit reached!
% 0.10/0.36 % (12246)------------------------------
% 0.10/0.36 % (12246)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.36 % (12246)Termination reason: Unknown
% 0.10/0.36 % (12246)Termination phase: Saturation
% 0.10/0.36
% 0.10/0.36 % (12246)Memory used [KB]: 1023
% 0.10/0.36 % (12246)Time elapsed: 0.005 s
% 0.10/0.36 % (12246)Instructions burned: 8 (million)
% 0.10/0.36 % (12246)------------------------------
% 0.10/0.36 % (12246)------------------------------
% 0.10/0.36 % (12247)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.10/0.36 % (12239)First to succeed.
% 0.10/0.36 % (12248)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)
% 0.10/0.36 % (12248)Instruction limit reached!
% 0.10/0.36 % (12248)------------------------------
% 0.10/0.36 % (12248)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.36 % (12248)Termination reason: Unknown
% 0.10/0.36 % (12248)Termination phase: SInE selection
% 0.10/0.36
% 0.10/0.37 % (12248)Memory used [KB]: 895
% 0.10/0.37 % (12248)Time elapsed: 0.003 s
% 0.10/0.37 % (12248)Instructions burned: 3 (million)
% 0.10/0.37 % (12248)------------------------------
% 0.10/0.37 % (12248)------------------------------
% 0.17/0.37 % (12242)Instruction limit reached!
% 0.17/0.37 % (12242)------------------------------
% 0.17/0.37 % (12242)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (12242)Termination reason: Unknown
% 0.17/0.37 % (12242)Termination phase: Saturation
% 0.17/0.37
% 0.17/0.37 % (12242)Memory used [KB]: 5628
% 0.17/0.37 % (12242)Time elapsed: 0.020 s
% 0.17/0.37 % (12242)Instructions burned: 38 (million)
% 0.17/0.37 % (12242)------------------------------
% 0.17/0.37 % (12242)------------------------------
% 0.17/0.37 % (12249)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)
% 0.17/0.37 % (12249)Instruction limit reached!
% 0.17/0.37 % (12249)------------------------------
% 0.17/0.37 % (12249)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (12249)Termination reason: Unknown
% 0.17/0.37 % (12249)Termination phase: Property scanning
% 0.17/0.37
% 0.17/0.37 % (12249)Memory used [KB]: 1023
% 0.17/0.37 % (12249)Time elapsed: 0.004 s
% 0.17/0.37 % (12249)Instructions burned: 4 (million)
% 0.17/0.37 % (12249)------------------------------
% 0.17/0.37 % (12249)------------------------------
% 0.17/0.37 % (12247)Instruction limit reached!
% 0.17/0.37 % (12247)------------------------------
% 0.17/0.37 % (12247)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (12247)Termination reason: Unknown
% 0.17/0.37 % (12247)Termination phase: Saturation
% 0.17/0.37
% 0.17/0.37 % (12247)Memory used [KB]: 5756
% 0.17/0.37 % (12247)Time elapsed: 0.011 s
% 0.17/0.37 % (12247)Instructions burned: 16 (million)
% 0.17/0.37 % (12247)------------------------------
% 0.17/0.37 % (12247)------------------------------
% 0.17/0.37 % (12239)Refutation found. Thanks to Tanya!
% 0.17/0.37 % SZS status Theorem for theBenchmark
% 0.17/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.37 % (12239)------------------------------
% 0.17/0.37 % (12239)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (12239)Termination reason: Refutation
% 0.17/0.37
% 0.17/0.37 % (12239)Memory used [KB]: 5884
% 0.17/0.37 % (12239)Time elapsed: 0.039 s
% 0.17/0.37 % (12239)Instructions burned: 61 (million)
% 0.17/0.37 % (12239)------------------------------
% 0.17/0.37 % (12239)------------------------------
% 0.17/0.37 % (12233)Success in time 0.044 s
% 0.17/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------