%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG274^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.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 : Wed Feb 25 08:37:48 AM UTC 2026
% Result : Theorem 1.09s 1.67s
% Output : Refutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 16
% Syntax : Number of formulae : 192 ( 44 unt; 0 typ; 9 def)
% Number of atoms : 1542 ( 648 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 3728 ( 202 ~; 288 |; 120 &;2616 @)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 26 usr; 19 con; 0-2 aty)
% ( 313 !!; 177 ??; 0 @@+; 0 @@-)
% Number of variables : 835 ( 575 ^; 251 !; 9 ?; 835 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGROUP4: ( g > g > g ) > $o ).
thf(func_def_3,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_4,type,
cGRP_DIVISORS: ( g > g > g ) > $o ).
thf(func_def_5,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_6,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_23,type,
sK1: g > g > g ).
thf(func_def_24,type,
sK2: g ).
thf(func_def_25,type,
sK3: g > g > g ).
thf(func_def_26,type,
sK4: g > g > g ).
thf(func_def_27,type,
sK5: g ).
thf(func_def_28,type,
sK6: g ).
thf(func_def_29,type,
sK7: g ).
thf(func_def_30,type,
sK8: g ).
thf(func_def_31,type,
sK9: g ).
thf(func_def_32,type,
sK10: g > g ).
thf(func_def_33,type,
sK11: g > g ).
thf(f1491,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f109,f113,f129,f138,f212,f213,f223,f305,f418,f428,f438,f442,f449,f1490]) ).
thf(f1490,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f1489]) ).
thf(f1489,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(equality_resolution,[status(thm)],[f1472]) ).
thf(f1472,plain,
( ! [X0: g,X1: g] :
( ( sK3 @ X0 @ X0 )
!= X1 )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f591,f73]) ).
thf(f73,plain,
( ! [X2: g,X3: g] :
( ( sK1 @ X2 @ ( sK3 @ X3 @ X2 ) )
= X3 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl0_1
<=> ! [X2: g,X3: g] :
( ( sK1 @ X2 @ ( sK3 @ X3 @ X2 ) )
= X3 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f591,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ ( sK11 @ ( sK3 @ X0 @ X0 ) ) @ X1 )
!= ( sK3 @ X0 @ X0 ) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f590]) ).
thf(f590,plain,
( ! [X0: g,X1: g] :
( ( ( sK1 @ ( sK11 @ ( sK3 @ X0 @ X0 ) ) @ X1 )
!= ( sK3 @ X0 @ X0 ) )
| ( ( sK10 @ ( sK3 @ X0 @ X0 ) )
!= ( sK10 @ ( sK3 @ X0 @ X0 ) ) ) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f207,f547]) ).
thf(f547,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK3 @ X1 @ X1 ) )
= X0 )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f476,f88]) ).
thf(f88,plain,
( ! [X2: g,X3: g] :
( ( sK1 @ ( sK4 @ X3 @ X2 ) @ X2 )
= X3 )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl0_3
<=> ! [X2: g,X3: g] :
( ( sK1 @ ( sK4 @ X3 @ X2 ) @ X2 )
= X3 ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f476,plain,
( ! [X2: g,X0: g,X1: g] :
( ( sK1 @ X2 @ ( sK3 @ X1 @ X0 ) )
= ( sK1 @ ( sK4 @ X2 @ X0 ) @ X1 ) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f434,f73]) ).
thf(f434,plain,
( ! [X2: g,X0: g,X1: g] :
( ( sK1 @ ( sK4 @ X0 @ X1 ) @ ( sK1 @ X1 @ X2 ) )
= ( sK1 @ X0 @ X2 ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f76,f88]) ).
thf(f76,plain,
( ! [X1: g,X4: g,X5: g] :
( ( sK1 @ ( sK1 @ X1 @ X5 ) @ X4 )
= ( sK1 @ X1 @ ( sK1 @ X5 @ X4 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f75]) ).
thf(f75,definition,
( spl0_2
<=> ! [X4: g,X5: g,X1: g] :
( ( sK1 @ ( sK1 @ X1 @ X5 ) @ X4 )
= ( sK1 @ X1 @ ( sK1 @ X5 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f207,plain,
( ! [X1: g,X4: g] :
( ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
!= ( sK10 @ X1 ) )
| ( ( sK1 @ ( sK11 @ X1 ) @ X4 )
!= X1 ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f206]) ).
thf(f206,definition,
( spl0_8
<=> ! [X4: g,X1: g] :
( ( ( sK1 @ ( sK11 @ X1 ) @ X4 )
!= X1 )
| ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
!= ( sK10 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f449,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f448]) ).
thf(f448,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(equality_resolution,[status(thm)],[f447]) ).
thf(f447,plain,
( ! [X0: g] : ( sK2 != X0 )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f445,f73]) ).
thf(f445,plain,
( ! [X0: g] :
( ( sK1 @ ( sK11 @ sK2 ) @ X0 )
!= sK2 )
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f444]) ).
thf(f444,plain,
( ! [X0: g] :
( ( ( sK1 @ ( sK11 @ sK2 ) @ X0 )
!= sK2 )
| ( ( sK10 @ sK2 )
!= ( sK10 @ sK2 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f207,f108]) ).
thf(f108,plain,
( ! [X2: g] :
( ( sK1 @ X2 @ sK2 )
= X2 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl0_4
<=> ! [X2: g] :
( ( sK1 @ X2 @ sK2 )
= X2 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f442,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f441]) ).
thf(f441,plain,
( $false
| ~ spl0_1
| ~ spl0_7 ),
inference(equality_resolution,[status(thm)],[f440]) ).
thf(f440,plain,
( ! [X0: g] : ( sK7 != X0 )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f204,f73]) ).
thf(f204,plain,
( ! [X3: g] :
( ( sK1 @ sK5 @ X3 )
!= sK7 )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f203]) ).
thf(f203,definition,
( spl0_7
<=> ! [X3: g] :
( ( sK1 @ sK5 @ X3 )
!= sK7 ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f438,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f437]) ).
thf(f437,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(equality_resolution,[status(thm)],[f436]) ).
thf(f436,plain,
( ! [X0: g] : ( sK7 != X0 )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f201,f88]) ).
thf(f201,plain,
( ! [X2: g] :
( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f200]) ).
thf(f200,definition,
( spl0_6
<=> ! [X2: g] :
( sK7
!= ( sK1 @ X2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f428,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f427]) ).
thf(f427,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f422]) ).
thf(f422,plain,
( ( sK2 != sK2 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f420,f128]) ).
thf(f128,plain,
( ! [X3: g] :
( sK2
= ( sK1 @ X3 @ ( sK3 @ sK2 @ X3 ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f127]) ).
thf(f127,definition,
( spl0_5
<=> ! [X3: g] :
( sK2
= ( sK1 @ X3 @ ( sK3 @ sK2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f420,plain,
( ! [X0: g] :
( ( sK1 @ ( sK11 @ sK2 ) @ X0 )
!= sK2 )
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f419]) ).
thf(f419,plain,
( ! [X0: g] :
( ( ( sK10 @ sK2 )
!= ( sK10 @ sK2 ) )
| ( ( sK1 @ ( sK11 @ sK2 ) @ X0 )
!= sK2 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f207,f108]) ).
thf(f418,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f417]) ).
thf(f417,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(equality_resolution,[status(thm)],[f412]) ).
thf(f412,plain,
( ! [X0: g] : ( sK7 != X0 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f401,f108]) ).
thf(f401,plain,
( ! [X1: g] :
( ( sK1 @ X1 @ sK2 )
!= sK7 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f307,f318]) ).
thf(f318,plain,
( ! [X0: g] :
( ( sK1 @ ( sK3 @ sK2 @ X0 ) @ X0 )
= sK2 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f262,f258]) ).
thf(f258,plain,
( ! [X0: g] :
( ( sK1 @ sK2 @ ( sK3 @ sK2 @ ( sK3 @ sK2 @ X0 ) ) )
= X0 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f245,f108]) ).
thf(f245,plain,
( ! [X0: g] :
( ( sK1 @ sK2 @ ( sK3 @ sK2 @ ( sK3 @ sK2 @ X0 ) ) )
= ( sK1 @ X0 @ sK2 ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f215,f128]) ).
thf(f215,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ ( sK3 @ sK2 @ X0 ) @ X1 ) )
= ( sK1 @ sK2 @ X1 ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f76,f128]) ).
thf(f262,plain,
( ! [X0: g] :
( sK2
= ( sK1 @ X0 @ ( sK1 @ sK2 @ ( sK3 @ sK2 @ X0 ) ) ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f218,f108]) ).
thf(f218,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ X1 @ ( sK3 @ sK2 @ ( sK1 @ X0 @ X1 ) ) ) )
= sK2 )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f76,f128]) ).
thf(f307,plain,
( ! [X2: g,X0: g,X1: g] :
( sK7
!= ( sK1 @ X2 @ ( sK1 @ X0 @ ( sK1 @ X1 @ sK5 ) ) ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f306,f76]) ).
thf(f306,plain,
( ! [X0: g,X1: g] :
( sK7
!= ( sK1 @ X0 @ ( sK1 @ X1 @ sK5 ) ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f201,f76]) ).
thf(f305,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f304]) ).
thf(f304,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(equality_resolution,[status(thm)],[f300]) ).
thf(f300,plain,
( ! [X0: g] : ( sK7 != X0 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f253,f258]) ).
thf(f253,plain,
( ! [X0: g] :
( ( sK1 @ sK2 @ X0 )
!= sK7 )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f204,f215]) ).
thf(f223,plain,
( ~ spl0_2
| spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f222]) ).
thf(f222,plain,
( $false
| ~ spl0_2
| spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f219]) ).
thf(f219,plain,
( ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) ) )
| ~ spl0_2
| spl0_9 ),
inference(superposition,[status(thm)],[f211,f76]) ).
thf(f211,plain,
( ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f209]) ).
thf(f209,definition,
( spl0_9
<=> ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f213,plain,
spl0_2,
inference(avatar_split_clause,[status(thm)],[f54,f75]) ).
thf(f54,plain,
! [X2: g,X3: g,X1: g] :
( ( sK1 @ ( sK1 @ X1 @ X3 ) @ X2 )
= ( sK1 @ X1 @ ( sK1 @ X3 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ ( sK1 @ X1 @ X3 ) @ X2 )
= ( sK1 @ X1 @ ( sK1 @ X3 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: g,X3: g,X1: g] :
( ( ^ [Y0: g] :
( ( sK1 @ ( sK1 @ X1 @ Y0 ) @ X2 )
= ( sK1 @ X1 @ ( sK1 @ Y0 @ X2 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: g,X1: g] :
( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ X1 @ Y0 ) @ X2 )
= ( sK1 @ X1 @ ( sK1 @ Y0 @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: g,X1: g] :
( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ X1 @ Y1 ) @ Y0 )
= ( sK1 @ X1 @ ( sK1 @ Y1 @ Y0 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: g] :
( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ X1 @ Y1 ) @ Y0 )
= ( sK1 @ X1 @ ( sK1 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(duplicate_literal_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( ^ [Y0: g] :
( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y3 ) @ Y2 )
= ( sK1 @ Y1 @ ( sK1 @ Y3 @ Y2 ) ) ) ) ) ) )
@ sK2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y3 ) @ Y2 )
= ( sK1 @ Y1 @ ( sK1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ?? @ g
@ ^ [Y0: g] :
( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y3 ) @ Y2 )
= ( sK1 @ Y1 @ ( sK1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( $false
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y3 ) @ Y2 )
= ( sK1 @ Y1 @ ( sK1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
= ( ^ [Y0: g > g > g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y4 ) @ Y3 )
= ( Y0 @ Y2 @ ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ Y3 )
= Y2 ) )
& ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y1 )
= Y2 ) ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( $false
= ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y4 ) @ Y3 )
= ( Y0 @ Y2 @ ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ Y3 )
= Y2 ) )
& ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y1 )
= Y2 ) ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y4 ) @ Y3 )
= ( Y0 @ Y2 @ ( Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ Y3 )
= Y2 ) )
& ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y1 )
= Y2 ) ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ^ [Y2: g > g > g,Y3: g] :
( ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ?? @ g
@ ^ [Y7: g] :
( ( Y4 @ Y6 @ Y7 )
= Y5 ) ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ( Y4 @ Y6 @ Y5 )
= Y6 ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g] :
( !! @ g
@ ^ [Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( !! @ g
@ ^ [Y7: g] :
( ( Y4 @ ( Y4 @ Y5 @ Y7 ) @ Y6 )
= ( Y4 @ Y5 @ ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
@ Y2 ) )
@ Y0
@ Y1 ) )
= ( ^ [Y1: g > g > g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y3 @ Y5 )
= Y4 ) )
& ( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y3 )
= Y4 ) ) ) ) )
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y3 @ Y5 ) @ Y4 )
= ( Y2 @ Y3 @ ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
@ Y1 ) )
@ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f26,f31,f32]) ).
thf(f32,plain,
( cGROUP4
= ( ^ [Y0: g > g > g] :
( ( ^ [Y1: g > g > g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( ?? @ g
@ ^ [Y4: g] :
( ( Y1 @ Y2 @ Y4 )
= Y3 ) )
& ( ?? @ g
@ ^ [Y4: g] :
( ( Y1 @ Y4 @ Y2 )
= Y3 ) ) ) ) )
@ Y0 )
& ( ^ [Y1: g > g > g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y1 @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ Y2 @ ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f30,f29]) ).
thf(f29,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X3 @ X1 ) @ X2 )
= ( X0 @ X3 @ ( X0 @ X1 @ X2 ) ) ) )
= cGRP_ASSOC ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: g > g > g] :
! [X2: g,X3: g,X1: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) )
= cGRP_ASSOC ),
file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGRP_ASSOC_def) ).
thf(f30,plain,
( cGRP_DIVISORS
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ Y3 )
= Y2 ) )
& ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y1 )
= Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( cGRP_DIVISORS
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ Y3 )
= Y2 ) )
& ( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y1 )
= Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( cGRP_DIVISORS
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g] :
( ? [X3: g] :
( ( X0 @ X3 @ X2 )
= X1 )
& ? [X4: g] :
( ( X0 @ X2 @ X4 )
= X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( cGRP_DIVISORS
= ( ^ [X0: g > g > g] :
! [X2: g,X1: g] :
( ? [X5: g] :
( ( X0 @ X5 @ X1 )
= X2 )
& ? [X4: g] :
( ( X0 @ X1 @ X4 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGRP_DIVISORS_def) ).
thf(f24,plain,
( cGROUP4
= ( ^ [Y0: g > g > g] :
( ( cGRP_DIVISORS @ Y0 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( cGROUP4
= ( ^ [Y0: g > g > g] :
( ( cGRP_DIVISORS @ Y0 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( cGROUP4
= ( ^ [X0: g > g > g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_DIVISORS @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( cGROUP4
= ( ^ [X0: g > g > g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_DIVISORS @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGROUP4_def) ).
thf(f31,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y3 @ Y5 ) @ Y4 )
= ( Y2 @ Y3 @ ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f25,f27,f29]) ).
thf(f27,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) )
= cGRP_RIGHT_UNIT ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: g > g > g,X6: g] :
! [X1: g] :
( ( X0 @ X1 @ X6 )
= X1 ) )
= cGRP_RIGHT_UNIT ),
file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGRP_RIGHT_UNIT_def) ).
thf(f25,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X0: g > g > g,X6: g] :
! [X1: g] :
? [X2: g] :
( ( X0 @ X1 @ X2 )
= X6 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGRP_RIGHT_INVERSE_def) ).
thf(f28,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 )
& ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( cGROUP3
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( cGROUP3
= ( ^ [X0: g > g > g,X6: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X6 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGROUP3_def) ).
thf(f26,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( ( ?? @ g
@ ^ [Y1: g] : ( cGROUP3 @ Y0 @ Y1 ) )
= ( cGROUP4 @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( ( ?? @ g
@ ^ [Y1: g] : ( cGROUP3 @ Y0 @ Y1 ) )
= ( cGROUP4 @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
~ ! [X0: g > g > g] :
( ? [X1: g] : ( cGROUP3 @ X0 @ X1 )
<=> ( cGROUP4 @ X0 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ! [X0: g > g > g] :
( ? [X6: g] : ( cGROUP3 @ X0 @ X6 )
<=> ( cGROUP4 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
! [X0: g > g > g] :
( ? [X6: g] : ( cGROUP3 @ X0 @ X6 )
<=> ( cGROUP4 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cEQUIV_03_04) ).
thf(f212,plain,
( spl0_6
| spl0_7
| spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f198,f209,f206,f203,f200]) ).
thf(f198,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( sK1 @ sK5 @ X3 )
!= sK7 )
| ( ( sK1 @ ( sK11 @ X1 ) @ X4 )
!= X1 )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
!= ( sK10 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f197]) ).
thf(f197,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( $false
= ( ( sK1 @ ( sK11 @ X1 ) @ X4 )
= X1 ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| ( ( sK1 @ sK5 @ X3 )
!= sK7 )
| ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
!= ( sK10 @ X1 ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f196]) ).
thf(f196,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( sK1 @ sK5 @ X3 )
!= sK7 )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
!= ( sK10 @ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ ( sK11 @ X1 ) @ Y0 )
= X1 )
@ X4 ) ) ),
inference(pi_clausification,[status(thm)],[f195]) ).
thf(f195,plain,
! [X2: g,X3: g,X1: g] :
( ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK11 @ X1 ) @ Y0 )
= X1 ) ) )
| ( ( sK1 @ sK5 @ X3 )
!= sK7 )
| ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
!= ( sK10 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f194]) ).
thf(f194,plain,
! [X2: g,X3: g,X1: g] :
( ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
!= ( sK10 @ X1 ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| ( $false
= ( ( sK1 @ sK5 @ X3 )
= sK7 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK11 @ X1 ) @ Y0 )
= X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f193]) ).
thf(f193,plain,
! [X2: g,X3: g,X1: g] :
( ( $false
= ( ( sK1 @ sK5 @ X3 )
= sK7 ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
!= ( sK10 @ X1 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) )
@ ( sK11 @ X1 ) ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) ) ),
inference(sigma_clausification,[status(thm)],[f192]) ).
thf(f192,plain,
! [X2: g,X3: g,X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) ) )
| ( $false
= ( ( sK1 @ sK5 @ X3 )
= sK7 ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
!= ( sK10 @ X1 ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
! [X2: g,X3: g,X1: g] :
( ( $false
= ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
= ( sK10 @ X1 ) ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) ) )
| ( $false
= ( ( sK1 @ sK5 @ X3 )
= sK7 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f190]) ).
thf(f190,plain,
! [X2: g,X3: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 )
@ X3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) ) )
| ( $false
= ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
= ( sK10 @ X1 ) ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) ) ),
inference(pi_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
! [X2: g,X1: g] :
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( $false
= ( ( sK1 @ ( sK10 @ X1 ) @ X1 )
= ( sK10 @ X1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f188]) ).
thf(f188,plain,
! [X2: g,X1: g] :
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 )
@ ( sK10 @ X1 ) ) )
| ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) ) ),
inference(sigma_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) )
!= ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 )
= ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( sK7
!= ( sK1 @ X2 @ sK5 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f185]) ).
thf(f185,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK1 @ X2 @ sK5 )
= sK7 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( $false
= ( ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 )
= ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( $false
= ( ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 )
= ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) ) ) )
| ( $false
= ( ( sK1 @ X2 @ sK5 )
= sK7 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f183]) ).
thf(f183,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 )
@ X2 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( $false
= ( ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 )
= ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
! [X1: g] :
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 ) ) )
| ( $false
= ( ( sK1 @ ( sK1 @ sK6 @ sK9 ) @ sK8 )
= ( sK1 @ sK6 @ ( sK1 @ sK9 @ sK8 ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f181]) ).
thf(f181,plain,
! [X1: g] :
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y0 ) @ sK8 )
= ( sK1 @ sK6 @ ( sK1 @ Y0 @ sK8 ) ) )
@ sK9 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y0 ) @ sK8 )
= ( sK1 @ sK6 @ ( sK1 @ Y0 @ sK8 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f179]) ).
thf(f179,plain,
! [X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) )
@ sK8 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f178]) ).
thf(f178,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
! [X1: g] :
( ( $false
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f176]) ).
thf(f176,plain,
! [X1: g] :
( ( $false
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f175]) ).
thf(f175,plain,
! [X1: g] :
( ( $false
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) )
@ sK6 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f174]) ).
thf(f174,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK5 @ Y0 )
= sK7 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK5 )
= sK7 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f173]) ).
thf(f173,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ sK5 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ sK5 )
= Y0 ) ) )
@ sK7 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ sK5 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ sK5 )
= Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
! [X1: g] :
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ sK5 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ sK5 )
= Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK6 @ Y1 ) @ Y0 )
= ( sK1 @ sK6 @ ( sK1 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f170]) ).
thf(f170,plain,
! [X1: g] :
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ sK5 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ sK5 )
= Y0 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) )
@ sK6 ) ) ),
inference(sigma_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ sK5 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ sK5 )
= Y0 ) ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f168]) ).
thf(f168,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) )
@ sK5 ) ) ),
inference(sigma_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= X1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f166]) ).
thf(f166,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y3 ) @ Y2 )
= ( sK1 @ Y1 @ ( sK1 @ Y3 @ Y2 ) ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y3 ) @ Y2 )
= ( sK1 @ Y1 @ ( sK1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y3 ) @ Y2 )
= ( sK1 @ Y1 @ ( sK1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f138,plain,
( spl0_5
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f137,f72,f127]) ).
thf(f137,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK3 @ X2 @ X1 ) )
= X2 )
| ( sK2
= ( sK1 @ X3 @ ( sK3 @ sK2 @ X3 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK3 @ X2 @ X1 ) )
= X2 )
| ( ( ( sK1 @ X3 @ ( sK3 @ sK2 @ X3 ) )
= sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f135]) ).
thf(f135,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK3 @ X2 @ X1 ) )
= X2 )
| ( ( ^ [Y0: g] :
( ( sK1 @ X3 @ Y0 )
= sK2 )
@ ( sK3 @ sK2 @ X3 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X3 @ Y0 )
= sK2 ) )
= $true )
| ( ( sK1 @ X1 @ ( sK3 @ X2 @ X1 ) )
= X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f133]) ).
thf(f133,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) )
@ X3 )
= $true )
| ( ( sK1 @ X1 @ ( sK3 @ X2 @ X1 ) )
= X2 ) ),
inference(pi_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK3 @ X2 @ X1 ) )
= X2 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
! [X2: g,X1: g] :
( ( ( ( sK1 @ X1 @ ( sK3 @ X2 @ X1 ) )
= X2 )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true )
| ( ( ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= X2 )
@ ( sK3 @ X2 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
! [X2: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= X2 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
! [X2: g,X1: g] :
( ( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= X2 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X2 ) ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f114]) ).
thf(f114,plain,
! [X2: g,X1: g] :
( ( ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ X1 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ X1 )
= Y0 ) ) )
@ X2 )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ X1 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ X1 )
= Y0 ) ) ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ X1 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ X1 )
= Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
! [X1: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) )
@ X1 )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ Y2 )
= Y1 ) )
& ( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 )
= ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f129,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f125,f87,f127]) ).
thf(f125,plain,
! [X2: g,X3: g,X1: g] :
( ( sK2
= ( sK1 @ X3 @ ( sK3 @ sK2 @ X3 ) ) )
| ( ( sK1 @ ( sK4 @ X2 @ X1 ) @ X1 )
= X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ( sK1 @ ( sK4 @ X2 @ X1 ) @ X1 )
= X2 )
= $true )
| ( sK2
= ( sK1 @ X3 @ ( sK3 @ sK2 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f123]) ).
thf(f123,plain,
! [X2: g,X3: g,X1: g] :
( ( sK2
= ( sK1 @ X3 @ ( sK3 @ sK2 @ X3 ) ) )
| ( ( ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X2 )
@ ( sK4 @ X2 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X2 ) )
= $true )
| ( sK2
= ( sK1 @ X3 @ ( sK3 @ sK2 @ X3 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ( sK1 @ X3 @ ( sK3 @ sK2 @ X3 ) )
= sK2 )
= $true )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X2 ) )
= $true )
| ( ( ^ [Y0: g] :
( ( sK1 @ X3 @ Y0 )
= sK2 )
@ ( sK3 @ sK2 @ X3 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X3 @ Y0 )
= sK2 ) )
= $true )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f118]) ).
thf(f118,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) )
@ X3 )
= $true )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X2 ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
! [X2: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f113,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f112,f87,f107]) ).
thf(f112,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X2 @ sK2 )
= X2 )
| ( ( sK1 @ ( sK4 @ X3 @ X1 ) @ X1 )
= X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( sK1 @ ( sK4 @ X3 @ X1 ) @ X1 )
= X3 ) )
| ( ( sK1 @ X2 @ sK2 )
= X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f110]) ).
thf(f110,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X2 @ sK2 )
= X2 )
| ( ( ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X3 )
@ ( sK4 @ X3 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X2 @ sK2 )
= X2 )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X2 @ sK2 )
= X2 )
| ( $true
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= X3 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X3 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( sK1 @ X2 @ sK2 )
= X2 ) )
| ( $true
= ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= X3 ) )
& ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ X1 )
= X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ X1 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ X1 )
= Y0 ) ) )
@ X3 ) )
| ( $true
= ( ( sK1 @ X2 @ sK2 )
= X2 ) ) ),
inference(pi_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ X1 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ X1 )
= Y0 ) ) ) )
= $true )
| ( $true
= ( ( sK1 @ X2 @ sK2 )
= X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 )
@ X2 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ X1 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ X1 )
= Y0 ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ X1 @ Y1 )
= Y0 ) )
& ( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ X1 )
= Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f109,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f105,f107,f72]) ).
thf(f105,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X2 @ sK2 )
= X2 )
| ( ( sK1 @ X1 @ ( sK3 @ X3 @ X1 ) )
= X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ( sK1 @ X1 @ ( sK3 @ X3 @ X1 ) )
= X3 )
= $true )
| ( ( sK1 @ X2 @ sK2 )
= X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f103]) ).
thf(f103,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= X3 )
@ ( sK3 @ X3 @ X1 ) )
= $true )
| ( ( sK1 @ X2 @ sK2 )
= X2 ) ),
inference(sigma_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= X3 ) )
= $true )
| ( ( sK1 @ X2 @ sK2 )
= X2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ALG274^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Mon Feb 23 22:42:40 EST 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.31 ---- Original DTF file ---
% 0.06/0.31 thf(spec,logic,$$dhol).
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 % File : ALG274^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.06/0.31 % Domain : General Algebra
% 0.06/0.31 % Problem : TPS problem from GRP-THMS
% 0.06/0.31 % Version : Especial.
% 0.06/0.31 % English :
% 0.06/0.31
% 0.06/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.06/0.31 % Source : [Bro09]
% 0.06/0.31 % Names : tps_0639 [Bro09]
% 0.06/0.31
% 0.06/0.31 % Status : Theorem
% 0.06/0.31 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.22 v7.3.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.86 v6.0.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% 0.06/0.31 % Syntax : Number of formulae : 14 ( 6 unt; 7 typ; 6 def)
% 0.06/0.31 % Number of atoms : 24 ( 11 equ; 0 cnn)
% 0.06/0.31 % Maximal formula atoms : 2 ( 3 avg)
% 0.06/0.31 % Number of connectives : 31 ( 0 ~; 0 |; 4 &; 26 @)
% 0.06/0.31 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.06/0.31 % Maximal formula depth : 6 ( 2 avg)
% 0.06/0.31 % Number of types : 2 ( 1 usr)
% 0.06/0.31 % Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% 0.06/0.31 % Number of symbols : 7 ( 6 usr; 0 con; 1-2 aty)
% 0.06/0.31 % Number of variables : 21 ( 9 ^; 8 !; 4 ?; 21 :)
% 0.06/0.31 % SPC : TH0_THM_EQU_NAR
% 0.06/0.31
% 0.06/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.06/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.06/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.06/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.06/0.31 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.06/0.31 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 thf(g_type,type,
% 0.06/0.31 g: $tType ).
% 0.06/0.31
% 0.06/0.31 thf(cGROUP3_type,type,
% 0.06/0.31 cGROUP3: ( g > g > g ) > g > $o ).
% 0.06/0.31
% 0.06/0.31 thf(cGROUP4_type,type,
% 0.06/0.31 cGROUP4: ( g > g > g ) > $o ).
% 0.06/0.31
% 0.06/0.31 thf(cGRP_ASSOC_type,type,
% 0.06/0.31 cGRP_ASSOC: ( g > g > g ) > $o ).
% 0.06/0.31
% 0.06/0.31 thf(cGRP_DIVISORS_type,type,
% 0.06/0.31 cGRP_DIVISORS: ( g > g > g ) > $o ).
% 0.06/0.31
% 0.06/0.31 thf(cGRP_RIGHT_INVERSE_type,type,
% 0.06/0.31 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 0.06/0.31
% 0.06/0.31 thf(cGRP_RIGHT_UNIT_type,type,
% 0.06/0.31 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 0.06/0.31
% 0.06/0.31 thf(cGRP_ASSOC_def,definition,
% 0.06/0.31 ( cGRP_ASSOC
% 0.06/0.31 = ( ^ [Xf: g > g > g] :
% 0.06/0.31 ! [Xa: g,Xb: g,Xc: g] :
% 0.06/0.31 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 0.06/0.31 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(cGRP_DIVISORS_def,definition,
% 0.06/0.31 ( cGRP_DIVISORS
% 0.06/0.31 = ( ^ [Xf: g > g > g] :
% 0.06/0.31 ! [Xa: g,Xb: g] :
% 0.06/0.31 ( ? [Xx: g] :
% 0.06/0.31 ( ( Xf @ Xa @ Xx )
% 0.06/0.31 = Xb )
% 0.06/0.31 & ? [Xy: g] :
% 0.06/0.31 ( ( Xf @ Xy @ Xa )
% 0.06/0.31 = Xb ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(cGRP_RIGHT_INVERSE_def,definition,
% 0.06/0.31 ( cGRP_RIGHT_INVERSE
% 0.06/0.31 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.06/0.31 ! [Xa: g] :
% 0.06/0.31 ? [Xb: g] :
% 0.06/0.31 ( ( Xf @ Xa @ Xb )
% 0.06/0.31 = Xe ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(cGRP_RIGHT_UNIT_def,definition,
% 0.06/0.31 ( cGRP_RIGHT_UNIT
% 0.06/0.31 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.06/0.31 ! [Xa: g] :
% 0.06/0.31 ( ( Xf @ Xa @ Xe )
% 0.06/0.31 = Xa ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(cGROUP3_def,definition,
% 0.06/0.31 ( cGROUP3
% 0.06/0.31 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.06/0.31 ( ( cGRP_ASSOC @ Xf )
% 0.06/0.31 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 0.06/0.31 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(cGROUP4_def,definition,
% 0.06/0.31 ( cGROUP4
% 0.06/0.31 = ( ^ [Xf: g > g > g] :
% 0.06/0.31 ( ( cGRP_ASSOC @ Xf )
% 0.06/0.31 & ( cGRP_DIVISORS @ Xf ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(cEQUIV_03_04,conjecture,
% 0.06/0.31 ! [Xf: g > g > g] :
% 0.06/0.31 ( ? [Xe: g] : ( cGROUP3 @ Xf @ Xe )
% 0.06/0.31 <=> ( cGROUP4 @ Xf ) ) ).
% 0.06/0.31
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 ------------------------
% 0.98/1.45 ---- Embedded in THF ---
% 0.98/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.98/1.46 %%% Generated on Mon Feb 23 22:42:41 EST 2026
% 0.98/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 0.98/1.46 %%% Logic specification used:
% 0.98/1.46 %%% thf(spec, logic, $$dhol).
% 0.98/1.46
% 0.98/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2DTF4007.p
% See solution above
% 0.98/1.46 ------------------------
% 0.98/1.46 ---- Cleaned THF ---
% 0.98/1.46 thf(g_type,type,
% 0.98/1.46 g: $tType ).
% 0.98/1.46
% 0.98/1.46 thf(cGROUP3_type,type,
% 0.98/1.46 cGROUP3: ( g > g > g ) > g > $o ).
% 0.98/1.46
% 0.98/1.46 thf(cGROUP4_type,type,
% 0.98/1.46 cGROUP4: ( g > g > g ) > $o ).
% 0.98/1.46
% 0.98/1.46 thf(cGRP_ASSOC_type,type,
% 0.98/1.46 cGRP_ASSOC: ( g > g > g ) > $o ).
% 0.98/1.46
% 0.98/1.46 thf(cGRP_DIVISORS_type,type,
% 0.98/1.46 cGRP_DIVISORS: ( g > g > g ) > $o ).
% 0.98/1.46
% 0.98/1.46 thf(cGRP_RIGHT_INVERSE_type,type,
% 0.98/1.46 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 0.98/1.46
% 0.98/1.46 thf(cGRP_RIGHT_UNIT_type,type,
% 0.98/1.46 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 0.98/1.46
% 0.98/1.46 thf(cGRP_ASSOC_def,definition,
% 0.98/1.46 ( cGRP_ASSOC
% 0.98/1.46 = ( ^ [Xf: g > g > g] :
% 0.98/1.46 ! [Xa: g,Xb: g,Xc: g] :
% 0.98/1.46 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 0.98/1.46 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 0.98/1.46
% 0.98/1.46 thf(cGRP_DIVISORS_def,definition,
% 0.98/1.46 ( cGRP_DIVISORS
% 0.98/1.46 = ( ^ [Xf: g > g > g] :
% 0.98/1.46 ! [Xa: g,Xb: g] :
% 0.98/1.46 ( ? [Xx: g] :
% 0.98/1.46 ( ( Xf @ Xa @ Xx )
% 0.98/1.46 = Xb )
% 0.98/1.46 & ? [Xy: g] :
% 0.98/1.46 ( ( Xf @ Xy @ Xa )
% 0.98/1.46 = Xb ) ) ) ) ).
% 0.98/1.46
% 0.98/1.46 thf(cGRP_RIGHT_INVERSE_def,definition,
% 0.98/1.46 ( cGRP_RIGHT_INVERSE
% 0.98/1.46 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.98/1.46 ! [Xa: g] :
% 0.98/1.46 ? [Xb: g] :
% 0.98/1.46 ( ( Xf @ Xa @ Xb )
% 0.98/1.46 = Xe ) ) ) ).
% 0.98/1.46
% 0.98/1.46 thf(cGRP_RIGHT_UNIT_def,definition,
% 0.98/1.46 ( cGRP_RIGHT_UNIT
% 0.98/1.46 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.98/1.46 ! [Xa: g] :
% 0.98/1.46 ( ( Xf @ Xa @ Xe )
% 0.98/1.46 = Xa ) ) ) ).
% 0.98/1.46
% 0.98/1.46 thf(cGROUP3_def,definition,
% 0.98/1.46 ( cGROUP3
% 0.98/1.46 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.98/1.46 ( ( cGRP_ASSOC @ Xf )
% 0.98/1.46 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 0.98/1.46 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.98/1.46
% 0.98/1.46 thf(cGROUP4_def,definition,
% 0.98/1.46 ( cGROUP4
% 0.98/1.46 = ( ^ [Xf: g > g > g] :
% 0.98/1.46 ( ( cGRP_ASSOC @ Xf )
% 0.98/1.46 & ( cGRP_DIVISORS @ Xf ) ) ) ) ).
% 0.98/1.46
% 0.98/1.46 thf(cEQUIV_03_04,conjecture,
% 0.98/1.46 ! [Xf: g > g > g] :
% 0.98/1.46 ( ? [Xe: g] : ( cGROUP3 @ Xf @ Xe )
% 0.98/1.46 <=> ( cGROUP4 @ Xf ) ) ).
% 0.98/1.46 ------------------------
% 0.98/1.47 % (4124)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4007 for (3000ds/2Mi)
% 0.98/1.47 % (4125)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_4007 for (3000ds/2Mi)
% 0.98/1.47 % (4123)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 DTF2THF_4007 for (3000ds/27Mi)
% 0.98/1.47 % (4121)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4007 for (3000ds/183Mi)
% 0.98/1.47 % (4127)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4007 for (3000ds/18Mi)
% 0.98/1.47 % (4122)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 DTF2THF_4007 for (3000ds/4Mi)
% 0.98/1.47 % (4126)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_4007 for (3000ds/275Mi)
% 0.98/1.48 % (4124)Instruction limit reached!
% 0.98/1.48 % (4124)------------------------------
% 0.98/1.48 % (4124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/1.48 % (4124)Termination reason: Unknown
% 0.98/1.48 % (4124)Termination phase: Property scanning
% 0.98/1.48 % (4125)Instruction limit reached!
% 0.98/1.48 % (4125)------------------------------
% 0.98/1.48 % (4125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/1.48 % (4125)Termination reason: Unknown
% 0.98/1.48 % (4125)Termination phase: Function definition elimination
% 0.98/1.48
% 0.98/1.48 % (4125)Memory used [KB]: 1023
% 0.98/1.48 % (4125)Time elapsed: 0.002 s
% 0.98/1.48 % (4125)Instructions burned: 3 (million)
% 0.98/1.48 % (4125)------------------------------
% 0.98/1.48 % (4125)------------------------------
% 0.98/1.48
% 0.98/1.48 % (4124)Memory used [KB]: 1023
% 0.98/1.48 % (4124)Time elapsed: 0.002 s
% 0.98/1.48 % (4124)Instructions burned: 2 (million)
% 0.98/1.48 % (4124)------------------------------
% 0.98/1.48 % (4124)------------------------------
% 0.98/1.48 % (4122)Instruction limit reached!
% 0.98/1.48 % (4122)------------------------------
% 0.98/1.48 % (4122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/1.48 % (4122)Termination reason: Unknown
% 0.98/1.48 % (4122)Termination phase: Saturation
% 0.98/1.48
% 0.98/1.48 % (4122)Memory used [KB]: 5500
% 0.98/1.48 % (4122)Time elapsed: 0.003 s
% 0.98/1.48 % (4122)Instructions burned: 5 (million)
% 0.98/1.48 % (4122)------------------------------
% 0.98/1.48 % (4122)------------------------------
% 0.98/1.48 % (4127)Instruction limit reached!
% 0.98/1.48 % (4127)------------------------------
% 0.98/1.48 % (4127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/1.48 % (4127)Termination reason: Unknown
% 0.98/1.48 % (4127)Termination phase: Saturation
% 0.98/1.48
% 0.98/1.48 % (4127)Memory used [KB]: 5628
% 0.98/1.48 % (4127)Time elapsed: 0.007 s
% 0.98/1.48 % (4127)Instructions burned: 18 (million)
% 0.98/1.48 % (4127)------------------------------
% 0.98/1.48 % (4127)------------------------------
% 0.98/1.48 % (4123)Instruction limit reached!
% 0.98/1.48 % (4123)------------------------------
% 0.98/1.48 % (4123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/1.48 % (4123)Termination reason: Unknown
% 0.98/1.48 % (4123)Termination phase: Saturation
% 0.98/1.48
% 0.98/1.48 % (4123)Memory used [KB]: 5756
% 0.98/1.48 % (4123)Time elapsed: 0.010 s
% 0.98/1.48 % (4123)Instructions burned: 28 (million)
% 0.98/1.48 % (4123)------------------------------
% 0.98/1.48 % (4123)------------------------------
% 0.98/1.48 % (4128)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/3Mi)
% 0.98/1.48 % (4129)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 DTF2THF_4007 for (2999ds/37Mi)
% 0.98/1.49 % (4128)Instruction limit reached!
% 0.98/1.49 % (4128)------------------------------
% 0.98/1.49 % (4128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/1.49 % (4128)Termination reason: Unknown
% 0.98/1.49 % (4128)Termination phase: Property scanning
% 0.98/1.49
% 0.98/1.49 % (4128)Memory used [KB]: 1023
% 0.98/1.49 % (4128)Time elapsed: 0.002 s
% 0.98/1.49 % (4128)Instructions burned: 4 (million)
% 0.98/1.49 % (4128)------------------------------
% 0.98/1.49 % (4128)------------------------------
% 0.98/1.49 % (4130)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 DTF2THF_4007 for (2999ds/15Mi)
% 0.98/1.49 % (4131)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/3Mi)
% 0.98/1.49 % (4130)Instruction limit reached!
% 0.98/1.49 % (4130)------------------------------
% 0.98/1.49 % (4130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/1.49 % (4130)Termination reason: Unknown
% 0.98/1.49 % (4130)Termination phase: Saturation
% 0.98/1.49
% 0.98/1.49 % (4130)Memory used [KB]: 5500
% 0.98/1.49 % (4130)Time elapsed: 0.005 s
% 0.98/1.49 % (4130)Instructions burned: 15 (million)
% 0.98/1.49 % (4130)------------------------------
% 0.98/1.49 % (4130)------------------------------
% 0.98/1.49 % (4131)Instruction limit reached!
% 0.98/1.49 % (4131)------------------------------
% 0.98/1.49 % (4131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/1.49 % (4131)Termination reason: Unknown
% 0.98/1.49 % (4131)Termination phase: Saturation
% 0.98/1.49
% 0.98/1.49 % (4131)Memory used [KB]: 1023
% 0.98/1.49 % (4131)Time elapsed: 0.002 s
% 0.98/1.49 % (4131)Instructions burned: 4 (million)
% 0.98/1.49 % (4131)------------------------------
% 0.98/1.49 % (4131)------------------------------
% 0.98/1.49 % (4132)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 DTF2THF_4007 for (2999ds/1041Mi)
% 0.98/1.50 % (4133)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/7Mi)
% 1.09/1.50 % (4129)Instruction limit reached!
% 1.09/1.50 % (4129)------------------------------
% 1.09/1.50 % (4129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.50 % (4129)Termination reason: Unknown
% 1.09/1.50 % (4129)Termination phase: Saturation
% 1.09/1.50
% 1.09/1.50 % (4129)Memory used [KB]: 5756
% 1.09/1.50 % (4129)Time elapsed: 0.013 s
% 1.09/1.50 % (4129)Instructions burned: 39 (million)
% 1.09/1.50 % (4129)------------------------------
% 1.09/1.50 % (4129)------------------------------
% 1.09/1.50 % (4133)Instruction limit reached!
% 1.09/1.50 % (4133)------------------------------
% 1.09/1.50 % (4133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.50 % (4133)Termination reason: Unknown
% 1.09/1.50 % (4133)Termination phase: Saturation
% 1.09/1.50
% 1.09/1.50 % (4133)Memory used [KB]: 1023
% 1.09/1.50 % (4133)Time elapsed: 0.003 s
% 1.09/1.50 % (4133)Instructions burned: 7 (million)
% 1.09/1.50 % (4133)------------------------------
% 1.09/1.50 % (4133)------------------------------
% 1.09/1.50 % (4134)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/16Mi)
% 1.09/1.50 % (4135)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 DTF2THF_4007 for (2999ds/3Mi)
% 1.09/1.50 % (4135)Instruction limit reached!
% 1.09/1.50 % (4135)------------------------------
% 1.09/1.50 % (4135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.50 % (4135)Termination reason: Unknown
% 1.09/1.50 % (4135)Termination phase: Property scanning
% 1.09/1.50
% 1.09/1.50 % (4135)Memory used [KB]: 1023
% 1.09/1.50 % (4135)Time elapsed: 0.002 s
% 1.09/1.50 % (4135)Instructions burned: 3 (million)
% 1.09/1.50 % (4135)------------------------------
% 1.09/1.50 % (4135)------------------------------
% 1.09/1.51 % (4134)Instruction limit reached!
% 1.09/1.51 % (4134)------------------------------
% 1.09/1.51 % (4134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.51 % (4134)Termination reason: Unknown
% 1.09/1.51 % (4134)Termination phase: Saturation
% 1.09/1.51
% 1.09/1.51 % (4134)Memory used [KB]: 5756
% 1.09/1.51 % (4134)Time elapsed: 0.007 s
% 1.09/1.51 % (4134)Instructions burned: 18 (million)
% 1.09/1.51 % (4134)------------------------------
% 1.09/1.51 % (4134)------------------------------
% 1.09/1.51 % (4136)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 DTF2THF_4007 for (2999ds/3Mi)
% 1.09/1.51 % (4137)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/7Mi)
% 1.09/1.51 % (4136)Instruction limit reached!
% 1.09/1.51 % (4136)------------------------------
% 1.09/1.51 % (4136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.51 % (4136)Termination reason: Unknown
% 1.09/1.51 % (4136)Termination phase: Property scanning
% 1.09/1.51
% 1.09/1.51 % (4136)Memory used [KB]: 1023
% 1.09/1.51 % (4136)Time elapsed: 0.002 s
% 1.09/1.51 % (4136)Instructions burned: 4 (million)
% 1.09/1.51 % (4136)------------------------------
% 1.09/1.51 % (4136)------------------------------
% 1.09/1.51 % (4137)Instruction limit reached!
% 1.09/1.51 % (4137)------------------------------
% 1.09/1.51 % (4137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.51 % (4137)Termination reason: Unknown
% 1.09/1.51 % (4137)Termination phase: Saturation
% 1.09/1.51
% 1.09/1.51 % (4137)Memory used [KB]: 5500
% 1.09/1.51 % (4137)Time elapsed: 0.003 s
% 1.09/1.51 % (4137)Instructions burned: 7 (million)
% 1.09/1.51 % (4137)------------------------------
% 1.09/1.51 % (4137)------------------------------
% 1.09/1.51 % (4138)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/3Mi)
% 1.09/1.51 % (4138)Instruction limit reached!
% 1.09/1.51 % (4138)------------------------------
% 1.09/1.51 % (4138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.51 % (4138)Termination reason: Unknown
% 1.09/1.51 % (4138)Termination phase: Saturation
% 1.09/1.51
% 1.09/1.51 % (4138)Memory used [KB]: 5500
% 1.09/1.51 % (4138)Time elapsed: 0.002 s
% 1.09/1.51 % (4138)Instructions burned: 4 (million)
% 1.09/1.51 % (4138)------------------------------
% 1.09/1.51 % (4138)------------------------------
% 1.09/1.51 % (4139)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/4Mi)
% 1.09/1.52 % (4139)Instruction limit reached!
% 1.09/1.52 % (4139)------------------------------
% 1.09/1.52 % (4139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.52 % (4139)Termination reason: Unknown
% 1.09/1.52 % (4139)Termination phase: Saturation
% 1.09/1.52
% 1.09/1.52 % (4139)Memory used [KB]: 1023
% 1.09/1.52 % (4139)Time elapsed: 0.002 s
% 1.09/1.52 % (4139)Instructions burned: 4 (million)
% 1.09/1.52 % (4139)------------------------------
% 1.09/1.52 % (4139)------------------------------
% 1.09/1.52 % (4140)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/18Mi)
% 1.09/1.52 % (4141)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/710Mi)
% 1.09/1.52 % (4142)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/6Mi)
% 1.09/1.52 % (4140)Instruction limit reached!
% 1.09/1.52 % (4140)------------------------------
% 1.09/1.52 % (4140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.52 % (4140)Termination reason: Unknown
% 1.09/1.52 % (4140)Termination phase: Saturation
% 1.09/1.52
% 1.09/1.52 % (4140)Memory used [KB]: 5628
% 1.09/1.52 % (4140)Time elapsed: 0.007 s
% 1.09/1.52 % (4140)Instructions burned: 18 (million)
% 1.09/1.52 % (4140)------------------------------
% 1.09/1.52 % (4140)------------------------------
% 1.09/1.52 % (4142)Instruction limit reached!
% 1.09/1.52 % (4142)------------------------------
% 1.09/1.52 % (4142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.52 % (4142)Termination reason: Unknown
% 1.09/1.52 % (4142)Termination phase: Saturation
% 1.09/1.52
% 1.09/1.52 % (4142)Memory used [KB]: 5500
% 1.09/1.52 % (4142)Time elapsed: 0.003 s
% 1.09/1.52 % (4142)Instructions burned: 7 (million)
% 1.09/1.52 % (4142)------------------------------
% 1.09/1.52 % (4142)------------------------------
% 1.09/1.53 % (4143)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 DTF2THF_4007 for (2999ds/902Mi)
% 1.09/1.53 % (4143)Refutation not found, incomplete strategy
% 1.09/1.53 % (4143)------------------------------
% 1.09/1.53 % (4143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.53 % (4143)Termination reason: Refutation not found, incomplete strategy
% 1.09/1.53
% 1.09/1.53
% 1.09/1.53 % (4143)Memory used [KB]: 5500
% 1.09/1.53 % (4143)Time elapsed: 0.002 s
% 1.09/1.53 % (4143)Instructions burned: 3 (million)
% 1.09/1.53 % (4143)------------------------------
% 1.09/1.53 % (4143)------------------------------
% 1.09/1.53 % (4121)Instruction limit reached!
% 1.09/1.53 % (4121)------------------------------
% 1.09/1.53 % (4121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.53 % (4121)Termination reason: Unknown
% 1.09/1.53 % (4121)Termination phase: Saturation
% 1.09/1.53
% 1.09/1.53 % (4121)Memory used [KB]: 6780
% 1.09/1.53 % (4121)Time elapsed: 0.057 s
% 1.09/1.53 % (4121)Instructions burned: 183 (million)
% 1.09/1.53 % (4121)------------------------------
% 1.09/1.53 % (4121)------------------------------
% 1.09/1.53 % (4144)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 DTF2THF_4007 for (2999ds/21Mi)
% 1.09/1.53 % (4145)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/5Mi)
% 1.09/1.53 % (4145)Instruction limit reached!
% 1.09/1.53 % (4145)------------------------------
% 1.09/1.53 % (4145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.53 % (4145)Termination reason: Unknown
% 1.09/1.53 % (4145)Termination phase: Saturation
% 1.09/1.53
% 1.09/1.53 % (4145)Memory used [KB]: 5500
% 1.09/1.53 % (4145)Time elapsed: 0.003 s
% 1.09/1.53 % (4145)Instructions burned: 7 (million)
% 1.09/1.53 % (4145)------------------------------
% 1.09/1.53 % (4145)------------------------------
% 1.09/1.54 % (4146)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 DTF2THF_4007 for (2999ds/6Mi)
% 1.09/1.54 % (4146)Instruction limit reached!
% 1.09/1.54 % (4146)------------------------------
% 1.09/1.54 % (4146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.54 % (4146)Termination reason: Unknown
% 1.09/1.54 % (4146)Termination phase: Saturation
% 1.09/1.54
% 1.09/1.54 % (4146)Memory used [KB]: 5500
% 1.09/1.54 % (4146)Time elapsed: 0.003 s
% 1.09/1.54 % (4146)Instructions burned: 7 (million)
% 1.09/1.54 % (4146)------------------------------
% 1.09/1.54 % (4146)------------------------------
% 1.09/1.54 % (4147)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/377Mi)
% 1.09/1.54 % (4144)Instruction limit reached!
% 1.09/1.54 % (4144)------------------------------
% 1.09/1.54 % (4144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.54 % (4144)Termination reason: Unknown
% 1.09/1.54 % (4144)Termination phase: Saturation
% 1.09/1.54
% 1.09/1.54 % (4144)Memory used [KB]: 5628
% 1.09/1.54 % (4144)Time elapsed: 0.009 s
% 1.09/1.54 % (4144)Instructions burned: 23 (million)
% 1.09/1.54 % (4144)------------------------------
% 1.09/1.54 % (4144)------------------------------
% 1.09/1.54 % (4148)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 DTF2THF_4007 for (2999ds/779Mi)
% 1.09/1.55 % (4149)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 DTF2THF_4007 for (2999ds/19Mi)
% 1.09/1.55 % (4150)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/879Mi)
% 1.09/1.55 % (4149)Instruction limit reached!
% 1.09/1.55 % (4149)------------------------------
% 1.09/1.55 % (4149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.55 % (4149)Termination reason: Unknown
% 1.09/1.55 % (4149)Termination phase: Saturation
% 1.09/1.55
% 1.09/1.55 % (4149)Memory used [KB]: 5628
% 1.09/1.55 % (4149)Time elapsed: 0.007 s
% 1.09/1.55 % (4149)Instructions burned: 21 (million)
% 1.09/1.55 % (4149)------------------------------
% 1.09/1.55 % (4149)------------------------------
% 1.09/1.56 % (4126)Instruction limit reached!
% 1.09/1.56 % (4126)------------------------------
% 1.09/1.56 % (4126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.56 % (4126)Termination reason: Unknown
% 1.09/1.56 % (4126)Termination phase: Saturation
% 1.09/1.56
% 1.09/1.56 % (4126)Memory used [KB]: 6396
% 1.09/1.56 % (4126)Time elapsed: 0.084 s
% 1.09/1.56 % (4126)Instructions burned: 275 (million)
% 1.09/1.56 % (4126)------------------------------
% 1.09/1.56 % (4126)------------------------------
% 1.09/1.56 % (4151)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/17Mi)
% 1.09/1.57 % (4152)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4007 for (2999ds/3Mi)
% 1.09/1.57 % (4152)Instruction limit reached!
% 1.09/1.57 % (4152)------------------------------
% 1.09/1.57 % (4152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.57 % (4152)Termination reason: Unknown
% 1.09/1.57 % (4152)Termination phase: Function definition elimination
% 1.09/1.57
% 1.09/1.57 % (4152)Memory used [KB]: 1023
% 1.09/1.57 % (4152)Time elapsed: 0.002 s
% 1.09/1.57 % (4152)Instructions burned: 3 (million)
% 1.09/1.57 % (4152)------------------------------
% 1.09/1.57 % (4152)------------------------------
% 1.09/1.57 % (4151)Instruction limit reached!
% 1.09/1.57 % (4151)------------------------------
% 1.09/1.57 % (4151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.57 % (4151)Termination reason: Unknown
% 1.09/1.57 % (4151)Termination phase: Saturation
% 1.09/1.57
% 1.09/1.57 % (4151)Memory used [KB]: 5628
% 1.09/1.57 % (4151)Time elapsed: 0.007 s
% 1.09/1.57 % (4151)Instructions burned: 19 (million)
% 1.09/1.57 % (4151)------------------------------
% 1.09/1.57 % (4151)------------------------------
% 1.09/1.58 % (4153)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_4007 for (2998ds/30Mi)
% 1.09/1.58 % (4154)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_4007 for (2998ds/127Mi)
% 1.09/1.58 % (4153)Refutation not found, incomplete strategy
% 1.09/1.58 % (4153)------------------------------
% 1.09/1.58 % (4153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.58 % (4153)Termination reason: Refutation not found, incomplete strategy
% 1.09/1.58
% 1.09/1.58
% 1.09/1.58 % (4153)Memory used [KB]: 5500
% 1.09/1.58 % (4153)Time elapsed: 0.004 s
% 1.09/1.58 % (4153)Instructions burned: 10 (million)
% 1.09/1.58 % (4153)------------------------------
% 1.09/1.58 % (4153)------------------------------
% 1.09/1.59 % (4155)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_4007 for (2998ds/100Mi)
% 1.09/1.62 % (4154)Instruction limit reached!
% 1.09/1.62 % (4154)------------------------------
% 1.09/1.62 % (4154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.62 % (4154)Termination reason: Unknown
% 1.09/1.62 % (4154)Termination phase: Saturation
% 1.09/1.62
% 1.09/1.62 % (4154)Memory used [KB]: 6012
% 1.09/1.62 % (4154)Time elapsed: 0.040 s
% 1.09/1.62 % (4154)Instructions burned: 129 (million)
% 1.09/1.62 % (4154)------------------------------
% 1.09/1.62 % (4154)------------------------------
% 1.09/1.62 % (4155)Instruction limit reached!
% 1.09/1.62 % (4155)------------------------------
% 1.09/1.62 % (4155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.62 % (4155)Termination reason: Unknown
% 1.09/1.62 % (4155)Termination phase: Saturation
% 1.09/1.62
% 1.09/1.62 % (4155)Memory used [KB]: 6012
% 1.09/1.62 % (4155)Time elapsed: 0.032 s
% 1.09/1.62 % (4155)Instructions burned: 100 (million)
% 1.09/1.62 % (4155)------------------------------
% 1.09/1.62 % (4155)------------------------------
% 1.09/1.63 % (4156)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 DTF2THF_4007 for (2998ds/3Mi)
% 1.09/1.63 % (4156)Instruction limit reached!
% 1.09/1.63 % (4156)------------------------------
% 1.09/1.63 % (4156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.63 % (4156)Termination reason: Unknown
% 1.09/1.63 % (4156)Termination phase: Property scanning
% 1.09/1.63
% 1.09/1.63 % (4156)Memory used [KB]: 1023
% 1.09/1.63 % (4156)Time elapsed: 0.002 s
% 1.09/1.63 % (4156)Instructions burned: 3 (million)
% 1.09/1.63 % (4156)------------------------------
% 1.09/1.63 % (4156)------------------------------
% 1.09/1.63 % (4157)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 DTF2THF_4007 for (2998ds/20Mi)
% 1.09/1.64 % (4158)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 DTF2THF_4007 for (2998ds/86Mi)
% 1.09/1.64 % (4157)Instruction limit reached!
% 1.09/1.64 % (4157)------------------------------
% 1.09/1.64 % (4157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.64 % (4157)Termination reason: Unknown
% 1.09/1.64 % (4157)Termination phase: Saturation
% 1.09/1.64
% 1.09/1.64 % (4157)Memory used [KB]: 5628
% 1.09/1.64 % (4157)Time elapsed: 0.008 s
% 1.09/1.64 % (4157)Instructions burned: 22 (million)
% 1.09/1.64 % (4157)------------------------------
% 1.09/1.64 % (4157)------------------------------
% 1.09/1.65 % (4159)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 DTF2THF_4007 for (2998ds/107Mi)
% 1.09/1.66 % (4147)Instruction limit reached!
% 1.09/1.66 % (4147)------------------------------
% 1.09/1.66 % (4147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.66 % (4147)Termination reason: Unknown
% 1.09/1.66 % (4147)Termination phase: Saturation
% 1.09/1.66
% 1.09/1.66 % (4147)Memory used [KB]: 7036
% 1.09/1.66 % (4147)Time elapsed: 0.121 s
% 1.09/1.66 % (4147)Instructions burned: 378 (million)
% 1.09/1.66 % (4147)------------------------------
% 1.09/1.66 % (4147)------------------------------
% 1.09/1.66 % (4158)Instruction limit reached!
% 1.09/1.66 % (4158)------------------------------
% 1.09/1.66 % (4158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.66 % (4158)Termination reason: Unknown
% 1.09/1.66 % (4158)Termination phase: Saturation
% 1.09/1.66
% 1.09/1.66 % (4158)Memory used [KB]: 6140
% 1.09/1.66 % (4158)Time elapsed: 0.028 s
% 1.09/1.66 % (4158)Instructions burned: 89 (million)
% 1.09/1.66 % (4158)------------------------------
% 1.09/1.66 % (4158)------------------------------
% 1.09/1.67 % (4148)First to succeed.
% 1.09/1.67 % (4160)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 DTF2THF_4007 for (2998ds/39Mi)
% 1.09/1.67 % (4148)Refutation found. Thanks to Tanya!
% 1.09/1.67 % SZS status Theorem for DTF2THF_4007
% 1.09/1.67 % SZS output start Proof for DTF2THF_4007
% 1.09/1.67 thf(type_def_5, type, g: $tType).
% 1.09/1.67 thf(func_def_0, type, g: $tType).
% 1.09/1.67 thf(func_def_1, type, cGROUP3: (g > g > g) > g > $o).
% 1.09/1.67 thf(func_def_2, type, cGROUP4: (g > g > g) > $o).
% 1.09/1.67 thf(func_def_3, type, cGRP_ASSOC: (g > g > g) > $o).
% 1.09/1.67 thf(func_def_4, type, cGRP_DIVISORS: (g > g > g) > $o).
% 1.09/1.67 thf(func_def_5, type, cGRP_RIGHT_INVERSE: (g > g > g) > g > $o).
% 1.09/1.67 thf(func_def_6, type, cGRP_RIGHT_UNIT: (g > g > g) > g > $o).
% 1.09/1.67 thf(func_def_23, type, sK1: g > g > g).
% 1.09/1.67 thf(func_def_24, type, sK2: g).
% 1.09/1.67 thf(func_def_25, type, sK3: g > g > g).
% 1.09/1.67 thf(func_def_26, type, sK4: g > g > g).
% 1.09/1.67 thf(func_def_27, type, sK5: g).
% 1.09/1.67 thf(func_def_28, type, sK6: g).
% 1.09/1.67 thf(func_def_29, type, sK7: g).
% 1.09/1.67 thf(func_def_30, type, sK8: g).
% 1.09/1.67 thf(func_def_31, type, sK9: g).
% 1.09/1.67 thf(func_def_32, type, sK10: g > g).
% 1.09/1.67 thf(func_def_33, type, sK11: g > g).
% 1.09/1.67 thf(f1491,plain,(
% 1.09/1.67 $false),
% 1.09/1.67 inference(avatar_sat_refutation,[status(thm)],[f109,f113,f129,f138,f212,f213,f223,f305,f418,f428,f438,f442,f449,f1490])).
% 1.09/1.67 thf(f1490,plain,(
% 1.09/1.67 ~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_8),
% 1.09/1.67 inference(avatar_contradiction_clause,[status(thm)],[f1489])).
% 1.09/1.67 thf(f1489,plain,(
% 1.09/1.67 $false | (~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_8)),
% 1.09/1.67 inference(equality_resolution,[status(thm)],[f1472])).
% 1.09/1.67 thf(f1472,plain,(
% 1.09/1.67 ( ! [X0 : g,X1 : g] : (((sK3 @ X0 @ X0) != X1)) ) | (~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_8)),
% 1.09/1.67 inference(superposition,[status(thm)],[f591,f73])).
% 1.09/1.67 thf(f73,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g] : (((sK1 @ X2 @ (sK3 @ X3 @ X2)) = X3)) ) | ~spl0_1),
% 1.09/1.67 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.09/1.67 thf(f72,definition,(
% 1.09/1.67 spl0_1 <=> ! [X2 : g,X3 : g] : ((sK1 @ X2 @ (sK3 @ X3 @ X2)) = X3)),
% 1.09/1.67 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.09/1.67 thf(f591,plain,(
% 1.09/1.67 ( ! [X0 : g,X1 : g] : (((sK1 @ (sK11 @ (sK3 @ X0 @ X0)) @ X1) != (sK3 @ X0 @ X0))) ) | (~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_8)),
% 1.09/1.67 inference(trivial_inequality_removal,[status(thm)],[f590])).
% 1.09/1.67 thf(f590,plain,(
% 1.09/1.67 ( ! [X0 : g,X1 : g] : (((sK1 @ (sK11 @ (sK3 @ X0 @ X0)) @ X1) != (sK3 @ X0 @ X0)) | ((sK10 @ (sK3 @ X0 @ X0)) != (sK10 @ (sK3 @ X0 @ X0)))) ) | (~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_8)),
% 1.09/1.67 inference(superposition,[status(thm)],[f207,f547])).
% 1.09/1.67 thf(f547,plain,(
% 1.09/1.67 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK3 @ X1 @ X1)) = X0)) ) | (~spl0_1 | ~spl0_2 | ~spl0_3)),
% 1.09/1.67 inference(superposition,[status(thm)],[f476,f88])).
% 1.09/1.67 thf(f88,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g] : (((sK1 @ (sK4 @ X3 @ X2) @ X2) = X3)) ) | ~spl0_3),
% 1.09/1.67 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.09/1.67 thf(f87,definition,(
% 1.09/1.67 spl0_3 <=> ! [X2 : g,X3 : g] : ((sK1 @ (sK4 @ X3 @ X2) @ X2) = X3)),
% 1.09/1.67 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.09/1.67 thf(f476,plain,(
% 1.09/1.67 ( ! [X2 : g,X0 : g,X1 : g] : (((sK1 @ X2 @ (sK3 @ X1 @ X0)) = (sK1 @ (sK4 @ X2 @ X0) @ X1))) ) | (~spl0_1 | ~spl0_2 | ~spl0_3)),
% 1.09/1.67 inference(superposition,[status(thm)],[f434,f73])).
% 1.09/1.67 thf(f434,plain,(
% 1.09/1.67 ( ! [X2 : g,X0 : g,X1 : g] : (((sK1 @ (sK4 @ X0 @ X1) @ (sK1 @ X1 @ X2)) = (sK1 @ X0 @ X2))) ) | (~spl0_2 | ~spl0_3)),
% 1.09/1.67 inference(superposition,[status(thm)],[f76,f88])).
% 1.09/1.67 thf(f76,plain,(
% 1.09/1.67 ( ! [X1 : g,X4 : g,X5 : g] : (((sK1 @ (sK1 @ X1 @ X5) @ X4) = (sK1 @ X1 @ (sK1 @ X5 @ X4)))) ) | ~spl0_2),
% 1.09/1.67 inference(avatar_component_clause,[status(thm)],[f75])).
% 1.09/1.67 thf(f75,definition,(
% 1.09/1.67 spl0_2 <=> ! [X4 : g,X5 : g,X1 : g] : ((sK1 @ (sK1 @ X1 @ X5) @ X4) = (sK1 @ X1 @ (sK1 @ X5 @ X4)))),
% 1.09/1.67 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.09/1.67 thf(f207,plain,(
% 1.09/1.67 ( ! [X1 : g,X4 : g] : (((sK1 @ (sK10 @ X1) @ X1) != (sK10 @ X1)) | ((sK1 @ (sK11 @ X1) @ X4) != X1)) ) | ~spl0_8),
% 1.09/1.67 inference(avatar_component_clause,[status(thm)],[f206])).
% 1.09/1.67 thf(f206,definition,(
% 1.09/1.67 spl0_8 <=> ! [X4 : g,X1 : g] : (((sK1 @ (sK11 @ X1) @ X4) != X1) | ((sK1 @ (sK10 @ X1) @ X1) != (sK10 @ X1)))),
% 1.09/1.67 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.09/1.67 thf(f449,plain,(
% 1.09/1.67 ~spl0_1 | ~spl0_4 | ~spl0_8),
% 1.09/1.67 inference(avatar_contradiction_clause,[status(thm)],[f448])).
% 1.09/1.67 thf(f448,plain,(
% 1.09/1.67 $false | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.09/1.67 inference(equality_resolution,[status(thm)],[f447])).
% 1.09/1.67 thf(f447,plain,(
% 1.09/1.67 ( ! [X0 : g] : ((sK2 != X0)) ) | (~spl0_1 | ~spl0_4 | ~spl0_8)),
% 1.09/1.67 inference(superposition,[status(thm)],[f445,f73])).
% 1.09/1.67 thf(f445,plain,(
% 1.09/1.67 ( ! [X0 : g] : (((sK1 @ (sK11 @ sK2) @ X0) != sK2)) ) | (~spl0_4 | ~spl0_8)),
% 1.09/1.67 inference(trivial_inequality_removal,[status(thm)],[f444])).
% 1.09/1.67 thf(f444,plain,(
% 1.09/1.67 ( ! [X0 : g] : (((sK1 @ (sK11 @ sK2) @ X0) != sK2) | ((sK10 @ sK2) != (sK10 @ sK2))) ) | (~spl0_4 | ~spl0_8)),
% 1.09/1.67 inference(superposition,[status(thm)],[f207,f108])).
% 1.09/1.67 thf(f108,plain,(
% 1.09/1.67 ( ! [X2 : g] : (((sK1 @ X2 @ sK2) = X2)) ) | ~spl0_4),
% 1.09/1.67 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.09/1.67 thf(f107,definition,(
% 1.09/1.67 spl0_4 <=> ! [X2 : g] : ((sK1 @ X2 @ sK2) = X2)),
% 1.09/1.67 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.09/1.67 thf(f442,plain,(
% 1.09/1.67 ~spl0_1 | ~spl0_7),
% 1.09/1.67 inference(avatar_contradiction_clause,[status(thm)],[f441])).
% 1.09/1.67 thf(f441,plain,(
% 1.09/1.67 $false | (~spl0_1 | ~spl0_7)),
% 1.09/1.67 inference(equality_resolution,[status(thm)],[f440])).
% 1.09/1.67 thf(f440,plain,(
% 1.09/1.67 ( ! [X0 : g] : ((sK7 != X0)) ) | (~spl0_1 | ~spl0_7)),
% 1.09/1.67 inference(superposition,[status(thm)],[f204,f73])).
% 1.09/1.67 thf(f204,plain,(
% 1.09/1.67 ( ! [X3 : g] : (((sK1 @ sK5 @ X3) != sK7)) ) | ~spl0_7),
% 1.09/1.67 inference(avatar_component_clause,[status(thm)],[f203])).
% 1.09/1.67 thf(f203,definition,(
% 1.09/1.67 spl0_7 <=> ! [X3 : g] : ((sK1 @ sK5 @ X3) != sK7)),
% 1.09/1.67 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.09/1.67 thf(f438,plain,(
% 1.09/1.67 ~spl0_3 | ~spl0_6),
% 1.09/1.67 inference(avatar_contradiction_clause,[status(thm)],[f437])).
% 1.09/1.67 thf(f437,plain,(
% 1.09/1.67 $false | (~spl0_3 | ~spl0_6)),
% 1.09/1.67 inference(equality_resolution,[status(thm)],[f436])).
% 1.09/1.67 thf(f436,plain,(
% 1.09/1.67 ( ! [X0 : g] : ((sK7 != X0)) ) | (~spl0_3 | ~spl0_6)),
% 1.09/1.67 inference(superposition,[status(thm)],[f201,f88])).
% 1.09/1.67 thf(f201,plain,(
% 1.09/1.67 ( ! [X2 : g] : ((sK7 != (sK1 @ X2 @ sK5))) ) | ~spl0_6),
% 1.09/1.67 inference(avatar_component_clause,[status(thm)],[f200])).
% 1.09/1.67 thf(f200,definition,(
% 1.09/1.67 spl0_6 <=> ! [X2 : g] : (sK7 != (sK1 @ X2 @ sK5))),
% 1.09/1.67 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.09/1.67 thf(f428,plain,(
% 1.09/1.67 ~spl0_4 | ~spl0_5 | ~spl0_8),
% 1.09/1.67 inference(avatar_contradiction_clause,[status(thm)],[f427])).
% 1.09/1.67 thf(f427,plain,(
% 1.09/1.67 $false | (~spl0_4 | ~spl0_5 | ~spl0_8)),
% 1.09/1.67 inference(trivial_inequality_removal,[status(thm)],[f422])).
% 1.09/1.67 thf(f422,plain,(
% 1.09/1.67 (sK2 != sK2) | (~spl0_4 | ~spl0_5 | ~spl0_8)),
% 1.09/1.67 inference(superposition,[status(thm)],[f420,f128])).
% 1.09/1.67 thf(f128,plain,(
% 1.09/1.67 ( ! [X3 : g] : ((sK2 = (sK1 @ X3 @ (sK3 @ sK2 @ X3)))) ) | ~spl0_5),
% 1.09/1.67 inference(avatar_component_clause,[status(thm)],[f127])).
% 1.09/1.67 thf(f127,definition,(
% 1.09/1.67 spl0_5 <=> ! [X3 : g] : (sK2 = (sK1 @ X3 @ (sK3 @ sK2 @ X3)))),
% 1.09/1.67 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.09/1.67 thf(f420,plain,(
% 1.09/1.67 ( ! [X0 : g] : (((sK1 @ (sK11 @ sK2) @ X0) != sK2)) ) | (~spl0_4 | ~spl0_8)),
% 1.09/1.67 inference(trivial_inequality_removal,[status(thm)],[f419])).
% 1.09/1.67 thf(f419,plain,(
% 1.09/1.67 ( ! [X0 : g] : (((sK10 @ sK2) != (sK10 @ sK2)) | ((sK1 @ (sK11 @ sK2) @ X0) != sK2)) ) | (~spl0_4 | ~spl0_8)),
% 1.09/1.67 inference(superposition,[status(thm)],[f207,f108])).
% 1.09/1.67 thf(f418,plain,(
% 1.09/1.67 ~spl0_2 | ~spl0_4 | ~spl0_5 | ~spl0_6),
% 1.09/1.67 inference(avatar_contradiction_clause,[status(thm)],[f417])).
% 1.09/1.67 thf(f417,plain,(
% 1.09/1.67 $false | (~spl0_2 | ~spl0_4 | ~spl0_5 | ~spl0_6)),
% 1.09/1.67 inference(equality_resolution,[status(thm)],[f412])).
% 1.09/1.67 thf(f412,plain,(
% 1.09/1.67 ( ! [X0 : g] : ((sK7 != X0)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5 | ~spl0_6)),
% 1.09/1.67 inference(superposition,[status(thm)],[f401,f108])).
% 1.09/1.67 thf(f401,plain,(
% 1.09/1.67 ( ! [X1 : g] : (((sK1 @ X1 @ sK2) != sK7)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5 | ~spl0_6)),
% 1.09/1.67 inference(superposition,[status(thm)],[f307,f318])).
% 1.09/1.67 thf(f318,plain,(
% 1.09/1.67 ( ! [X0 : g] : (((sK1 @ (sK3 @ sK2 @ X0) @ X0) = sK2)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
% 1.09/1.67 inference(superposition,[status(thm)],[f262,f258])).
% 1.09/1.67 thf(f258,plain,(
% 1.09/1.67 ( ! [X0 : g] : (((sK1 @ sK2 @ (sK3 @ sK2 @ (sK3 @ sK2 @ X0))) = X0)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
% 1.09/1.67 inference(forward_demodulation,[status(thm)],[f245,f108])).
% 1.09/1.67 thf(f245,plain,(
% 1.09/1.67 ( ! [X0 : g] : (((sK1 @ sK2 @ (sK3 @ sK2 @ (sK3 @ sK2 @ X0))) = (sK1 @ X0 @ sK2))) ) | (~spl0_2 | ~spl0_5)),
% 1.09/1.67 inference(superposition,[status(thm)],[f215,f128])).
% 1.09/1.67 thf(f215,plain,(
% 1.09/1.67 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ (sK3 @ sK2 @ X0) @ X1)) = (sK1 @ sK2 @ X1))) ) | (~spl0_2 | ~spl0_5)),
% 1.09/1.67 inference(superposition,[status(thm)],[f76,f128])).
% 1.09/1.67 thf(f262,plain,(
% 1.09/1.67 ( ! [X0 : g] : ((sK2 = (sK1 @ X0 @ (sK1 @ sK2 @ (sK3 @ sK2 @ X0))))) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
% 1.09/1.67 inference(superposition,[status(thm)],[f218,f108])).
% 1.09/1.67 thf(f218,plain,(
% 1.09/1.67 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ X1 @ (sK3 @ sK2 @ (sK1 @ X0 @ X1)))) = sK2)) ) | (~spl0_2 | ~spl0_5)),
% 1.09/1.67 inference(superposition,[status(thm)],[f76,f128])).
% 1.09/1.67 thf(f307,plain,(
% 1.09/1.67 ( ! [X2 : g,X0 : g,X1 : g] : ((sK7 != (sK1 @ X2 @ (sK1 @ X0 @ (sK1 @ X1 @ sK5))))) ) | (~spl0_2 | ~spl0_6)),
% 1.09/1.67 inference(superposition,[status(thm)],[f306,f76])).
% 1.09/1.67 thf(f306,plain,(
% 1.09/1.67 ( ! [X0 : g,X1 : g] : ((sK7 != (sK1 @ X0 @ (sK1 @ X1 @ sK5)))) ) | (~spl0_2 | ~spl0_6)),
% 1.09/1.67 inference(superposition,[status(thm)],[f201,f76])).
% 1.09/1.67 thf(f305,plain,(
% 1.09/1.67 ~spl0_2 | ~spl0_4 | ~spl0_5 | ~spl0_7),
% 1.09/1.67 inference(avatar_contradiction_clause,[status(thm)],[f304])).
% 1.09/1.67 thf(f304,plain,(
% 1.09/1.67 $false | (~spl0_2 | ~spl0_4 | ~spl0_5 | ~spl0_7)),
% 1.09/1.67 inference(equality_resolution,[status(thm)],[f300])).
% 1.09/1.67 thf(f300,plain,(
% 1.09/1.67 ( ! [X0 : g] : ((sK7 != X0)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5 | ~spl0_7)),
% 1.09/1.67 inference(superposition,[status(thm)],[f253,f258])).
% 1.09/1.67 thf(f253,plain,(
% 1.09/1.67 ( ! [X0 : g] : (((sK1 @ sK2 @ X0) != sK7)) ) | (~spl0_2 | ~spl0_5 | ~spl0_7)),
% 1.09/1.67 inference(superposition,[status(thm)],[f204,f215])).
% 1.09/1.67 thf(f223,plain,(
% 1.09/1.67 ~spl0_2 | spl0_9),
% 1.09/1.67 inference(avatar_contradiction_clause,[status(thm)],[f222])).
% 1.09/1.67 thf(f222,plain,(
% 1.09/1.67 $false | (~spl0_2 | spl0_9)),
% 1.09/1.67 inference(trivial_inequality_removal,[status(thm)],[f219])).
% 1.09/1.67 thf(f219,plain,(
% 1.09/1.67 ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ sK6 @ (sK1 @ sK9 @ sK8))) | (~spl0_2 | spl0_9)),
% 1.09/1.67 inference(superposition,[status(thm)],[f211,f76])).
% 1.09/1.67 thf(f211,plain,(
% 1.09/1.67 ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | spl0_9),
% 1.09/1.67 inference(avatar_component_clause,[status(thm)],[f209])).
% 1.09/1.67 thf(f209,definition,(
% 1.09/1.67 spl0_9 <=> ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) = (sK1 @ (sK1 @ sK6 @ sK9) @ sK8))),
% 1.09/1.67 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.09/1.67 thf(f213,plain,(
% 1.09/1.67 spl0_2),
% 1.09/1.67 inference(avatar_split_clause,[status(thm)],[f54,f75])).
% 1.09/1.67 thf(f54,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ (sK1 @ X1 @ X3) @ X2) = (sK1 @ X1 @ (sK1 @ X3 @ X2)))) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f53])).
% 1.09/1.67 thf(f53,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK1 @ (sK1 @ X1 @ X3) @ X2) = (sK1 @ X1 @ (sK1 @ X3 @ X2))) = $true)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.09/1.67 thf(f52,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((((^[Y0 : g]: ((sK1 @ (sK1 @ X1 @ Y0) @ X2) = (sK1 @ X1 @ (sK1 @ Y0 @ X2)))) @ X3) = $true)) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f51])).
% 1.09/1.67 thf(f51,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ X1 @ Y0) @ X2) = (sK1 @ X1 @ (sK1 @ Y0 @ X2))))) = $true)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.09/1.67 thf(f50,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ X1 @ Y1) @ Y0) = (sK1 @ X1 @ (sK1 @ Y1 @ Y0)))))) @ X2) = $true)) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f49])).
% 1.09/1.67 thf(f49,plain,(
% 1.09/1.67 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ X1 @ Y1) @ Y0) = (sK1 @ X1 @ (sK1 @ Y1 @ Y0))))))) = $true)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.09/1.67 thf(f48,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))) @ X1))) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f47])).
% 1.09/1.67 thf(f47,plain,(
% 1.09/1.67 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))) = $true)),
% 1.09/1.67 inference(duplicate_literal_removal,[status(thm)],[f45])).
% 1.09/1.67 thf(f45,plain,(
% 1.09/1.67 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))) = $true) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))) = $true)),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.09/1.67 thf(f43,plain,(
% 1.09/1.67 (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) = $true) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))) = $true)),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.09/1.67 thf(f42,plain,(
% 1.09/1.67 ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) = $true) | (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) = $true)),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.09/1.67 thf(f41,plain,(
% 1.09/1.67 (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) = $true) | (((^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y3) @ Y2) = (sK1 @ Y1 @ (sK1 @ Y3 @ Y2))))))))))) @ sK2) = $true)),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f39])).
% 1.09/1.67 thf(f39,plain,(
% 1.09/1.67 ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y3) @ Y2) = (sK1 @ Y1 @ (sK1 @ Y3 @ Y2)))))))))))) = $true) | (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) = $true)),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.09/1.67 thf(f38,plain,(
% 1.09/1.67 (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) != (?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y3) @ Y2) = (sK1 @ Y1 @ (sK1 @ Y3 @ Y2)))))))))))))),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.09/1.67 thf(f37,plain,(
% 1.09/1.67 ($false = ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y3) @ Y2) = (sK1 @ Y1 @ (sK1 @ Y3 @ Y2)))))))))))) = ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))))))),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.09/1.67 thf(f36,plain,(
% 1.09/1.67 ($false = ((^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (((!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))))) & (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y2 @ Y4) @ Y3) = (Y0 @ Y2 @ (Y0 @ Y4 @ Y3)))))))))))) = ((!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ Y3) = Y2))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y1) = Y2)))))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ Y1 @ (Y0 @ Y3 @ Y2)))))))))))) @ sK1))),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f35])).
% 1.09/1.67 thf(f35,plain,(
% 1.09/1.67 ($false = (!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (((!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))))) & (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y2 @ Y4) @ Y3) = (Y0 @ Y2 @ (Y0 @ Y4 @ Y3)))))))))))) = ((!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ Y3) = Y2))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y1) = Y2)))))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ Y1 @ (Y0 @ Y3 @ Y2))))))))))))))),
% 1.09/1.67 inference(not_proxy_clausification,[status(thm)],[f34])).
% 1.09/1.67 thf(f34,plain,(
% 1.09/1.67 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (((!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))))) & (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y2 @ Y4) @ Y3) = (Y0 @ Y2 @ (Y0 @ Y4 @ Y3)))))))))))) = ((!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ Y3) = Y2))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y1) = Y2)))))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ Y1 @ (Y0 @ Y3 @ Y2)))))))))))))) = $true)),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.09/1.67 thf(f33,plain,(
% 1.09/1.67 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: ((^[Y2 : g > g > g]: ((^[Y3 : g]: ((((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (?? @ g @ (^[Y7 : g]: ((Y4 @ Y6 @ Y7) = Y5)))))))) @ Y2 @ Y3) & ((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: ((Y4 @ Y6 @ Y5) = Y6)))))) @ Y2 @ Y3)) & ((^[Y4 : g > g > g]: (!! @ g @ (^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (!! @ g @ (^[Y7 : g]: ((Y4 @ (Y4 @ Y5 @ Y7) @ Y6) = (Y4 @ Y5 @ (Y4 @ Y7 @ Y6)))))))))) @ Y2))))) @ Y0 @ Y1))) = ((^[Y1 : g > g > g]: (((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((?? @ g @ (^[Y5 : g]: ((Y2 @ Y3 @ Y5) = Y4))) & (?? @ g @ (^[Y5 : g]: ((Y2 @ Y5 @ Y3) = Y4))))))))) @ Y1) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ (Y2 @ Y3 @ Y5) @ Y4) = (Y2 @ Y3 @ (Y2 @ Y5 @ Y4)))))))))) @ Y1))) @ Y0))))) = $true)),
% 1.09/1.67 inference(definition_unfolding,[status(thm)],[f26,f31,f32])).
% 1.09/1.67 thf(f32,plain,(
% 1.09/1.67 (cGROUP4 = (^[Y0 : g > g > g]: (((^[Y1 : g > g > g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((?? @ g @ (^[Y4 : g]: ((Y1 @ Y2 @ Y4) = Y3))) & (?? @ g @ (^[Y4 : g]: ((Y1 @ Y4 @ Y2) = Y3))))))))) @ Y0) & ((^[Y1 : g > g > g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y1 @ (Y1 @ Y2 @ Y4) @ Y3) = (Y1 @ Y2 @ (Y1 @ Y4 @ Y3)))))))))) @ Y0))))),
% 1.09/1.67 inference(definition_unfolding,[status(thm)],[f24,f30,f29])).
% 1.09/1.67 thf(f29,plain,(
% 1.09/1.67 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ Y1 @ (Y0 @ Y3 @ Y2)))))))))))),
% 1.09/1.67 inference(cnf_transformation,[status(thm)],[f19])).
% 1.09/1.67 thf(f19,plain,(
% 1.09/1.67 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y1 @ Y3) @ Y2) = (Y0 @ Y1 @ (Y0 @ Y3 @ Y2)))))))))))),
% 1.09/1.67 inference(fool_elimination,[status(thm)],[f18])).
% 1.09/1.67 thf(f18,plain,(
% 1.09/1.67 ((^[X0 : g > g > g] : (! [X1 : g,X2 : g,X3 : g] : ((X0 @ (X0 @ X3 @ X1) @ X2) = (X0 @ X3 @ (X0 @ X1 @ X2))))) = cGRP_ASSOC)),
% 1.09/1.67 inference(rectify,[status(thm)],[f1])).
% 1.09/1.67 thf(f1,axiom,(
% 1.09/1.67 ((^[X0 : g > g > g] : (! [X2 : g,X3 : g,X1 : g] : ((X0 @ (X0 @ X1 @ X2) @ X3) = (X0 @ X1 @ (X0 @ X2 @ X3))))) = cGRP_ASSOC)),
% 1.09/1.67 file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGRP_ASSOC_def)).
% 1.09/1.67 thf(f30,plain,(
% 1.09/1.67 (cGRP_DIVISORS = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ Y3) = Y2))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y1) = Y2))))))))))),
% 1.09/1.67 inference(cnf_transformation,[status(thm)],[f17])).
% 1.09/1.67 thf(f17,plain,(
% 1.09/1.67 (cGRP_DIVISORS = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ Y3) = Y2))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y1) = Y2))))))))))),
% 1.09/1.67 inference(fool_elimination,[status(thm)],[f16])).
% 1.09/1.67 thf(f16,plain,(
% 1.09/1.67 (cGRP_DIVISORS = (^[X0 : g > g > g] : (! [X1 : g,X2 : g] : (? [X3 : g] : ((X0 @ X3 @ X2) = X1) & ? [X4 : g] : ((X0 @ X2 @ X4) = X1)))))),
% 1.09/1.67 inference(rectify,[status(thm)],[f2])).
% 1.09/1.67 thf(f2,axiom,(
% 1.09/1.67 (cGRP_DIVISORS = (^[X0 : g > g > g] : (! [X2 : g,X1 : g] : (? [X5 : g] : ((X0 @ X5 @ X1) = X2) & ? [X4 : g] : ((X0 @ X1 @ X4) = X2)))))),
% 1.09/1.67 file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGRP_DIVISORS_def)).
% 1.09/1.67 thf(f24,plain,(
% 1.09/1.67 (cGROUP4 = (^[Y0 : g > g > g]: ((cGRP_DIVISORS @ Y0) & (cGRP_ASSOC @ Y0))))),
% 1.09/1.67 inference(cnf_transformation,[status(thm)],[f15])).
% 1.09/1.67 thf(f15,plain,(
% 1.09/1.67 (cGROUP4 = (^[Y0 : g > g > g]: ((cGRP_DIVISORS @ Y0) & (cGRP_ASSOC @ Y0))))),
% 1.09/1.67 inference(fool_elimination,[status(thm)],[f14])).
% 1.09/1.67 thf(f14,plain,(
% 1.09/1.67 (cGROUP4 = (^[X0 : g > g > g] : ((cGRP_ASSOC @ X0) & (cGRP_DIVISORS @ X0))))),
% 1.09/1.67 inference(rectify,[status(thm)],[f6])).
% 1.09/1.67 thf(f6,axiom,(
% 1.09/1.67 (cGROUP4 = (^[X0 : g > g > g] : ((cGRP_ASSOC @ X0) & (cGRP_DIVISORS @ X0))))),
% 1.09/1.67 file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGROUP4_def)).
% 1.09/1.67 thf(f31,plain,(
% 1.09/1.67 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: ((Y2 @ Y4 @ Y5) = Y3)))))))) @ Y0 @ Y1) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y2 @ Y4 @ Y3) = Y4)))))) @ Y0 @ Y1)) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ (Y2 @ Y3 @ Y5) @ Y4) = (Y2 @ Y3 @ (Y2 @ Y5 @ Y4)))))))))) @ Y0))))))),
% 1.09/1.67 inference(definition_unfolding,[status(thm)],[f28,f25,f27,f29])).
% 1.09/1.67 thf(f27,plain,(
% 1.09/1.67 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 1.09/1.67 inference(cnf_transformation,[status(thm)],[f11])).
% 1.09/1.67 thf(f11,plain,(
% 1.09/1.67 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 1.09/1.67 inference(fool_elimination,[status(thm)],[f10])).
% 1.09/1.67 thf(f10,plain,(
% 1.09/1.67 ((^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ((X0 @ X2 @ X1) = X2))) = cGRP_RIGHT_UNIT)),
% 1.09/1.67 inference(rectify,[status(thm)],[f4])).
% 1.09/1.67 thf(f4,axiom,(
% 1.09/1.67 ((^[X0 : g > g > g, X6 : g] : (! [X1 : g] : ((X0 @ X1 @ X6) = X1))) = cGRP_RIGHT_UNIT)),
% 1.09/1.67 file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGRP_RIGHT_UNIT_def)).
% 1.09/1.67 thf(f25,plain,(
% 1.09/1.67 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 1.09/1.67 inference(cnf_transformation,[status(thm)],[f21])).
% 1.09/1.67 thf(f21,plain,(
% 1.09/1.67 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 1.09/1.67 inference(fool_elimination,[status(thm)],[f20])).
% 1.09/1.67 thf(f20,plain,(
% 1.09/1.67 (cGRP_RIGHT_INVERSE = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : ((X0 @ X2 @ X3) = X1))))),
% 1.09/1.67 inference(rectify,[status(thm)],[f3])).
% 1.09/1.67 thf(f3,axiom,(
% 1.09/1.67 (cGRP_RIGHT_INVERSE = (^[X0 : g > g > g, X6 : g] : (! [X1 : g] : ? [X2 : g] : ((X0 @ X1 @ X2) = X6))))),
% 1.09/1.67 file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGRP_RIGHT_INVERSE_def)).
% 1.09/1.67 thf(f28,plain,(
% 1.09/1.67 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_INVERSE @ Y0 @ Y1) & (cGRP_RIGHT_UNIT @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))),
% 1.09/1.67 inference(cnf_transformation,[status(thm)],[f13])).
% 1.09/1.67 thf(f13,plain,(
% 1.09/1.67 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_INVERSE @ Y0 @ Y1) & (cGRP_RIGHT_UNIT @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))),
% 1.09/1.67 inference(fool_elimination,[status(thm)],[f12])).
% 1.09/1.67 thf(f12,plain,(
% 1.09/1.67 (cGROUP3 = (^[X0 : g > g > g, X1 : g] : ((cGRP_ASSOC @ X0) & (cGRP_RIGHT_UNIT @ X0 @ X1) & (cGRP_RIGHT_INVERSE @ X0 @ X1))))),
% 1.09/1.67 inference(rectify,[status(thm)],[f5])).
% 1.09/1.67 thf(f5,axiom,(
% 1.09/1.67 (cGROUP3 = (^[X0 : g > g > g, X6 : g] : ((cGRP_ASSOC @ X0) & (cGRP_RIGHT_UNIT @ X0 @ X6) & (cGRP_RIGHT_INVERSE @ X0 @ X6))))),
% 1.09/1.67 file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cGROUP3_def)).
% 1.09/1.67 thf(f26,plain,(
% 1.09/1.67 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (cGROUP3 @ Y0 @ Y1))) = (cGROUP4 @ Y0))))) = $true)),
% 1.09/1.67 inference(cnf_transformation,[status(thm)],[f23])).
% 1.09/1.67 thf(f23,plain,(
% 1.09/1.67 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (cGROUP3 @ Y0 @ Y1))) = (cGROUP4 @ Y0))))) = $true)),
% 1.09/1.67 inference(fool_elimination,[status(thm)],[f22])).
% 1.09/1.67 thf(f22,plain,(
% 1.09/1.67 ~! [X0 : g > g > g] : (? [X1 : g] : (cGROUP3 @ X0 @ X1) <=> (cGROUP4 @ X0))),
% 1.09/1.67 inference(rectify,[status(thm)],[f8])).
% 1.09/1.67 thf(f8,negated_conjecture,(
% 1.09/1.67 ~! [X0 : g > g > g] : (? [X6 : g] : (cGROUP3 @ X0 @ X6) <=> (cGROUP4 @ X0))),
% 1.09/1.67 inference(negated_conjecture,[status(cth)],[f7])).
% 1.09/1.67 thf(f7,conjecture,(
% 1.09/1.67 ! [X0 : g > g > g] : (? [X6 : g] : (cGROUP3 @ X0 @ X6) <=> (cGROUP4 @ X0))),
% 1.09/1.67 file('/export/starexec/sandbox/tmp/tmp.0jRdx2aHDa/DTF2THF_4007.p',cEQUIV_03_04)).
% 1.09/1.67 thf(f212,plain,(
% 1.09/1.67 spl0_6 | spl0_7 | spl0_8 | ~spl0_9),
% 1.09/1.67 inference(avatar_split_clause,[status(thm)],[f198,f209,f206,f203,f200])).
% 1.09/1.67 thf(f198,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ sK5 @ X3) != sK7) | ((sK1 @ (sK11 @ X1) @ X4) != X1) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | (sK7 != (sK1 @ X2 @ sK5)) | ((sK1 @ (sK10 @ X1) @ X1) != (sK10 @ X1))) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f197])).
% 1.09/1.67 thf(f197,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (($false = ((sK1 @ (sK11 @ X1) @ X4) = X1)) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | ((sK1 @ sK5 @ X3) != sK7) | ((sK1 @ (sK10 @ X1) @ X1) != (sK10 @ X1)) | (sK7 != (sK1 @ X2 @ sK5))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f196])).
% 1.09/1.67 thf(f196,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ sK5 @ X3) != sK7) | (sK7 != (sK1 @ X2 @ sK5)) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | ((sK1 @ (sK10 @ X1) @ X1) != (sK10 @ X1)) | ($false = ((^[Y0 : g]: ((sK1 @ (sK11 @ X1) @ Y0) = X1)) @ X4))) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f195])).
% 1.09/1.67 thf(f195,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((sK7 != (sK1 @ X2 @ sK5)) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ (sK11 @ X1) @ Y0) = X1)))) | ((sK1 @ sK5 @ X3) != sK7) | ((sK1 @ (sK10 @ X1) @ X1) != (sK10 @ X1))) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f194])).
% 1.09/1.67 thf(f194,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((sK7 != (sK1 @ X2 @ sK5)) | ((sK1 @ (sK10 @ X1) @ X1) != (sK10 @ X1)) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | ($false = ((sK1 @ sK5 @ X3) = sK7)) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ (sK11 @ X1) @ Y0) = X1))))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f193])).
% 1.09/1.67 thf(f193,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (($false = ((sK1 @ sK5 @ X3) = sK7)) | (sK7 != (sK1 @ X2 @ sK5)) | ((sK1 @ (sK10 @ X1) @ X1) != (sK10 @ X1)) | ($false = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))) @ (sK11 @ X1))) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8))) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f192])).
% 1.09/1.67 thf(f192,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) | ($false = ((sK1 @ sK5 @ X3) = sK7)) | (sK7 != (sK1 @ X2 @ sK5)) | ((sK1 @ (sK10 @ X1) @ X1) != (sK10 @ X1)) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8))) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f191])).
% 1.09/1.67 thf(f191,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (($false = ((sK1 @ (sK10 @ X1) @ X1) = (sK10 @ X1))) | (sK7 != (sK1 @ X2 @ sK5)) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) | ($false = ((sK1 @ sK5 @ X3) = sK7))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f190])).
% 1.09/1.67 thf(f190,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (($false = ((^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)) @ X3)) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) | ($false = ((sK1 @ (sK10 @ X1) @ X1) = (sK10 @ X1))) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | (sK7 != (sK1 @ X2 @ sK5))) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f189])).
% 1.09/1.67 thf(f189,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | ($false = ((sK1 @ (sK10 @ X1) @ X1) = (sK10 @ X1))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | (sK7 != (sK1 @ X2 @ sK5))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f188])).
% 1.09/1.67 thf(f188,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) | (sK7 != (sK1 @ X2 @ sK5)) | ($false = ((^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)) @ (sK10 @ X1))) | ((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8))) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f187])).
% 1.09/1.67 thf(f187,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (((sK1 @ sK6 @ (sK1 @ sK9 @ sK8)) != (sK1 @ (sK1 @ sK6 @ sK9) @ sK8)) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))) | (sK7 != (sK1 @ X2 @ sK5)) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))))) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f186])).
% 1.09/1.67 thf(f186,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (($false = ((sK1 @ (sK1 @ sK6 @ sK9) @ sK8) = (sK1 @ sK6 @ (sK1 @ sK9 @ sK8)))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | (sK7 != (sK1 @ X2 @ sK5)) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f185])).
% 1.09/1.67 thf(f185,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (($false = ((sK1 @ X2 @ sK5) = sK7)) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | ($false = ((sK1 @ (sK1 @ sK6 @ sK9) @ sK8) = (sK1 @ sK6 @ (sK1 @ sK9 @ sK8))))) )),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f184])).
% 1.09/1.67 thf(f184,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | ($false = ((sK1 @ (sK1 @ sK6 @ sK9) @ sK8) = (sK1 @ sK6 @ (sK1 @ sK9 @ sK8)))) | ($false = ((sK1 @ X2 @ sK5) = sK7))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f183])).
% 1.09/1.67 thf(f183,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (($false = ((^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7)) @ X2)) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | ($false = ((sK1 @ (sK1 @ sK6 @ sK9) @ sK8) = (sK1 @ sK6 @ (sK1 @ sK9 @ sK8))))) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f182])).
% 1.09/1.67 thf(f182,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7)))) | ($false = ((sK1 @ (sK1 @ sK6 @ sK9) @ sK8) = (sK1 @ sK6 @ (sK1 @ sK9 @ sK8)))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f181])).
% 1.09/1.67 thf(f181,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | ($false = ((^[Y0 : g]: ((sK1 @ (sK1 @ sK6 @ Y0) @ sK8) = (sK1 @ sK6 @ (sK1 @ Y0 @ sK8)))) @ sK9)) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7)))) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))))) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f180])).
% 1.09/1.67 thf(f180,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ sK6 @ Y0) @ sK8) = (sK1 @ sK6 @ (sK1 @ Y0 @ sK8)))))) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7)))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7))))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f179])).
% 1.09/1.67 thf(f179,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0)))))) @ sK8)) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7)))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7))))) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f178])).
% 1.09/1.67 thf(f178,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0)))))))) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7)))) | ($false = (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7))))) )),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f177])).
% 1.09/1.67 thf(f177,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7))))) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0))))))))) )),
% 1.09/1.67 inference(duplicate_literal_removal,[status(thm)],[f176])).
% 1.09/1.67 thf(f176,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7))))) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0)))))))) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0)))))))) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f175])).
% 1.09/1.67 thf(f175,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7))))) | ($false = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))) @ sK6)) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0))))))))) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f174])).
% 1.09/1.67 thf(f174,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0)))))))) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) | ($false = ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK5 @ Y0) = sK7))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK5) = sK7)))))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f173])).
% 1.09/1.67 thf(f173,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0)))))))) | ($false = ((^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ sK5 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ sK5) = Y0))))) @ sK7)) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))))) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f172])).
% 1.09/1.67 thf(f172,plain,(
% 1.09/1.67 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ sK5 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ sK5) = Y0)))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0)))))))) | ($false = ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))))) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))))) )),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f171])).
% 1.09/1.67 thf(f171,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))))) | ((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ sK5 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ sK5) = Y0)))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK6 @ Y1) @ Y0) = (sK1 @ sK6 @ (sK1 @ Y1 @ Y0))))))))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f170])).
% 1.09/1.67 thf(f170,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))))) | ((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ sK5 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ sK5) = Y0)))))) = $false) | ($false = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))) @ sK6))) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f169])).
% 1.09/1.67 thf(f169,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) | ((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ sK5 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ sK5) = Y0)))))) = $false) | ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f168])).
% 1.09/1.67 thf(f168,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) | ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))))) | ($false = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1))))))) @ sK5))) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f167])).
% 1.09/1.67 thf(f167,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1))))))))) | ($false = (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))))) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f166])).
% 1.09/1.67 thf(f166,plain,(
% 1.09/1.67 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) | ($false = ((^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y3) @ Y2) = (sK1 @ Y1 @ (sK1 @ Y3 @ Y2))))))))))) @ X1)) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))))) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f165])).
% 1.09/1.67 thf(f165,plain,(
% 1.09/1.67 ($false = (?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y3) @ Y2) = (sK1 @ Y1 @ (sK1 @ Y3 @ Y2))))))))))))) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) | ($false = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))))),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.09/1.67 thf(f40,plain,(
% 1.09/1.67 ($false = ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1))))))))))) | ($false = (?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))))) & (!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y3) @ Y2) = (sK1 @ Y1 @ (sK1 @ Y3 @ Y2)))))))))))))),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.09/1.67 thf(f138,plain,(
% 1.09/1.67 spl0_5 | spl0_1),
% 1.09/1.67 inference(avatar_split_clause,[status(thm)],[f137,f72,f127])).
% 1.09/1.67 thf(f137,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X1 @ (sK3 @ X2 @ X1)) = X2) | (sK2 = (sK1 @ X3 @ (sK3 @ sK2 @ X3)))) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f136])).
% 1.09/1.67 thf(f136,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X1 @ (sK3 @ X2 @ X1)) = X2) | (((sK1 @ X3 @ (sK3 @ sK2 @ X3)) = sK2) = $true)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f135])).
% 1.09/1.67 thf(f135,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X1 @ (sK3 @ X2 @ X1)) = X2) | (((^[Y0 : g]: ((sK1 @ X3 @ Y0) = sK2)) @ (sK3 @ sK2 @ X3)) = $true)) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f134])).
% 1.09/1.67 thf(f134,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ X3 @ Y0) = sK2))) = $true) | ((sK1 @ X1 @ (sK3 @ X2 @ X1)) = X2)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f133])).
% 1.09/1.67 thf(f133,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))) @ X3) = $true) | ((sK1 @ X1 @ (sK3 @ X2 @ X1)) = X2)) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f132])).
% 1.09/1.67 thf(f132,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ (sK3 @ X2 @ X1)) = X2) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true)) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f131])).
% 1.09/1.67 thf(f131,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : ((((sK1 @ X1 @ (sK3 @ X2 @ X1)) = X2) = $true) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f130])).
% 1.09/1.67 thf(f130,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true) | (((^[Y0 : g]: ((sK1 @ X1 @ Y0) = X2)) @ (sK3 @ X2 @ X1)) = $true)) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f117])).
% 1.09/1.67 thf(f117,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (($true = (?? @ g @ (^[Y0 : g]: ((sK1 @ X1 @ Y0) = X2)))) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true)) )),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.09/1.67 thf(f115,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : ((((?? @ g @ (^[Y0 : g]: ((sK1 @ X1 @ Y0) = X2))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X2)))) = $true) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f114])).
% 1.09/1.67 thf(f114,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ X1 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ X1) = Y0))))) @ X2) = $true) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true)) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f95])).
% 1.09/1.67 thf(f95,plain,(
% 1.09/1.67 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ X1 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ X1) = Y0)))))) = $true) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true)) )),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.09/1.67 thf(f93,plain,(
% 1.09/1.67 ( ! [X1 : g] : ((((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) = $true) | ((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ X1 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ X1) = Y0)))))) = $true)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.09/1.67 thf(f92,plain,(
% 1.09/1.67 ( ! [X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1))))))) @ X1) = $true) | (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) = $true)) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f91])).
% 1.09/1.67 thf(f91,plain,(
% 1.09/1.67 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))) = $true) | (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) = $true)),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.09/1.67 thf(f44,plain,(
% 1.09/1.67 (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ Y2) = Y1))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y0) = Y1)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y2) @ Y1) = (sK1 @ Y0 @ (sK1 @ Y2 @ Y1)))))))))) = $true) | (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) & (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) = $true)),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.09/1.67 thf(f129,plain,(
% 1.09/1.67 spl0_5 | spl0_3),
% 1.09/1.67 inference(avatar_split_clause,[status(thm)],[f125,f87,f127])).
% 1.09/1.67 thf(f125,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((sK2 = (sK1 @ X3 @ (sK3 @ sK2 @ X3))) | ((sK1 @ (sK4 @ X2 @ X1) @ X1) = X2)) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f124])).
% 1.09/1.67 thf(f124,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK1 @ (sK4 @ X2 @ X1) @ X1) = X2) = $true) | (sK2 = (sK1 @ X3 @ (sK3 @ sK2 @ X3)))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f123])).
% 1.09/1.67 thf(f123,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((sK2 = (sK1 @ X3 @ (sK3 @ sK2 @ X3))) | (((^[Y0 : g]: ((sK1 @ Y0 @ X1) = X2)) @ (sK4 @ X2 @ X1)) = $true)) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f122])).
% 1.09/1.67 thf(f122,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X2))) = $true) | (sK2 = (sK1 @ X3 @ (sK3 @ sK2 @ X3)))) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f121])).
% 1.09/1.67 thf(f121,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK1 @ X3 @ (sK3 @ sK2 @ X3)) = sK2) = $true) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X2))) = $true)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.09/1.67 thf(f120,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X2))) = $true) | (((^[Y0 : g]: ((sK1 @ X3 @ Y0) = sK2)) @ (sK3 @ sK2 @ X3)) = $true)) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f119])).
% 1.09/1.67 thf(f119,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ X3 @ Y0) = sK2))) = $true) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X2))) = $true)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f118])).
% 1.09/1.67 thf(f118,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))) @ X3) = $true) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X2))) = $true)) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f116])).
% 1.09/1.67 thf(f116,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X2))) = $true)) )),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.09/1.67 thf(f113,plain,(
% 1.09/1.67 spl0_4 | spl0_3),
% 1.09/1.67 inference(avatar_split_clause,[status(thm)],[f112,f87,f107])).
% 1.09/1.67 thf(f112,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X2 @ sK2) = X2) | ((sK1 @ (sK4 @ X3 @ X1) @ X1) = X3)) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f111])).
% 1.09/1.67 thf(f111,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK1 @ (sK4 @ X3 @ X1) @ X1) = X3)) | ((sK1 @ X2 @ sK2) = X2)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f110])).
% 1.09/1.67 thf(f110,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X2 @ sK2) = X2) | (((^[Y0 : g]: ((sK1 @ Y0 @ X1) = X3)) @ (sK4 @ X3 @ X1)) = $true)) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f101])).
% 1.09/1.67 thf(f101,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X2 @ sK2) = X2) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X3))) = $true)) )),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.09/1.67 thf(f100,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X2 @ sK2) = X2) | ($true = ((?? @ g @ (^[Y0 : g]: ((sK1 @ X1 @ Y0) = X3))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X3)))))) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f99])).
% 1.09/1.67 thf(f99,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK1 @ X2 @ sK2) = X2)) | ($true = ((?? @ g @ (^[Y0 : g]: ((sK1 @ X1 @ Y0) = X3))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = X3)))))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.09/1.67 thf(f98,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ X1 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ X1) = Y0))))) @ X3)) | ($true = ((sK1 @ X2 @ sK2) = X2))) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f97])).
% 1.09/1.67 thf(f97,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ X1 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ X1) = Y0)))))) = $true) | ($true = ((sK1 @ X2 @ sK2) = X2))) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.09/1.67 thf(f96,plain,(
% 1.09/1.67 ( ! [X2 : g,X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)) @ X2)) | ((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ X1 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ X1) = Y0)))))) = $true)) )),
% 1.09/1.67 inference(pi_clausification,[status(thm)],[f94])).
% 1.09/1.67 thf(f94,plain,(
% 1.09/1.67 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) = $true) | ((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ X1 @ Y1) = Y0))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ X1) = Y0)))))) = $true)) )),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.09/1.67 thf(f109,plain,(
% 1.09/1.67 spl0_1 | spl0_4),
% 1.09/1.67 inference(avatar_split_clause,[status(thm)],[f105,f107,f72])).
% 1.09/1.67 thf(f105,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X2 @ sK2) = X2) | ((sK1 @ X1 @ (sK3 @ X3 @ X1)) = X3)) )),
% 1.09/1.67 inference(equality_proxy_clausification,[status(thm)],[f104])).
% 1.09/1.67 thf(f104,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK1 @ X1 @ (sK3 @ X3 @ X1)) = X3) = $true) | ((sK1 @ X2 @ sK2) = X2)) )),
% 1.09/1.67 inference(beta_eta_normalization,[status(thm)],[f103])).
% 1.09/1.67 thf(f103,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : ((((^[Y0 : g]: ((sK1 @ X1 @ Y0) = X3)) @ (sK3 @ X3 @ X1)) = $true) | ((sK1 @ X2 @ sK2) = X2)) )),
% 1.09/1.67 inference(sigma_clausification,[status(thm)],[f102])).
% 1.09/1.67 thf(f102,plain,(
% 1.09/1.67 ( ! [X2 : g,X3 : g,X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ X1 @ Y0) = X3))) = $true) | ((sK1 @ X2 @ sK2) = X2)) )),
% 1.09/1.67 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.09/1.67 % SZS output end Proof for DTF2THF_4007
% 1.09/1.67 % (4148)------------------------------
% 1.09/1.67 % (4148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/1.67 % (4148)Termination reason: Refutation
% 1.09/1.67
% 1.09/1.67 % (4148)Memory used [KB]: 6908
% 1.09/1.67 % (4148)Time elapsed: 0.129 s
% 1.09/1.67 % (4148)Instructions burned: 413 (million)
% 1.09/1.67 % (4148)------------------------------
% 1.09/1.67 % (4148)------------------------------
% 1.09/1.67 % (4120)Success in time 0.205 s
%------------------------------------------------------------------------------