%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG271^5 : 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 : n003.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 08:37:47 AM UTC 2026
% Result : Theorem 1.77s 1.61s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 20
% Syntax : Number of formulae : 192 ( 41 unt; 0 typ; 12 def)
% Number of atoms : 1665 ( 820 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 3876 ( 168 ~; 306 |; 215 &;2745 @)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 30 usr; 24 con; 0-2 aty)
% ( 336 !!; 91 ??; 0 @@+; 0 @@-)
% Number of variables : 711 ( 531 ^; 176 !; 4 ?; 711 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(func_def_3,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_4,type,
cGRP_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_6,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_7,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_24,type,
sK1: g > g > g ).
thf(func_def_25,type,
sK2: g ).
thf(func_def_26,type,
sK3: g > g ).
thf(func_def_27,type,
sK4: g > g ).
thf(func_def_28,type,
sK5: g ).
thf(func_def_29,type,
sK6: g ).
thf(func_def_30,type,
sK7: g ).
thf(func_def_31,type,
sK8: g ).
thf(func_def_32,type,
sK9: g ).
thf(func_def_33,type,
sK10: g ).
thf(func_def_34,type,
sK11: g ).
thf(f425,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f66,f142,f173,f185,f187,f242,f245,f255,f259,f305,f357,f373,f401,f420,f424]) ).
thf(f424,plain,
( ~ spl0_3
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f423]) ).
thf(f423,plain,
( $false
| ~ spl0_3
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f422]) ).
thf(f422,plain,
( ( sK2 != sK2 )
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f241,f82]) ).
thf(f82,plain,
( ! [X2: g] :
( ( sK1 @ X2 @ ( sK3 @ X2 ) )
= sK2 )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl0_3
<=> ! [X2: g] :
( ( sK1 @ X2 @ ( sK3 @ X2 ) )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f241,plain,
( ! [X1: g] :
( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f240]) ).
thf(f240,definition,
( spl0_12
<=> ! [X1: g] :
( ( sK1 @ sK8 @ X1 )
!= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f420,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f419]) ).
thf(f419,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f411,f88]) ).
thf(f88,plain,
( ! [X2: g] :
( ( sK1 @ ( sK3 @ X2 ) @ X2 )
= sK2 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl0_4
<=> ! [X2: g] :
( ( sK1 @ ( sK3 @ X2 ) @ X2 )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f411,plain,
( ( sK2
!= ( sK1 @ ( sK3 @ sK7 ) @ sK7 ) )
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f408]) ).
thf(f408,plain,
( ( sK2
!= ( sK1 @ ( sK3 @ sK7 ) @ sK7 ) )
| ( sK2 != sK2 )
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f222,f82]) ).
thf(f222,plain,
( ! [X2: g] :
( ( ( sK1 @ sK7 @ X2 )
!= sK2 )
| ( ( sK1 @ X2 @ sK7 )
!= sK2 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f221]) ).
thf(f221,definition,
( spl0_7
<=> ! [X2: g] :
( ( ( sK1 @ X2 @ sK7 )
!= sK2 )
| ( ( sK1 @ sK7 @ X2 )
!= sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f401,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f400]) ).
thf(f400,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f399]) ).
thf(f399,plain,
( ( sK2 != sK2 )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f382,f378]) ).
thf(f378,plain,
( ! [X0: g] :
( ( sK1 @ ( sK4 @ X0 ) @ X0 )
= sK2 )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f159,f342]) ).
thf(f342,plain,
( ! [X0: g] :
( ( sK4 @ ( sK4 @ X0 ) )
= X0 )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f70,f266]) ).
thf(f266,plain,
( ! [X0: g] :
( ( sK1 @ sK2 @ ( sK4 @ ( sK4 @ X0 ) ) )
= X0 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f260,f65]) ).
thf(f65,plain,
( ! [X1: g] :
( ( sK1 @ X1 @ sK2 )
= X1 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl0_1
<=> ! [X1: g] :
( ( sK1 @ X1 @ sK2 )
= X1 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f260,plain,
( ! [X0: g] :
( ( sK1 @ sK2 @ ( sK4 @ ( sK4 @ X0 ) ) )
= ( sK1 @ X0 @ sK2 ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f246,f159]) ).
thf(f246,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ ( sK4 @ X0 ) @ X1 ) )
= ( sK1 @ sK2 @ X1 ) )
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f102,f159]) ).
thf(f102,plain,
( ! [X3: g,X1: g,X4: g] :
( ( sK1 @ ( sK1 @ X1 @ X3 ) @ X4 )
= ( sK1 @ X1 @ ( sK1 @ X3 @ X4 ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl0_5
<=> ! [X4: g,X1: g,X3: g] :
( ( sK1 @ ( sK1 @ X1 @ X3 ) @ X4 )
= ( sK1 @ X1 @ ( sK1 @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f70,plain,
( ! [X2: g] :
( ( sK1 @ sK2 @ X2 )
= X2 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f69,definition,
( spl0_2
<=> ! [X2: g] :
( ( sK1 @ sK2 @ X2 )
= X2 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f159,plain,
( ! [X2: g] :
( ( sK1 @ X2 @ ( sK4 @ X2 ) )
= sK2 )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f158]) ).
thf(f158,definition,
( spl0_6
<=> ! [X2: g] :
( ( sK1 @ X2 @ ( sK4 @ X2 ) )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f382,plain,
( ( ( sK1 @ ( sK4 @ sK7 ) @ sK7 )
!= sK2 )
| ~ spl0_6
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f379]) ).
thf(f379,plain,
( ( sK2 != sK2 )
| ( ( sK1 @ ( sK4 @ sK7 ) @ sK7 )
!= sK2 )
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f222,f159]) ).
thf(f373,plain,
( ~ spl0_6
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f372]) ).
thf(f372,plain,
( $false
| ~ spl0_6
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f368]) ).
thf(f368,plain,
( ( sK2 != sK2 )
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f241,f159]) ).
thf(f357,plain,
( ~ spl0_2
| spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f356]) ).
thf(f356,plain,
( $false
| ~ spl0_2
| spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f355]) ).
thf(f355,plain,
( ( sK6 != sK6 )
| ~ spl0_2
| spl0_10 ),
inference(superposition,[status(thm)],[f234,f70]) ).
thf(f234,plain,
( ( ( sK1 @ sK2 @ sK6 )
!= sK6 )
| spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f232]) ).
thf(f232,definition,
( spl0_10
<=> ( ( sK1 @ sK2 @ sK6 )
= sK6 ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f305,plain,
( spl0_2
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f294,f158,f101,f64,f69]) ).
thf(f294,plain,
( ! [X0: g] :
( ( sK1 @ sK2 @ X0 )
= X0 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f271,f266]) ).
thf(f271,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X1 @ ( sK4 @ ( sK4 @ X0 ) ) )
= ( sK1 @ X1 @ X0 ) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f247,f266]) ).
thf(f247,plain,
( ! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ sK2 @ X1 ) )
= ( sK1 @ X0 @ X1 ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f102,f65]) ).
thf(f259,plain,
( ~ spl0_1
| spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f258]) ).
thf(f258,plain,
( $false
| ~ spl0_1
| spl0_9 ),
inference(subsumption_resolution,[status(thm)],[f230,f65]) ).
thf(f230,plain,
( ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f228]) ).
thf(f228,definition,
( spl0_9
<=> ( ( sK1 @ sK9 @ sK2 )
= sK9 ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f255,plain,
( ~ spl0_5
| spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f254]) ).
thf(f254,plain,
( $false
| ~ spl0_5
| spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f253]) ).
thf(f253,plain,
( ( ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) )
!= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) )
| ~ spl0_5
| spl0_8 ),
inference(superposition,[status(thm)],[f226,f102]) ).
thf(f226,plain,
( ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
!= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) )
| spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f224]) ).
thf(f224,definition,
( spl0_8
<=> ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f245,plain,
( ~ spl0_1
| spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f244]) ).
thf(f244,plain,
( $false
| ~ spl0_1
| spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f243]) ).
thf(f243,plain,
( ( sK6 != sK6 )
| ~ spl0_1
| spl0_11 ),
inference(superposition,[status(thm)],[f238,f65]) ).
thf(f238,plain,
( ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f236]) ).
thf(f236,definition,
( spl0_11
<=> ( ( sK1 @ sK6 @ sK2 )
= sK6 ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f242,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f219,f240,f236,f232,f228,f224,f221]) ).
thf(f219,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X2 @ sK7 )
!= sK2 )
| ( ( sK1 @ sK7 @ X2 )
!= sK2 )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| ( ( sK1 @ sK2 @ sK6 )
!= sK6 )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
!= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f218]) ).
thf(f218,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X2 @ sK7 )
!= sK2 )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( $false
= ( ( sK1 @ sK7 @ X2 )
= sK2 ) )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
!= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) )
| ( ( sK1 @ sK2 @ sK6 )
!= sK6 )
| ( ( sK1 @ sK6 @ sK2 )
!= sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( ( sK1 @ X2 @ sK7 )
!= sK2 )
| ( ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) )
= $false )
| ( ( sK1 @ sK2 @ sK6 )
!= sK6 )
| ( $false
= ( ( sK1 @ sK7 @ X2 )
= sK2 ) )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( sK1 @ sK6 @ sK2 )
!= sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f216]) ).
thf(f216,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| ( ( ( sK1 @ X2 @ sK7 )
= sK2 )
= $false )
| ( ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) )
= $false )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( sK1 @ sK2 @ sK6 )
!= sK6 )
| ( $false
= ( ( sK1 @ sK7 @ X2 )
= sK2 ) )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 ) ),
inference(equality_proxy_clausification,[status(thm)],[f215]) ).
thf(f215,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( ( sK1 @ X2 @ sK7 )
= sK2 )
= $false )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( $false
= ( ( sK1 @ sK7 @ X2 )
= sK2 ) )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f214]) ).
thf(f214,plain,
! [X2: g,X1: g] :
( ( ( ( ( sK1 @ sK7 @ X2 )
= sK2 )
& ( ( sK1 @ X2 @ sK7 )
= sK2 ) )
= $false )
| ( ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( ( sK1 @ sK6 @ sK2 )
!= sK6 ) ),
inference(beta_eta_normalization,[status(thm)],[f213]) ).
thf(f213,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| ( ( ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) )
@ X2 )
= $false )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f212]) ).
thf(f212,plain,
! [X1: g] :
( ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ sK11 )
= ( sK1 @ sK5 @ ( sK1 @ sK10 @ sK11 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f211]) ).
thf(f211,plain,
! [X1: g] :
( ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( ( ^ [Y0: g] :
( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ Y0 )
= ( sK1 @ sK5 @ ( sK1 @ sK10 @ Y0 ) ) )
@ sK11 )
= $false )
| ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f210]) ).
thf(f210,plain,
! [X1: g] :
( ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ sK5 @ sK10 ) @ Y0 )
= ( sK1 @ sK5 @ ( sK1 @ sK10 @ Y0 ) ) ) )
= $false )
| ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f209]) ).
thf(f209,plain,
! [X1: g] :
( ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) )
@ sK10 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f208]) ).
thf(f208,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( sK1 @ sK6 @ sK2 )
!= sK6 )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 ) ),
inference(equality_proxy_clausification,[status(thm)],[f207]) ).
thf(f207,plain,
! [X1: g] :
( ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( ( sK1 @ sK6 @ sK2 )
= sK6 )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( sK1 @ sK9 @ sK2 )
!= sK9 ) ),
inference(equality_proxy_clausification,[status(thm)],[f206]) ).
thf(f206,plain,
! [X1: g] :
( ( ( ( sK1 @ sK9 @ sK2 )
= sK9 )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( sK1 @ sK8 @ X1 )
!= sK2 )
| ( ( ( sK1 @ sK6 @ sK2 )
= sK6 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f205]) ).
thf(f205,plain,
! [X1: g] :
( ( ( ( sK1 @ sK8 @ X1 )
= sK2 )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK6 @ sK2 )
= sK6 )
= $false )
| ( ( ( sK1 @ sK9 @ sK2 )
= sK9 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f204]) ).
thf(f204,plain,
! [X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( ( sK1 @ sK8 @ X1 )
= sK2 )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK6 @ sK2 )
= sK6 )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 )
@ sK9 ) ) ),
inference(sigma_clausification,[status(thm)],[f203]) ).
thf(f203,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( ( sK1 @ sK6 @ sK2 )
= sK6 )
= $false )
| ( ( ( sK1 @ sK8 @ X1 )
= sK2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f202]) ).
thf(f202,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( $false
= ( ^ [Y0: g] :
( ( sK1 @ sK8 @ Y0 )
= sK2 )
@ X1 ) )
| ( ( ( sK1 @ sK6 @ sK2 )
= sK6 )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) ) ),
inference(pi_clausification,[status(thm)],[f201]) ).
thf(f201,plain,
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ sK8 @ Y0 )
= sK2 ) )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( ( sK1 @ sK6 @ sK2 )
= sK6 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f200]) ).
thf(f200,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( ( sK1 @ sK6 @ sK2 )
= sK6 )
= $false )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) )
@ sK8 ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f199]) ).
thf(f199,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ( sK1 @ sK6 @ sK2 )
= sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f198]) ).
thf(f198,plain,
( ( $false
= ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK2 )
= sK6 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK7 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ sK7 )
= sK2 ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f197]) ).
thf(f197,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
@ sK7 )
= $false )
| ( $false
= ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK2 )
= sK6 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f196]) ).
thf(f196,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( $false
= ( ( ( sK1 @ sK2 @ sK6 )
= sK6 )
& ( ( sK1 @ sK6 @ sK2 )
= sK6 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f195]) ).
thf(f195,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
@ sK6 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f194]) ).
thf(f194,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f193]) ).
thf(f193,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ sK5 @ Y0 ) @ Y1 )
= ( sK1 @ sK5 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f192]) ).
thf(f192,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) )
@ sK5 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f190]) ).
thf(f190,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f188]) ).
thf(f188,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
!= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( $false
= ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ^ [Y0: g] :
( ( ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y2 ) @ Y3 )
= ( sK1 @ Y1 @ ( sK1 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) ) )
= ( ( !! @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= Y1 )
& ( ( sK1 @ Y1 @ Y0 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( ( sK1 @ Y1 @ Y2 )
= Y0 )
& ( ( sK1 @ Y2 @ Y1 )
= Y0 ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y2 ) @ Y3 )
= ( sK1 @ Y1 @ ( sK1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ Y1 @ Y0 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y2 ) @ Y3 )
= ( sK1 @ Y1 @ ( sK1 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK1 @ Y1 @ Y2 )
= Y0 ) ) ) )
= ( ( !! @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= Y1 )
& ( ( sK1 @ Y1 @ Y0 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( ( sK1 @ Y1 @ Y2 )
= Y0 )
& ( ( sK1 @ Y2 @ Y1 )
= Y0 ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK1 @ ( sK1 @ Y1 @ Y2 ) @ Y3 )
= ( sK1 @ Y1 @ ( sK1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y4 )
= ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) )
= ( ( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y4 )
= ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y4 )
= ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) )
= ( ( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y4 )
= ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y4 )
= ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) )
= ( ( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y4 )
= ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,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] :
( ( Y4 @ Y6 @ Y5 )
= Y6 ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g] :
( !! @ g
@ ^ [Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( !! @ g
@ ^ [Y7: g] :
( ( Y4 @ ( Y4 @ Y5 @ Y6 ) @ Y7 )
= ( Y4 @ Y5 @ ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
@ Y2 )
& ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ?? @ g
@ ^ [Y7: g] :
( ( Y4 @ Y6 @ Y7 )
= Y5 ) ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
= ( ^ [Y2: g > g > g,Y3: g] :
( ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ( ( Y4 @ Y5 @ Y6 )
= Y6 )
& ( ( Y4 @ Y6 @ Y5 )
= Y6 ) ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ?? @ g
@ ^ [Y7: g] :
( ( ( Y4 @ Y6 @ Y7 )
= Y5 )
& ( ( Y4 @ Y7 @ Y6 )
= Y5 ) ) ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g] :
( !! @ g
@ ^ [Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( !! @ g
@ ^ [Y7: g] :
( ( Y4 @ ( Y4 @ Y5 @ Y6 ) @ Y7 )
= ( Y4 @ Y5 @ ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
@ Y2 ) )
@ Y0
@ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f32,f36,f35]) ).
thf(f35,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y3 @ Y4 ) @ Y5 )
= ( Y2 @ Y3 @ ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f34,f27,f30,f31]) ).
thf(f31,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ Y1 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ Y1 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
( cGRP_ASSOC
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X3 @ X2 ) @ X1 )
= ( X0 @ X3 @ ( X0 @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cGRP_ASSOC
= ( ^ [X0: g > g > g] :
! [X3: g,X2: g,X1: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_ASSOC_def) ).
thf(f30,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( ( X0 @ X3 @ X2 )
= X1 )
& ( ( X0 @ X2 @ X3 )
= X1 ) ) )
= cGRP_INVERSE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( ( X0 @ X2 @ X1 )
= X4 )
& ( ( X0 @ X1 @ X2 )
= X4 ) ) )
= cGRP_INVERSE ),
file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_INVERSE_def) ).
thf(f27,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
( cGRP_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( ( X0 @ X2 @ X1 )
= X2 )
& ( ( X0 @ X1 @ X2 )
= X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( cGRP_UNIT
= ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( ( X0 @ X1 @ X4 )
= X1 )
& ( ( X0 @ X4 @ X1 )
= X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_UNIT_def) ).
thf(f34,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_INVERSE @ X0 @ X1 )
& ( cGRP_UNIT @ X0 @ X1 ) ) )
= cGROUP1 ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_INVERSE @ X0 @ X4 )
& ( cGRP_UNIT @ X0 @ X4 ) ) )
= cGROUP1 ),
file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGROUP1_def) ).
thf(f36,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [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 @ Y4 ) @ Y5 )
= ( Y2 @ Y3 @ ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f28,f31,f29]) ).
thf(f29,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)],[f20]) ).
thf(f20,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)],[f19]) ).
thf(f19,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,X4: g] :
! [X1: g] :
? [X2: g] :
( ( X0 @ X1 @ X2 )
= X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_RIGHT_INVERSE_def) ).
thf(f28,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,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,X4: g] :
! [X1: g] :
( ( X0 @ X1 @ X4 )
= X1 ) )
= cGRP_RIGHT_UNIT ),
file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_RIGHT_UNIT_def) ).
thf(f33,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 ) ) )
= cGROUP3 ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X4 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X4 ) ) )
= cGROUP3 ),
file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGROUP3_def) ).
thf(f32,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( cGROUP3 @ Y0 @ Y1 )
= ( cGROUP1 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( cGROUP3 @ Y0 @ Y1 )
= ( cGROUP1 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ! [X0: g,X1: g > g > g] :
( ( cGROUP3 @ X1 @ X0 )
<=> ( cGROUP1 @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ! [X4: g,X0: g > g > g] :
( ( cGROUP3 @ X0 @ X4 )
<=> ( cGROUP1 @ X0 @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
! [X4: g,X0: g > g > g] :
( ( cGROUP3 @ X0 @ X4 )
<=> ( cGROUP1 @ X0 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cEQUIV_01_03) ).
thf(f187,plain,
( spl0_6
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f186,f81,f158]) ).
thf(f186,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X2 @ ( sK3 @ X2 ) )
= sK2 )
| ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
| ( $true
= ( ( sK1 @ X2 @ ( sK3 @ X2 ) )
= sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f181]) ).
thf(f181,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( ( sK1 @ X2 @ ( sK3 @ X2 ) )
= sK2 )
& ( ( sK1 @ ( sK3 @ X2 ) @ X2 )
= sK2 ) ) )
| ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f180]) ).
thf(f180,plain,
! [X2: g,X1: g] :
( ( ( ^ [Y0: g] :
( ( ( sK1 @ X2 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ X2 )
= sK2 ) )
@ ( sK3 @ X2 ) )
= $true )
| ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 ) ),
inference(sigma_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ X2 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ X2 )
= sK2 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f178]) ).
thf(f178,plain,
! [X2: g,X1: g] :
( ( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
= $true )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK1 @ X2 @ Y0 )
= sK2 )
& ( ( sK1 @ Y0 @ X2 )
= sK2 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f177]) ).
thf(f177,plain,
! [X2: g,X1: g] :
( ( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
= $true )
| ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
| ( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $true )
| ( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f163]) ).
thf(f163,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $true )
| ( ( ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK2 )
@ ( sK4 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
! [X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK2 ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f161]) ).
thf(f161,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $true )
| ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK2 ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f185,plain,
( spl0_6
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f184,f87,f158]) ).
thf(f184,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
| ( ( sK1 @ ( sK3 @ X2 ) @ X2 )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
| ( ( ( sK1 @ ( sK3 @ X2 ) @ X2 )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f181]) ).
thf(f173,plain,
( spl0_6
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f172,f69,f158]) ).
thf(f172,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
| ( ( sK1 @ sK2 @ X2 )
= X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
| ( $true
= ( ( sK1 @ sK2 @ X2 )
= X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
! [X2: g,X1: g] :
( ( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
= $true )
| ( $true
= ( ( sK1 @ sK2 @ X2 )
= X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: g,X1: g] :
( ( ( ( ( sK1 @ sK2 @ X2 )
= X2 )
& ( ( sK1 @ X2 @ sK2 )
= X2 ) )
= $true )
| ( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: g,X1: g] :
( ( ( ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
@ X2 )
= $true )
| ( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) ) )
| ( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f164]) ).
thf(f142,plain,
( spl0_5
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f141,f101,f101]) ).
thf(f141,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK1 @ X4 @ ( sK1 @ X5 @ X6 ) )
= ( sK1 @ ( sK1 @ X4 @ X5 ) @ X6 ) )
| ( ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) )
= ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) )
= ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( ( sK1 @ ( sK1 @ X4 @ X5 ) @ X6 )
= ( sK1 @ X4 @ ( sK1 @ X5 @ X6 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f139]) ).
thf(f139,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( ^ [Y0: g] :
( ( sK1 @ ( sK1 @ X4 @ X5 ) @ Y0 )
= ( sK1 @ X4 @ ( sK1 @ X5 @ Y0 ) ) )
@ X6 )
= $true )
| ( ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) )
= ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ X4 @ X5 ) @ Y0 )
= ( sK1 @ X4 @ ( sK1 @ X5 @ Y0 ) ) ) )
= $true )
| ( ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) )
= ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f137]) ).
thf(f137,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ X4 @ Y0 ) @ Y1 )
= ( sK1 @ X4 @ ( sK1 @ Y0 @ Y1 ) ) ) )
@ X5 ) )
| ( ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) )
= ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ X4 @ Y0 ) @ Y1 )
= ( sK1 @ X4 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) )
= ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f135]) ).
thf(f135,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) )
@ X4 )
= $true )
| ( ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) )
= ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
! [X2: g,X3: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ( ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) )
= ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 )
= ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) ) )
= $true )
| ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X2: g,X3: g,X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( ( ( sK1 @ ( sK1 @ X1 @ X2 ) @ X3 )
= ( sK1 @ X1 @ ( sK1 @ X2 @ X3 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK1 @ ( sK1 @ X1 @ X2 ) @ Y0 )
= ( sK1 @ X1 @ ( sK1 @ X2 @ Y0 ) ) )
@ X3 ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X2: g,X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ ( sK1 @ X1 @ X2 ) @ Y0 )
= ( sK1 @ X1 @ ( sK1 @ X2 @ Y0 ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
! [X2: g,X1: g] :
( ( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ X1 @ Y0 ) @ Y1 )
= ( sK1 @ X1 @ ( sK1 @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ ( sK1 @ X1 @ Y0 ) @ Y1 )
= ( sK1 @ X1 @ ( sK1 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) )
@ X1 ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f66,plain,
( spl0_1
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f62,f64,f64]) ).
thf(f62,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ sK2 )
= X1 )
| ( ( sK1 @ X2 @ sK2 )
= X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: g,X1: g] :
( ( ( sK1 @ X1 @ sK2 )
= X1 )
| ( ( ( sK1 @ X2 @ sK2 )
= X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: g,X1: g] :
( ( ( ( ( sK1 @ sK2 @ X2 )
= X2 )
& ( ( sK1 @ X2 @ sK2 )
= X2 ) )
= $true )
| ( ( sK1 @ X1 @ sK2 )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: g,X1: g] :
( ( ( ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) )
@ X2 )
= $true )
| ( ( sK1 @ X1 @ sK2 )
= X1 ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) ) )
| ( ( sK1 @ X1 @ sK2 )
= X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: g] :
( ( $true
= ( ( sK1 @ X1 @ sK2 )
= X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $true )
| ( $true
= ( ( sK1 @ X1 @ sK2 )
= X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 )
@ X1 ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK1 @ sK2 @ Y0 )
= Y0 )
& ( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK1 @ Y0 @ Y1 )
= sK2 )
& ( ( sK1 @ Y1 @ Y0 )
= sK2 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ ( sK1 @ Y0 @ Y1 ) @ Y2 )
= ( sK1 @ Y0 @ ( sK1 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK2 )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG271^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 03:42:55 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.48 ---- Original DTF file ---
% 0.33/0.48 thf(spec,logic,$$dhol).
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 % File : ALG271^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.33/0.48 % Domain : General Algebra
% 0.33/0.48 % Problem : TPS problem EQUIV-01-03
% 0.33/0.48 % Version : Especial.
% 0.33/0.48 % English :
% 0.33/0.48
% 0.33/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.48 % Source : [Bro09]
% 0.33/0.48 % Names : tps_0530 [Bro09]
% 0.33/0.48 % : EQUIV-01-03 [TPS]
% 0.33/0.48
% 0.33/0.48 % Status : Theorem
% 0.33/0.48 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% 0.33/0.48 % Syntax : Number of formulae : 16 ( 7 unt; 8 typ; 7 def)
% 0.33/0.48 % Number of atoms : 29 ( 14 equ; 0 cnn)
% 0.33/0.48 % Maximal formula atoms : 2 ( 3 avg)
% 0.33/0.48 % Number of connectives : 41 ( 0 ~; 0 |; 6 &; 34 @)
% 0.33/0.48 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.33/0.48 % Maximal formula depth : 6 ( 2 avg)
% 0.33/0.48 % Number of types : 2 ( 1 usr)
% 0.33/0.48 % Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% 0.33/0.48 % Number of symbols : 8 ( 7 usr; 0 con; 1-2 aty)
% 0.33/0.48 % Number of variables : 24 ( 13 ^; 9 !; 2 ?; 24 :)
% 0.33/0.48 % SPC : TH0_THM_EQU_NAR
% 0.33/0.48
% 0.33/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.33/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.33/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.33/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.33/0.48 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.33/0.48 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 thf(g_type,type,
% 0.33/0.48 g: $tType ).
% 0.33/0.48
% 0.33/0.48 thf(cGROUP1_type,type,
% 0.33/0.48 cGROUP1: ( g > g > g ) > g > $o ).
% 0.33/0.48
% 0.33/0.48 thf(cGROUP3_type,type,
% 0.33/0.48 cGROUP3: ( g > g > g ) > g > $o ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_ASSOC_type,type,
% 0.33/0.48 cGRP_ASSOC: ( g > g > g ) > $o ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_INVERSE_type,type,
% 0.33/0.48 cGRP_INVERSE: ( g > g > g ) > g > $o ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_RIGHT_INVERSE_type,type,
% 0.33/0.48 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_RIGHT_UNIT_type,type,
% 0.33/0.48 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_UNIT_type,type,
% 0.33/0.48 cGRP_UNIT: ( g > g > g ) > g > $o ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_ASSOC_def,definition,
% 0.33/0.48 ( cGRP_ASSOC
% 0.33/0.48 = ( ^ [Xf: g > g > g] :
% 0.33/0.48 ! [Xa: g,Xb: g,Xc: g] :
% 0.33/0.48 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 0.33/0.48 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_INVERSE_def,definition,
% 0.33/0.48 ( cGRP_INVERSE
% 0.33/0.48 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.33/0.48 ! [Xa: g] :
% 0.33/0.48 ? [Xb: g] :
% 0.33/0.48 ( ( ( Xf @ Xa @ Xb )
% 0.33/0.48 = Xe )
% 0.33/0.48 & ( ( Xf @ Xb @ Xa )
% 0.33/0.48 = Xe ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_RIGHT_INVERSE_def,definition,
% 0.33/0.48 ( cGRP_RIGHT_INVERSE
% 0.33/0.48 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.33/0.48 ! [Xa: g] :
% 0.33/0.48 ? [Xb: g] :
% 0.33/0.48 ( ( Xf @ Xa @ Xb )
% 0.33/0.48 = Xe ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_RIGHT_UNIT_def,definition,
% 0.33/0.48 ( cGRP_RIGHT_UNIT
% 0.33/0.48 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.33/0.48 ! [Xa: g] :
% 0.33/0.48 ( ( Xf @ Xa @ Xe )
% 0.33/0.48 = Xa ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(cGRP_UNIT_def,definition,
% 0.33/0.48 ( cGRP_UNIT
% 0.33/0.48 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.33/0.48 ! [Xa: g] :
% 0.33/0.48 ( ( ( Xf @ Xe @ Xa )
% 0.33/0.48 = Xa )
% 0.33/0.48 & ( ( Xf @ Xa @ Xe )
% 0.33/0.48 = Xa ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(cGROUP1_def,definition,
% 0.33/0.48 ( cGROUP1
% 0.33/0.48 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.33/0.48 ( ( cGRP_ASSOC @ Xf )
% 0.33/0.48 & ( cGRP_UNIT @ Xf @ Xe )
% 0.33/0.48 & ( cGRP_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(cGROUP3_def,definition,
% 0.33/0.48 ( cGROUP3
% 0.33/0.48 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.33/0.48 ( ( cGRP_ASSOC @ Xf )
% 0.33/0.48 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 0.33/0.48 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(cEQUIV_01_03,conjecture,
% 0.33/0.48 ! [Xf: g > g > g,Xe: g] :
% 0.33/0.48 ( ( cGROUP1 @ Xf @ Xe )
% 0.33/0.48 <=> ( cGROUP3 @ Xf @ Xe ) ) ).
% 0.33/0.48
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 ------------------------
% 1.71/1.43 ---- Embedded in THF ---
% 1.71/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.43 %%% Generated on Tue Feb 24 03:42:56 EST 2026
% 1.71/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.43 %%% Logic specification used:
% 1.71/1.43 %%% thf(spec, logic, $$dhol).
% 1.71/1.43
% 1.71/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2DTF32585.p
% See solution above
% 1.71/1.43 ------------------------
% 1.71/1.44 ---- Cleaned THF ---
% 1.71/1.44 thf(g_type,type,
% 1.71/1.44 g: $tType ).
% 1.71/1.44
% 1.71/1.44 thf(cGROUP1_type,type,
% 1.71/1.44 cGROUP1: ( g > g > g ) > g > $o ).
% 1.71/1.44
% 1.71/1.44 thf(cGROUP3_type,type,
% 1.71/1.44 cGROUP3: ( g > g > g ) > g > $o ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_ASSOC_type,type,
% 1.71/1.44 cGRP_ASSOC: ( g > g > g ) > $o ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_INVERSE_type,type,
% 1.71/1.44 cGRP_INVERSE: ( g > g > g ) > g > $o ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_RIGHT_INVERSE_type,type,
% 1.71/1.44 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_RIGHT_UNIT_type,type,
% 1.71/1.44 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_UNIT_type,type,
% 1.71/1.44 cGRP_UNIT: ( g > g > g ) > g > $o ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_ASSOC_def,definition,
% 1.71/1.44 ( cGRP_ASSOC
% 1.71/1.44 = ( ^ [Xf: g > g > g] :
% 1.71/1.44 ! [Xa: g,Xb: g,Xc: g] :
% 1.71/1.44 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 1.71/1.44 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_INVERSE_def,definition,
% 1.71/1.44 ( cGRP_INVERSE
% 1.71/1.44 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.71/1.44 ! [Xa: g] :
% 1.71/1.44 ? [Xb: g] :
% 1.71/1.44 ( ( ( Xf @ Xa @ Xb )
% 1.71/1.44 = Xe )
% 1.71/1.44 & ( ( Xf @ Xb @ Xa )
% 1.71/1.44 = Xe ) ) ) ) ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_RIGHT_INVERSE_def,definition,
% 1.71/1.44 ( cGRP_RIGHT_INVERSE
% 1.71/1.44 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.71/1.44 ! [Xa: g] :
% 1.71/1.44 ? [Xb: g] :
% 1.71/1.44 ( ( Xf @ Xa @ Xb )
% 1.71/1.44 = Xe ) ) ) ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_RIGHT_UNIT_def,definition,
% 1.71/1.44 ( cGRP_RIGHT_UNIT
% 1.71/1.44 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.71/1.44 ! [Xa: g] :
% 1.71/1.44 ( ( Xf @ Xa @ Xe )
% 1.71/1.44 = Xa ) ) ) ).
% 1.71/1.44
% 1.71/1.44 thf(cGRP_UNIT_def,definition,
% 1.71/1.44 ( cGRP_UNIT
% 1.71/1.44 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.71/1.44 ! [Xa: g] :
% 1.71/1.44 ( ( ( Xf @ Xe @ Xa )
% 1.71/1.44 = Xa )
% 1.71/1.44 & ( ( Xf @ Xa @ Xe )
% 1.71/1.44 = Xa ) ) ) ) ).
% 1.71/1.44
% 1.71/1.44 thf(cGROUP1_def,definition,
% 1.71/1.44 ( cGROUP1
% 1.71/1.44 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.71/1.44 ( ( cGRP_ASSOC @ Xf )
% 1.71/1.44 & ( cGRP_UNIT @ Xf @ Xe )
% 1.71/1.44 & ( cGRP_INVERSE @ Xf @ Xe ) ) ) ) ).
% 1.71/1.44
% 1.71/1.44 thf(cGROUP3_def,definition,
% 1.71/1.44 ( cGROUP3
% 1.71/1.44 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.71/1.44 ( ( cGRP_ASSOC @ Xf )
% 1.71/1.44 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 1.71/1.44 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 1.71/1.44
% 1.71/1.44 thf(cEQUIV_01_03,conjecture,
% 1.71/1.44 ! [Xf: g > g > g,Xe: g] :
% 1.71/1.44 ( ( cGROUP1 @ Xf @ Xe )
% 1.71/1.44 <=> ( cGROUP3 @ Xf @ Xe ) ) ).
% 1.71/1.44 ------------------------
% 1.71/1.45 % (32686)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_32585 for (2999ds/27Mi)
% 1.71/1.46 % (32685)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_32585 for (2999ds/4Mi)
% 1.71/1.46 % (32684)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/183Mi)
% 1.71/1.46 % (32688)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_32585 for (2999ds/2Mi)
% 1.71/1.46 % (32687)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/2Mi)
% 1.71/1.46 % (32689)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_32585 for (2999ds/275Mi)
% 1.71/1.46 % (32690)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/18Mi)
% 1.71/1.46 % (32685)Instruction limit reached!
% 1.71/1.46 % (32685)------------------------------
% 1.71/1.46 % (32685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.46 % (32685)Termination reason: Unknown
% 1.71/1.46 % (32685)Termination phase: Saturation
% 1.71/1.46
% 1.71/1.46 % (32685)Memory used [KB]: 5500
% 1.71/1.46 % (32685)Time elapsed: 0.003 s
% 1.71/1.46 % (32685)Instructions burned: 4 (million)
% 1.71/1.46 % (32685)------------------------------
% 1.71/1.46 % (32685)------------------------------
% 1.71/1.46 % (32687)Instruction limit reached!
% 1.71/1.46 % (32687)------------------------------
% 1.71/1.46 % (32687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.46 % (32687)Termination reason: Unknown
% 1.71/1.46 % (32687)Termination phase: Property scanning
% 1.71/1.46 % (32688)Instruction limit reached!
% 1.71/1.46 % (32688)------------------------------
% 1.71/1.46 % (32688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.46 % (32688)Termination reason: Unknown
% 1.71/1.46 % (32688)Termination phase: Function definition elimination
% 1.71/1.46
% 1.71/1.46 % (32688)Memory used [KB]: 1023
% 1.71/1.46 % (32688)Time elapsed: 0.003 s
% 1.71/1.46 % (32688)Instructions burned: 3 (million)
% 1.71/1.46 % (32688)------------------------------
% 1.71/1.46 % (32688)------------------------------
% 1.71/1.46
% 1.71/1.46 % (32687)Memory used [KB]: 1023
% 1.71/1.46 % (32687)Time elapsed: 0.003 s
% 1.71/1.46 % (32687)Instructions burned: 3 (million)
% 1.71/1.46 % (32687)------------------------------
% 1.71/1.46 % (32687)------------------------------
% 1.71/1.47 % (32686)Instruction limit reached!
% 1.71/1.47 % (32686)------------------------------
% 1.71/1.47 % (32686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.47 % (32686)Termination reason: Unknown
% 1.71/1.47 % (32686)Termination phase: Saturation
% 1.71/1.47
% 1.71/1.47 % (32686)Memory used [KB]: 5756
% 1.71/1.47 % (32686)Time elapsed: 0.013 s
% 1.71/1.47 % (32686)Instructions burned: 27 (million)
% 1.71/1.47 % (32686)------------------------------
% 1.71/1.47 % (32686)------------------------------
% 1.71/1.47 % (32690)Instruction limit reached!
% 1.71/1.47 % (32690)------------------------------
% 1.71/1.47 % (32690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.47 % (32690)Termination reason: Unknown
% 1.71/1.47 % (32690)Termination phase: Saturation
% 1.71/1.47
% 1.71/1.47 % (32690)Memory used [KB]: 5500
% 1.71/1.47 % (32690)Time elapsed: 0.010 s
% 1.71/1.47 % (32690)Instructions burned: 18 (million)
% 1.71/1.47 % (32690)------------------------------
% 1.71/1.47 % (32690)------------------------------
% 1.71/1.48 % (32691)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/3Mi)
% 1.71/1.48 % (32693)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_32585 for (2999ds/15Mi)
% 1.71/1.48 % (32692)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_32585 for (2999ds/37Mi)
% 1.71/1.48 % (32691)Instruction limit reached!
% 1.71/1.48 % (32691)------------------------------
% 1.71/1.48 % (32691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.48 % (32691)Termination reason: Unknown
% 1.71/1.48 % (32691)Termination phase: Saturation
% 1.71/1.48
% 1.71/1.48 % (32691)Memory used [KB]: 5500
% 1.71/1.48 % (32691)Time elapsed: 0.003 s
% 1.71/1.48 % (32691)Instructions burned: 4 (million)
% 1.71/1.48 % (32691)------------------------------
% 1.71/1.48 % (32691)------------------------------
% 1.71/1.48 % (32694)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_32585 for (2999ds/3Mi)
% 1.71/1.48 % (32695)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_32585 for (2999ds/1041Mi)
% 1.71/1.48 % (32694)Instruction limit reached!
% 1.71/1.48 % (32694)------------------------------
% 1.71/1.48 % (32694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.48 % (32694)Termination reason: Unknown
% 1.71/1.48 % (32694)Termination phase: Property scanning
% 1.71/1.48
% 1.71/1.48 % (32694)Memory used [KB]: 1023
% 1.71/1.48 % (32694)Time elapsed: 0.003 s
% 1.71/1.48 % (32694)Instructions burned: 4 (million)
% 1.71/1.48 % (32693)Instruction limit reached!
% 1.71/1.48 % (32693)------------------------------
% 1.71/1.48 % (32693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.48 % (32693)Termination reason: Unknown
% 1.71/1.48 % (32693)Termination phase: Saturation
% 1.71/1.48
% 1.71/1.48 % (32693)Memory used [KB]: 5500
% 1.71/1.48 % (32693)Time elapsed: 0.009 s
% 1.71/1.48 % (32693)Instructions burned: 16 (million)
% 1.71/1.48 % (32693)------------------------------
% 1.71/1.48 % (32693)------------------------------
% 1.71/1.48 % (32694)------------------------------
% 1.71/1.48 % (32694)------------------------------
% 1.71/1.49 % (32696)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/7Mi)
% 1.71/1.49 % (32692)Instruction limit reached!
% 1.71/1.49 % (32692)------------------------------
% 1.71/1.49 % (32692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.49 % (32692)Termination reason: Unknown
% 1.71/1.49 % (32692)Termination phase: Saturation
% 1.71/1.49
% 1.71/1.49 % (32692)Memory used [KB]: 5628
% 1.71/1.49 % (32692)Time elapsed: 0.020 s
% 1.71/1.49 % (32692)Instructions burned: 39 (million)
% 1.71/1.49 % (32692)------------------------------
% 1.71/1.49 % (32692)------------------------------
% 1.77/1.50 % (32696)Instruction limit reached!
% 1.77/1.50 % (32696)------------------------------
% 1.77/1.50 % (32696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.50 % (32696)Termination reason: Unknown
% 1.77/1.50 % (32696)Termination phase: Saturation
% 1.77/1.50
% 1.77/1.50 % (32696)Memory used [KB]: 1023
% 1.77/1.50 % (32696)Time elapsed: 0.005 s
% 1.77/1.50 % (32696)Instructions burned: 8 (million)
% 1.77/1.50 % (32696)------------------------------
% 1.77/1.50 % (32696)------------------------------
% 1.77/1.50 % (32697)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/16Mi)
% 1.77/1.50 % (32698)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_32585 for (2999ds/3Mi)
% 1.77/1.50 % (32698)Instruction limit reached!
% 1.77/1.50 % (32698)------------------------------
% 1.77/1.50 % (32698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.50 % (32698)Termination reason: Unknown
% 1.77/1.50 % (32698)Termination phase: Function definition elimination
% 1.77/1.50
% 1.77/1.50 % (32698)Memory used [KB]: 1023
% 1.77/1.50 % (32698)Time elapsed: 0.003 s
% 1.77/1.50 % (32698)Instructions burned: 3 (million)
% 1.77/1.50 % (32698)------------------------------
% 1.77/1.50 % (32698)------------------------------
% 1.77/1.51 % (32697)Instruction limit reached!
% 1.77/1.51 % (32697)------------------------------
% 1.77/1.51 % (32697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.51 % (32697)Termination reason: Unknown
% 1.77/1.51 % (32697)Termination phase: Saturation
% 1.77/1.51
% 1.77/1.51 % (32697)Memory used [KB]: 5884
% 1.77/1.51 % (32697)Time elapsed: 0.011 s
% 1.77/1.51 % (32697)Instructions burned: 17 (million)
% 1.77/1.51 % (32697)------------------------------
% 1.77/1.51 % (32697)------------------------------
% 1.77/1.51 % (32699)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_32585 for (2999ds/3Mi)
% 1.77/1.51 % (32699)Instruction limit reached!
% 1.77/1.51 % (32699)------------------------------
% 1.77/1.51 % (32699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.51 % (32699)Termination reason: Unknown
% 1.77/1.51 % (32699)Termination phase: Property scanning
% 1.77/1.51
% 1.77/1.51 % (32699)Memory used [KB]: 1023
% 1.77/1.51 % (32699)Time elapsed: 0.003 s
% 1.77/1.51 % (32699)Instructions burned: 3 (million)
% 1.77/1.51 % (32699)------------------------------
% 1.77/1.51 % (32699)------------------------------
% 1.77/1.51 % (32700)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/7Mi)
% 1.77/1.52 % (32700)Instruction limit reached!
% 1.77/1.52 % (32700)------------------------------
% 1.77/1.52 % (32700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.52 % (32700)Termination reason: Unknown
% 1.77/1.52 % (32700)Termination phase: Saturation
% 1.77/1.52
% 1.77/1.52 % (32700)Memory used [KB]: 5500
% 1.77/1.52 % (32700)Time elapsed: 0.005 s
% 1.77/1.52 % (32700)Instructions burned: 7 (million)
% 1.77/1.52 % (32700)------------------------------
% 1.77/1.52 % (32700)------------------------------
% 1.77/1.52 % (32701)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/3Mi)
% 1.77/1.52 % (32701)Instruction limit reached!
% 1.77/1.52 % (32701)------------------------------
% 1.77/1.52 % (32701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.52 % (32701)Termination reason: Unknown
% 1.77/1.52 % (32701)Termination phase: Property scanning
% 1.77/1.52
% 1.77/1.52 % (32701)Memory used [KB]: 1023
% 1.77/1.52 % (32701)Time elapsed: 0.003 s
% 1.77/1.52 % (32701)Instructions burned: 4 (million)
% 1.77/1.52 % (32701)------------------------------
% 1.77/1.52 % (32701)------------------------------
% 1.77/1.52 % (32702)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/4Mi)
% 1.77/1.53 % (32702)Instruction limit reached!
% 1.77/1.53 % (32702)------------------------------
% 1.77/1.53 % (32702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.53 % (32702)Termination reason: Unknown
% 1.77/1.53 % (32702)Termination phase: Property scanning
% 1.77/1.53
% 1.77/1.53 % (32702)Memory used [KB]: 1023
% 1.77/1.53 % (32702)Time elapsed: 0.003 s
% 1.77/1.53 % (32702)Instructions burned: 4 (million)
% 1.77/1.53 % (32702)------------------------------
% 1.77/1.53 % (32702)------------------------------
% 1.77/1.53 % (32703)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/18Mi)
% 1.77/1.53 % (32704)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/710Mi)
% 1.77/1.53 % (32705)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/6Mi)
% 1.77/1.54 % (32705)Instruction limit reached!
% 1.77/1.54 % (32705)------------------------------
% 1.77/1.54 % (32705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.54 % (32705)Termination reason: Unknown
% 1.77/1.54 % (32705)Termination phase: Saturation
% 1.77/1.54
% 1.77/1.54 % (32705)Memory used [KB]: 5500
% 1.77/1.54 % (32705)Time elapsed: 0.004 s
% 1.77/1.54 % (32705)Instructions burned: 6 (million)
% 1.77/1.54 % (32705)------------------------------
% 1.77/1.54 % (32705)------------------------------
% 1.77/1.54 % (32703)Instruction limit reached!
% 1.77/1.54 % (32703)------------------------------
% 1.77/1.54 % (32703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.54 % (32703)Termination reason: Unknown
% 1.77/1.54 % (32703)Termination phase: Saturation
% 1.77/1.54
% 1.77/1.54 % (32703)Memory used [KB]: 5628
% 1.77/1.54 % (32703)Time elapsed: 0.011 s
% 1.77/1.54 % (32703)Instructions burned: 18 (million)
% 1.77/1.54 % (32703)------------------------------
% 1.77/1.54 % (32703)------------------------------
% 1.77/1.54 % (32706)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_32585 for (2999ds/902Mi)
% 1.77/1.54 % (32706)Refutation not found, incomplete strategy
% 1.77/1.54 % (32706)------------------------------
% 1.77/1.54 % (32706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.54 % (32706)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.54
% 1.77/1.54
% 1.77/1.54 % (32706)Memory used [KB]: 5500
% 1.77/1.54 % (32706)Time elapsed: 0.003 s
% 1.77/1.54 % (32706)Instructions burned: 3 (million)
% 1.77/1.54 % (32706)------------------------------
% 1.77/1.54 % (32706)------------------------------
% 1.77/1.55 % (32684)Instruction limit reached!
% 1.77/1.55 % (32684)------------------------------
% 1.77/1.55 % (32684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.55 % (32684)Termination reason: Unknown
% 1.77/1.55 % (32684)Termination phase: Saturation
% 1.77/1.55
% 1.77/1.55 % (32684)Memory used [KB]: 6780
% 1.77/1.55 % (32684)Time elapsed: 0.091 s
% 1.77/1.55 % (32684)Instructions burned: 183 (million)
% 1.77/1.55 % (32684)------------------------------
% 1.77/1.55 % (32684)------------------------------
% 1.77/1.55 % (32707)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_32585 for (2999ds/21Mi)
% 1.77/1.55 % (32708)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/5Mi)
% 1.77/1.56 % (32708)Instruction limit reached!
% 1.77/1.56 % (32708)------------------------------
% 1.77/1.56 % (32708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.56 % (32708)Termination reason: Unknown
% 1.77/1.56 % (32708)Termination phase: Saturation
% 1.77/1.56
% 1.77/1.56 % (32708)Memory used [KB]: 5500
% 1.77/1.56 % (32708)Time elapsed: 0.004 s
% 1.77/1.56 % (32708)Instructions burned: 5 (million)
% 1.77/1.56 % (32708)------------------------------
% 1.77/1.56 % (32708)------------------------------
% 1.77/1.56 % (32709)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_32585 for (2999ds/6Mi)
% 1.77/1.56 % (32709)Instruction limit reached!
% 1.77/1.56 % (32709)------------------------------
% 1.77/1.56 % (32709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.56 % (32709)Termination reason: Unknown
% 1.77/1.56 % (32709)Termination phase: Saturation
% 1.77/1.56
% 1.77/1.56 % (32709)Memory used [KB]: 5500
% 1.77/1.56 % (32709)Time elapsed: 0.004 s
% 1.77/1.56 % (32709)Instructions burned: 6 (million)
% 1.77/1.56 % (32709)------------------------------
% 1.77/1.56 % (32709)------------------------------
% 1.77/1.56 % (32710)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32585 for (2999ds/377Mi)
% 1.77/1.56 % (32707)Instruction limit reached!
% 1.77/1.56 % (32707)------------------------------
% 1.77/1.56 % (32707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.56 % (32707)Termination reason: Unknown
% 1.77/1.56 % (32707)Termination phase: Saturation
% 1.77/1.56
% 1.77/1.56 % (32707)Memory used [KB]: 5628
% 1.77/1.56 % (32707)Time elapsed: 0.013 s
% 1.77/1.56 % (32707)Instructions burned: 21 (million)
% 1.77/1.56 % (32707)------------------------------
% 1.77/1.56 % (32707)------------------------------
% 1.77/1.57 % (32711)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_32585 for (2998ds/779Mi)
% 1.77/1.58 % (32712)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_32585 for (2998ds/19Mi)
% 1.77/1.58 % (32713)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32585 for (2998ds/879Mi)
% 1.77/1.59 % (32689)Instruction limit reached!
% 1.77/1.59 % (32689)------------------------------
% 1.77/1.59 % (32689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.59 % (32689)Termination reason: Unknown
% 1.77/1.59 % (32689)Termination phase: Saturation
% 1.77/1.59
% 1.77/1.59 % (32689)Memory used [KB]: 6396
% 1.77/1.59 % (32689)Time elapsed: 0.130 s
% 1.77/1.59 % (32689)Instructions burned: 276 (million)
% 1.77/1.59 % (32689)------------------------------
% 1.77/1.59 % (32689)------------------------------
% 1.77/1.59 % (32712)Instruction limit reached!
% 1.77/1.59 % (32712)------------------------------
% 1.77/1.59 % (32712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.59 % (32712)Termination reason: Unknown
% 1.77/1.59 % (32712)Termination phase: Saturation
% 1.77/1.59
% 1.77/1.59 % (32712)Memory used [KB]: 5628
% 1.77/1.59 % (32712)Time elapsed: 0.011 s
% 1.77/1.59 % (32712)Instructions burned: 19 (million)
% 1.77/1.59 % (32712)------------------------------
% 1.77/1.59 % (32712)------------------------------
% 1.77/1.60 % (32711)First to succeed.
% 1.77/1.60 % (32714)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32585 for (2998ds/17Mi)
% 1.77/1.60 % (32715)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32585 for (2998ds/3Mi)
% 1.77/1.61 % (32715)Instruction limit reached!
% 1.77/1.61 % (32715)------------------------------
% 1.77/1.61 % (32715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.61 % (32715)Termination reason: Unknown
% 1.77/1.61 % (32715)Termination phase: Function definition elimination
% 1.77/1.61
% 1.77/1.61 % (32715)Memory used [KB]: 1023
% 1.77/1.61 % (32715)Time elapsed: 0.003 s
% 1.77/1.61 % (32715)Instructions burned: 4 (million)
% 1.77/1.61 % (32715)------------------------------
% 1.77/1.61 % (32715)------------------------------
% 1.77/1.61 % (32711)Refutation found. Thanks to Tanya!
% 1.77/1.61 % SZS status Theorem for DTF2THF_32585
% 1.77/1.61 % SZS output start Proof for DTF2THF_32585
% 1.77/1.61 thf(type_def_5, type, g: $tType).
% 1.77/1.61 thf(func_def_0, type, g: $tType).
% 1.77/1.61 thf(func_def_1, type, cGROUP1: (g > g > g) > g > $o).
% 1.77/1.61 thf(func_def_2, type, cGROUP3: (g > g > g) > g > $o).
% 1.77/1.61 thf(func_def_3, type, cGRP_ASSOC: (g > g > g) > $o).
% 1.77/1.61 thf(func_def_4, type, cGRP_INVERSE: (g > g > g) > g > $o).
% 1.77/1.61 thf(func_def_5, type, cGRP_RIGHT_INVERSE: (g > g > g) > g > $o).
% 1.77/1.61 thf(func_def_6, type, cGRP_RIGHT_UNIT: (g > g > g) > g > $o).
% 1.77/1.61 thf(func_def_7, type, cGRP_UNIT: (g > g > g) > g > $o).
% 1.77/1.61 thf(func_def_24, type, sK1: g > g > g).
% 1.77/1.61 thf(func_def_25, type, sK2: g).
% 1.77/1.61 thf(func_def_26, type, sK3: g > g).
% 1.77/1.61 thf(func_def_27, type, sK4: g > g).
% 1.77/1.61 thf(func_def_28, type, sK5: g).
% 1.77/1.61 thf(func_def_29, type, sK6: g).
% 1.77/1.61 thf(func_def_30, type, sK7: g).
% 1.77/1.61 thf(func_def_31, type, sK8: g).
% 1.77/1.61 thf(func_def_32, type, sK9: g).
% 1.77/1.61 thf(func_def_33, type, sK10: g).
% 1.77/1.61 thf(func_def_34, type, sK11: g).
% 1.77/1.61 thf(f425,plain,(
% 1.77/1.61 $false),
% 1.77/1.61 inference(avatar_sat_refutation,[status(thm)],[f66,f142,f173,f185,f187,f242,f245,f255,f259,f305,f357,f373,f401,f420,f424])).
% 1.77/1.61 thf(f424,plain,(
% 1.77/1.61 ~spl0_3 | ~spl0_12),
% 1.77/1.61 inference(avatar_contradiction_clause,[status(thm)],[f423])).
% 1.77/1.61 thf(f423,plain,(
% 1.77/1.61 $false | (~spl0_3 | ~spl0_12)),
% 1.77/1.61 inference(trivial_inequality_removal,[status(thm)],[f422])).
% 1.77/1.61 thf(f422,plain,(
% 1.77/1.61 (sK2 != sK2) | (~spl0_3 | ~spl0_12)),
% 1.77/1.61 inference(superposition,[status(thm)],[f241,f82])).
% 1.77/1.61 thf(f82,plain,(
% 1.77/1.61 ( ! [X2 : g] : (((sK1 @ X2 @ (sK3 @ X2)) = sK2)) ) | ~spl0_3),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.77/1.61 thf(f81,definition,(
% 1.77/1.61 spl0_3 <=> ! [X2 : g] : ((sK1 @ X2 @ (sK3 @ X2)) = sK2)),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.77/1.61 thf(f241,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((sK1 @ sK8 @ X1) != sK2)) ) | ~spl0_12),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f240])).
% 1.77/1.61 thf(f240,definition,(
% 1.77/1.61 spl0_12 <=> ! [X1 : g] : ((sK1 @ sK8 @ X1) != sK2)),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.77/1.61 thf(f420,plain,(
% 1.77/1.61 ~spl0_3 | ~spl0_4 | ~spl0_7),
% 1.77/1.61 inference(avatar_contradiction_clause,[status(thm)],[f419])).
% 1.77/1.61 thf(f419,plain,(
% 1.77/1.61 $false | (~spl0_3 | ~spl0_4 | ~spl0_7)),
% 1.77/1.61 inference(subsumption_resolution,[status(thm)],[f411,f88])).
% 1.77/1.61 thf(f88,plain,(
% 1.77/1.61 ( ! [X2 : g] : (((sK1 @ (sK3 @ X2) @ X2) = sK2)) ) | ~spl0_4),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.77/1.61 thf(f87,definition,(
% 1.77/1.61 spl0_4 <=> ! [X2 : g] : ((sK1 @ (sK3 @ X2) @ X2) = sK2)),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.77/1.61 thf(f411,plain,(
% 1.77/1.61 (sK2 != (sK1 @ (sK3 @ sK7) @ sK7)) | (~spl0_3 | ~spl0_7)),
% 1.77/1.61 inference(trivial_inequality_removal,[status(thm)],[f408])).
% 1.77/1.61 thf(f408,plain,(
% 1.77/1.61 (sK2 != (sK1 @ (sK3 @ sK7) @ sK7)) | (sK2 != sK2) | (~spl0_3 | ~spl0_7)),
% 1.77/1.61 inference(superposition,[status(thm)],[f222,f82])).
% 1.77/1.61 thf(f222,plain,(
% 1.77/1.61 ( ! [X2 : g] : (((sK1 @ sK7 @ X2) != sK2) | ((sK1 @ X2 @ sK7) != sK2)) ) | ~spl0_7),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f221])).
% 1.77/1.61 thf(f221,definition,(
% 1.77/1.61 spl0_7 <=> ! [X2 : g] : (((sK1 @ X2 @ sK7) != sK2) | ((sK1 @ sK7 @ X2) != sK2))),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.77/1.61 thf(f401,plain,(
% 1.77/1.61 ~spl0_1 | ~spl0_2 | ~spl0_5 | ~spl0_6 | ~spl0_7),
% 1.77/1.61 inference(avatar_contradiction_clause,[status(thm)],[f400])).
% 1.77/1.61 thf(f400,plain,(
% 1.77/1.61 $false | (~spl0_1 | ~spl0_2 | ~spl0_5 | ~spl0_6 | ~spl0_7)),
% 1.77/1.61 inference(trivial_inequality_removal,[status(thm)],[f399])).
% 1.77/1.61 thf(f399,plain,(
% 1.77/1.61 (sK2 != sK2) | (~spl0_1 | ~spl0_2 | ~spl0_5 | ~spl0_6 | ~spl0_7)),
% 1.77/1.61 inference(superposition,[status(thm)],[f382,f378])).
% 1.77/1.61 thf(f378,plain,(
% 1.77/1.61 ( ! [X0 : g] : (((sK1 @ (sK4 @ X0) @ X0) = sK2)) ) | (~spl0_1 | ~spl0_2 | ~spl0_5 | ~spl0_6)),
% 1.77/1.61 inference(superposition,[status(thm)],[f159,f342])).
% 1.77/1.61 thf(f342,plain,(
% 1.77/1.61 ( ! [X0 : g] : (((sK4 @ (sK4 @ X0)) = X0)) ) | (~spl0_1 | ~spl0_2 | ~spl0_5 | ~spl0_6)),
% 1.77/1.61 inference(superposition,[status(thm)],[f70,f266])).
% 1.77/1.61 thf(f266,plain,(
% 1.77/1.61 ( ! [X0 : g] : (((sK1 @ sK2 @ (sK4 @ (sK4 @ X0))) = X0)) ) | (~spl0_1 | ~spl0_5 | ~spl0_6)),
% 1.77/1.61 inference(forward_demodulation,[status(thm)],[f260,f65])).
% 1.77/1.61 thf(f65,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((sK1 @ X1 @ sK2) = X1)) ) | ~spl0_1),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.77/1.61 thf(f64,definition,(
% 1.77/1.61 spl0_1 <=> ! [X1 : g] : ((sK1 @ X1 @ sK2) = X1)),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.77/1.61 thf(f260,plain,(
% 1.77/1.61 ( ! [X0 : g] : (((sK1 @ sK2 @ (sK4 @ (sK4 @ X0))) = (sK1 @ X0 @ sK2))) ) | (~spl0_5 | ~spl0_6)),
% 1.77/1.61 inference(superposition,[status(thm)],[f246,f159])).
% 1.77/1.61 thf(f246,plain,(
% 1.77/1.61 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ (sK4 @ X0) @ X1)) = (sK1 @ sK2 @ X1))) ) | (~spl0_5 | ~spl0_6)),
% 1.77/1.61 inference(superposition,[status(thm)],[f102,f159])).
% 1.77/1.61 thf(f102,plain,(
% 1.77/1.61 ( ! [X3 : g,X1 : g,X4 : g] : (((sK1 @ (sK1 @ X1 @ X3) @ X4) = (sK1 @ X1 @ (sK1 @ X3 @ X4)))) ) | ~spl0_5),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.77/1.61 thf(f101,definition,(
% 1.77/1.61 spl0_5 <=> ! [X4 : g,X1 : g,X3 : g] : ((sK1 @ (sK1 @ X1 @ X3) @ X4) = (sK1 @ X1 @ (sK1 @ X3 @ X4)))),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.77/1.61 thf(f70,plain,(
% 1.77/1.61 ( ! [X2 : g] : (((sK1 @ sK2 @ X2) = X2)) ) | ~spl0_2),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.77/1.61 thf(f69,definition,(
% 1.77/1.61 spl0_2 <=> ! [X2 : g] : ((sK1 @ sK2 @ X2) = X2)),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.77/1.61 thf(f159,plain,(
% 1.77/1.61 ( ! [X2 : g] : (((sK1 @ X2 @ (sK4 @ X2)) = sK2)) ) | ~spl0_6),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f158])).
% 1.77/1.61 thf(f158,definition,(
% 1.77/1.61 spl0_6 <=> ! [X2 : g] : ((sK1 @ X2 @ (sK4 @ X2)) = sK2)),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.77/1.61 thf(f382,plain,(
% 1.77/1.61 ((sK1 @ (sK4 @ sK7) @ sK7) != sK2) | (~spl0_6 | ~spl0_7)),
% 1.77/1.61 inference(trivial_inequality_removal,[status(thm)],[f379])).
% 1.77/1.61 thf(f379,plain,(
% 1.77/1.61 (sK2 != sK2) | ((sK1 @ (sK4 @ sK7) @ sK7) != sK2) | (~spl0_6 | ~spl0_7)),
% 1.77/1.61 inference(superposition,[status(thm)],[f222,f159])).
% 1.77/1.61 thf(f373,plain,(
% 1.77/1.61 ~spl0_6 | ~spl0_12),
% 1.77/1.61 inference(avatar_contradiction_clause,[status(thm)],[f372])).
% 1.77/1.61 thf(f372,plain,(
% 1.77/1.61 $false | (~spl0_6 | ~spl0_12)),
% 1.77/1.61 inference(trivial_inequality_removal,[status(thm)],[f368])).
% 1.77/1.61 thf(f368,plain,(
% 1.77/1.61 (sK2 != sK2) | (~spl0_6 | ~spl0_12)),
% 1.77/1.61 inference(superposition,[status(thm)],[f241,f159])).
% 1.77/1.61 thf(f357,plain,(
% 1.77/1.61 ~spl0_2 | spl0_10),
% 1.77/1.61 inference(avatar_contradiction_clause,[status(thm)],[f356])).
% 1.77/1.61 thf(f356,plain,(
% 1.77/1.61 $false | (~spl0_2 | spl0_10)),
% 1.77/1.61 inference(trivial_inequality_removal,[status(thm)],[f355])).
% 1.77/1.61 thf(f355,plain,(
% 1.77/1.61 (sK6 != sK6) | (~spl0_2 | spl0_10)),
% 1.77/1.61 inference(superposition,[status(thm)],[f234,f70])).
% 1.77/1.61 thf(f234,plain,(
% 1.77/1.61 ((sK1 @ sK2 @ sK6) != sK6) | spl0_10),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f232])).
% 1.77/1.61 thf(f232,definition,(
% 1.77/1.61 spl0_10 <=> ((sK1 @ sK2 @ sK6) = sK6)),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.77/1.61 thf(f305,plain,(
% 1.77/1.61 spl0_2 | ~spl0_1 | ~spl0_5 | ~spl0_6),
% 1.77/1.61 inference(avatar_split_clause,[status(thm)],[f294,f158,f101,f64,f69])).
% 1.77/1.61 thf(f294,plain,(
% 1.77/1.61 ( ! [X0 : g] : (((sK1 @ sK2 @ X0) = X0)) ) | (~spl0_1 | ~spl0_5 | ~spl0_6)),
% 1.77/1.61 inference(superposition,[status(thm)],[f271,f266])).
% 1.77/1.61 thf(f271,plain,(
% 1.77/1.61 ( ! [X0 : g,X1 : g] : (((sK1 @ X1 @ (sK4 @ (sK4 @ X0))) = (sK1 @ X1 @ X0))) ) | (~spl0_1 | ~spl0_5 | ~spl0_6)),
% 1.77/1.61 inference(superposition,[status(thm)],[f247,f266])).
% 1.77/1.61 thf(f247,plain,(
% 1.77/1.61 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ sK2 @ X1)) = (sK1 @ X0 @ X1))) ) | (~spl0_1 | ~spl0_5)),
% 1.77/1.61 inference(superposition,[status(thm)],[f102,f65])).
% 1.77/1.61 thf(f259,plain,(
% 1.77/1.61 ~spl0_1 | spl0_9),
% 1.77/1.61 inference(avatar_contradiction_clause,[status(thm)],[f258])).
% 1.77/1.61 thf(f258,plain,(
% 1.77/1.61 $false | (~spl0_1 | spl0_9)),
% 1.77/1.61 inference(subsumption_resolution,[status(thm)],[f230,f65])).
% 1.77/1.61 thf(f230,plain,(
% 1.77/1.61 ((sK1 @ sK9 @ sK2) != sK9) | spl0_9),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f228])).
% 1.77/1.61 thf(f228,definition,(
% 1.77/1.61 spl0_9 <=> ((sK1 @ sK9 @ sK2) = sK9)),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.77/1.61 thf(f255,plain,(
% 1.77/1.61 ~spl0_5 | spl0_8),
% 1.77/1.61 inference(avatar_contradiction_clause,[status(thm)],[f254])).
% 1.77/1.61 thf(f254,plain,(
% 1.77/1.61 $false | (~spl0_5 | spl0_8)),
% 1.77/1.61 inference(trivial_inequality_removal,[status(thm)],[f253])).
% 1.77/1.61 thf(f253,plain,(
% 1.77/1.61 ((sK1 @ sK5 @ (sK1 @ sK10 @ sK11)) != (sK1 @ sK5 @ (sK1 @ sK10 @ sK11))) | (~spl0_5 | spl0_8)),
% 1.77/1.61 inference(superposition,[status(thm)],[f226,f102])).
% 1.77/1.61 thf(f226,plain,(
% 1.77/1.61 ((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) != (sK1 @ sK5 @ (sK1 @ sK10 @ sK11))) | spl0_8),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f224])).
% 1.77/1.61 thf(f224,definition,(
% 1.77/1.61 spl0_8 <=> ((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) = (sK1 @ sK5 @ (sK1 @ sK10 @ sK11)))),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.77/1.61 thf(f245,plain,(
% 1.77/1.61 ~spl0_1 | spl0_11),
% 1.77/1.61 inference(avatar_contradiction_clause,[status(thm)],[f244])).
% 1.77/1.61 thf(f244,plain,(
% 1.77/1.61 $false | (~spl0_1 | spl0_11)),
% 1.77/1.61 inference(trivial_inequality_removal,[status(thm)],[f243])).
% 1.77/1.61 thf(f243,plain,(
% 1.77/1.61 (sK6 != sK6) | (~spl0_1 | spl0_11)),
% 1.77/1.61 inference(superposition,[status(thm)],[f238,f65])).
% 1.77/1.61 thf(f238,plain,(
% 1.77/1.61 ((sK1 @ sK6 @ sK2) != sK6) | spl0_11),
% 1.77/1.61 inference(avatar_component_clause,[status(thm)],[f236])).
% 1.77/1.61 thf(f236,definition,(
% 1.77/1.61 spl0_11 <=> ((sK1 @ sK6 @ sK2) = sK6)),
% 1.77/1.61 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.77/1.61 thf(f242,plain,(
% 1.77/1.61 spl0_7 | ~spl0_8 | ~spl0_9 | ~spl0_10 | ~spl0_11 | spl0_12),
% 1.77/1.61 inference(avatar_split_clause,[status(thm)],[f219,f240,f236,f232,f228,f224,f221])).
% 1.77/1.61 thf(f219,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X2 @ sK7) != sK2) | ((sK1 @ sK7 @ X2) != sK2) | ((sK1 @ sK9 @ sK2) != sK9) | ((sK1 @ sK6 @ sK2) != sK6) | ((sK1 @ sK2 @ sK6) != sK6) | ((sK1 @ sK8 @ X1) != sK2) | ((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) != (sK1 @ sK5 @ (sK1 @ sK10 @ sK11)))) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f218])).
% 1.77/1.61 thf(f218,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X2 @ sK7) != sK2) | ((sK1 @ sK8 @ X1) != sK2) | ($false = ((sK1 @ sK7 @ X2) = sK2)) | ((sK1 @ sK9 @ sK2) != sK9) | ((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) != (sK1 @ sK5 @ (sK1 @ sK10 @ sK11))) | ((sK1 @ sK2 @ sK6) != sK6) | ((sK1 @ sK6 @ sK2) != sK6)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f217])).
% 1.77/1.61 thf(f217,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ sK9 @ sK2) != sK9) | ((sK1 @ X2 @ sK7) != sK2) | (((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) = (sK1 @ sK5 @ (sK1 @ sK10 @ sK11))) = $false) | ((sK1 @ sK2 @ sK6) != sK6) | ($false = ((sK1 @ sK7 @ X2) = sK2)) | ((sK1 @ sK8 @ X1) != sK2) | ((sK1 @ sK6 @ sK2) != sK6)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f216])).
% 1.77/1.61 thf(f216,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ sK6 @ sK2) != sK6) | (((sK1 @ X2 @ sK7) = sK2) = $false) | (((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) = (sK1 @ sK5 @ (sK1 @ sK10 @ sK11))) = $false) | ((sK1 @ sK8 @ X1) != sK2) | ((sK1 @ sK2 @ sK6) != sK6) | ($false = ((sK1 @ sK7 @ X2) = sK2)) | ((sK1 @ sK9 @ sK2) != sK9)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f215])).
% 1.77/1.61 thf(f215,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ sK6 @ sK2) != sK6) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | (((sK1 @ X2 @ sK7) = sK2) = $false) | ((sK1 @ sK9 @ sK2) != sK9) | ($false = ((sK1 @ sK7 @ X2) = sK2)) | ((sK1 @ sK8 @ X1) != sK2) | (((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) = (sK1 @ sK5 @ (sK1 @ sK10 @ sK11))) = $false)) )),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f214])).
% 1.77/1.61 thf(f214,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((((sK1 @ sK7 @ X2) = sK2) & ((sK1 @ X2 @ sK7) = sK2)) = $false) | (((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) = (sK1 @ sK5 @ (sK1 @ sK10 @ sK11))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((sK1 @ sK8 @ X1) != sK2) | ((sK1 @ sK9 @ sK2) != sK9) | ((sK1 @ sK6 @ sK2) != sK6)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f213])).
% 1.77/1.61 thf(f213,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ sK6 @ sK2) != sK6) | (((^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2))) @ X2) = $false) | ((sK1 @ sK8 @ X1) != sK2) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((sK1 @ sK9 @ sK2) != sK9) | (((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) = (sK1 @ sK5 @ (sK1 @ sK10 @ sK11))) = $false)) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f212])).
% 1.77/1.61 thf(f212,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((sK1 @ sK6 @ sK2) != sK6) | ((sK1 @ sK9 @ sK2) != sK9) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | ((sK1 @ sK8 @ X1) != sK2) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | (((sK1 @ (sK1 @ sK5 @ sK10) @ sK11) = (sK1 @ sK5 @ (sK1 @ sK10 @ sK11))) = $false)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f211])).
% 1.77/1.61 thf(f211,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((sK1 @ sK9 @ sK2) != sK9) | (((^[Y0 : g]: ((sK1 @ (sK1 @ sK5 @ sK10) @ Y0) = (sK1 @ sK5 @ (sK1 @ sK10 @ Y0)))) @ sK11) = $false) | ((sK1 @ sK6 @ sK2) != sK6) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | ((sK1 @ sK8 @ X1) != sK2) | (((sK1 @ sK2 @ sK6) = sK6) = $false)) )),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f210])).
% 1.77/1.61 thf(f210,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((sK1 @ sK9 @ sK2) != sK9) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ sK5 @ sK10) @ Y0) = (sK1 @ sK5 @ (sK1 @ sK10 @ Y0))))) = $false) | ((sK1 @ sK6 @ sK2) != sK6) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((sK1 @ sK8 @ X1) != sK2) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f209])).
% 1.77/1.61 thf(f209,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((sK1 @ sK6 @ sK2) != sK6) | ((sK1 @ sK8 @ X1) != sK2) | ((sK1 @ sK9 @ sK2) != sK9) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | (((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1)))))) @ sK10) = $false)) )),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f208])).
% 1.77/1.61 thf(f208,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | ((sK1 @ sK8 @ X1) != sK2) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((sK1 @ sK6 @ sK2) != sK6) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | ((sK1 @ sK9 @ sK2) != sK9)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f207])).
% 1.77/1.61 thf(f207,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((sK1 @ sK8 @ X1) != sK2) | (((sK1 @ sK6 @ sK2) = sK6) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | ((sK1 @ sK9 @ sK2) != sK9)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f206])).
% 1.77/1.61 thf(f206,plain,(
% 1.77/1.61 ( ! [X1 : g] : ((((sK1 @ sK9 @ sK2) = sK9) = $false) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((sK1 @ sK8 @ X1) != sK2) | (((sK1 @ sK6 @ sK2) = sK6) = $false)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f205])).
% 1.77/1.61 thf(f205,plain,(
% 1.77/1.61 ( ! [X1 : g] : ((((sK1 @ sK8 @ X1) = sK2) = $false) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | (((sK1 @ sK6 @ sK2) = sK6) = $false) | (((sK1 @ sK9 @ sK2) = sK9) = $false)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f204])).
% 1.77/1.61 thf(f204,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | (((sK1 @ sK8 @ X1) = sK2) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | (((sK1 @ sK6 @ sK2) = sK6) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ($false = ((^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)) @ sK9))) )),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f203])).
% 1.77/1.61 thf(f203,plain,(
% 1.77/1.61 ( ! [X1 : g] : (($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | (((sK1 @ sK6 @ sK2) = sK6) = $false) | (((sK1 @ sK8 @ X1) = sK2) = $false)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f202])).
% 1.77/1.61 thf(f202,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | ($false = ((^[Y0 : g]: ((sK1 @ sK8 @ Y0) = sK2)) @ X1)) | (((sK1 @ sK6 @ sK2) = sK6) = $false) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))))) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f201])).
% 1.77/1.61 thf(f201,plain,(
% 1.77/1.61 ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK8 @ Y0) = sK2))) = $false) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | (((sK1 @ sK6 @ sK2) = sK6) = $false)),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f200])).
% 1.77/1.61 thf(f200,plain,(
% 1.77/1.61 ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | (((sK1 @ sK6 @ sK2) = sK6) = $false) | ($false = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))) @ sK8)) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false)),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f199])).
% 1.77/1.61 thf(f199,plain,(
% 1.77/1.61 ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | (((sK1 @ sK2 @ sK6) = sK6) = $false) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | (((sK1 @ sK6 @ sK2) = sK6) = $false)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f198])).
% 1.77/1.61 thf(f198,plain,(
% 1.77/1.61 ($false = (((sK1 @ sK2 @ sK6) = sK6) & ((sK1 @ sK6 @ sK2) = sK6))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ sK7 @ Y0) = sK2) & ((sK1 @ Y0 @ sK7) = sK2)))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))))),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f197])).
% 1.77/1.61 thf(f197,plain,(
% 1.77/1.61 ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | (((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))) @ sK7) = $false) | ($false = (((sK1 @ sK2 @ sK6) = sK6) & ((sK1 @ sK6 @ sK2) = sK6)))),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f196])).
% 1.77/1.61 thf(f196,plain,(
% 1.77/1.61 ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | ($false = (((sK1 @ sK2 @ sK6) = sK6) & ((sK1 @ sK6 @ sK2) = sK6))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false)),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f195])).
% 1.77/1.61 thf(f195,plain,(
% 1.77/1.61 ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) | ($false = ((^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0))) @ sK6)) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false)),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f194])).
% 1.77/1.61 thf(f194,plain,(
% 1.77/1.61 ($false = (!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0))))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))))),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f193])).
% 1.77/1.61 thf(f193,plain,(
% 1.77/1.61 (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ sK5 @ Y0) @ Y1) = (sK1 @ sK5 @ (sK1 @ Y0 @ Y1))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))))),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f192])).
% 1.77/1.61 thf(f192,plain,(
% 1.77/1.61 ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | (((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))) @ sK5) = $false)),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f191])).
% 1.77/1.61 thf(f191,plain,(
% 1.77/1.61 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2))))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))))),
% 1.77/1.61 inference(duplicate_literal_removal,[status(thm)],[f190])).
% 1.77/1.61 thf(f190,plain,(
% 1.77/1.61 ($false = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2))))))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2))))))))) = $false) | (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $false)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f189])).
% 1.77/1.61 thf(f189,plain,(
% 1.77/1.61 (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $false) | ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) | (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2))))))))) = $false)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f188])).
% 1.77/1.61 thf(f188,plain,(
% 1.77/1.61 ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2))))))))) = $false) | (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $false)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.77/1.61 thf(f46,plain,(
% 1.77/1.61 ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $false) | ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) = $false)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.77/1.61 thf(f44,plain,(
% 1.77/1.61 ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) != (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))))),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.77/1.61 thf(f43,plain,(
% 1.77/1.61 ($false = ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) = (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2))))))))))))),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.77/1.61 thf(f42,plain,(
% 1.77/1.61 (((^[Y0 : g]: ((((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y2) @ Y3) = (sK1 @ Y1 @ (sK1 @ Y2 @ Y3)))))))))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) = (((!! @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = Y1) & ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: (((sK1 @ Y1 @ Y2) = Y0) & ((sK1 @ Y2 @ Y1) = Y0))))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y2) @ Y3) = (sK1 @ Y1 @ (sK1 @ Y2 @ Y3)))))))))))) @ sK2) = $false)),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f41])).
% 1.77/1.61 thf(f41,plain,(
% 1.77/1.61 ($false = (!! @ g @ (^[Y0 : g]: ((((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y2) @ Y3) = (sK1 @ Y1 @ (sK1 @ Y2 @ Y3)))))))))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) = (((!! @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = Y1) & ((sK1 @ Y1 @ Y0) = Y1)))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: (((sK1 @ Y1 @ Y2) = Y0) & ((sK1 @ Y2 @ Y1) = Y0))))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ (sK1 @ Y1 @ Y2) @ Y3) = (sK1 @ Y1 @ (sK1 @ Y2 @ Y3))))))))))))))),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.77/1.61 thf(f40,plain,(
% 1.77/1.61 (((^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((((!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y2 @ Y3) @ Y4) = (Y0 @ Y2 @ (Y0 @ Y3 @ Y4)))))))))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))) = (((!! @ g @ (^[Y2 : g]: (((Y0 @ Y1 @ Y2) = Y2) & ((Y0 @ Y2 @ Y1) = Y2)))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: (((Y0 @ Y2 @ Y3) = Y1) & ((Y0 @ Y3 @ Y2) = Y1))))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y2 @ Y3) @ Y4) = (Y0 @ Y2 @ (Y0 @ Y3 @ Y4)))))))))))))) @ sK1) = $false)),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f39])).
% 1.77/1.61 thf(f39,plain,(
% 1.77/1.61 ((!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((((!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y2 @ Y3) @ Y4) = (Y0 @ Y2 @ (Y0 @ Y3 @ Y4)))))))))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))) = (((!! @ g @ (^[Y2 : g]: (((Y0 @ Y1 @ Y2) = Y2) & ((Y0 @ Y2 @ Y1) = Y2)))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: (((Y0 @ Y2 @ Y3) = Y1) & ((Y0 @ Y3 @ Y2) = Y1))))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y2 @ Y3) @ Y4) = (Y0 @ Y2 @ (Y0 @ Y3 @ Y4))))))))))))))) = $false)),
% 1.77/1.61 inference(not_proxy_clausification,[status(thm)],[f38])).
% 1.77/1.61 thf(f38,plain,(
% 1.77/1.61 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((((!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y2 @ Y3) @ Y4) = (Y0 @ Y2 @ (Y0 @ Y3 @ Y4)))))))))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))) = (((!! @ g @ (^[Y2 : g]: (((Y0 @ Y1 @ Y2) = Y2) & ((Y0 @ Y2 @ Y1) = Y2)))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: (((Y0 @ Y2 @ Y3) = Y1) & ((Y0 @ Y3 @ Y2) = Y1))))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y2 @ Y3) @ Y4) = (Y0 @ Y2 @ (Y0 @ Y3 @ Y4)))))))))))))))) = $true)),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.77/1.61 thf(f37,plain,(
% 1.77/1.61 ((~ (!! @ (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]: ((Y4 @ Y6 @ Y5) = Y6)))))) @ Y2 @ Y3) & ((^[Y4 : g > g > g]: (!! @ g @ (^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (!! @ g @ (^[Y7 : g]: ((Y4 @ (Y4 @ Y5 @ Y6) @ Y7) = (Y4 @ Y5 @ (Y4 @ Y6 @ Y7)))))))))) @ Y2)) & ((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (?? @ g @ (^[Y7 : g]: ((Y4 @ Y6 @ Y7) = Y5)))))))) @ Y2 @ Y3))))) @ Y0 @ Y1) = ((^[Y2 : g > g > g]: ((^[Y3 : g]: ((((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (((Y4 @ Y5 @ Y6) = Y6) & ((Y4 @ Y6 @ Y5) = Y6))))))) @ Y2 @ Y3) & ((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (?? @ g @ (^[Y7 : g]: (((Y4 @ Y6 @ Y7) = Y5) & ((Y4 @ Y7 @ Y6) = Y5))))))))) @ Y2 @ Y3)) & ((^[Y4 : g > g > g]: (!! @ g @ (^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (!! @ g @ (^[Y7 : g]: ((Y4 @ (Y4 @ Y5 @ Y6) @ Y7) = (Y4 @ Y5 @ (Y4 @ Y6 @ Y7)))))))))) @ Y2))))) @ Y0 @ Y1))))))) = $true)),
% 1.77/1.61 inference(definition_unfolding,[status(thm)],[f32,f36,f35])).
% 1.77/1.61 thf(f35,plain,(
% 1.77/1.61 (cGROUP1 = (^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (((Y2 @ Y3 @ Y4) = Y4) & ((Y2 @ Y4 @ Y3) = Y4))))))) @ Y0 @ Y1) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: (((Y2 @ Y4 @ Y5) = Y3) & ((Y2 @ Y5 @ Y4) = Y3))))))))) @ Y0 @ Y1)) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ (Y2 @ Y3 @ Y4) @ Y5) = (Y2 @ Y3 @ (Y2 @ Y4 @ Y5)))))))))) @ Y0))))))),
% 1.77/1.61 inference(definition_unfolding,[status(thm)],[f34,f27,f30,f31])).
% 1.77/1.61 thf(f31,plain,(
% 1.77/1.61 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ Y1 @ (Y0 @ Y2 @ Y3)))))))))))),
% 1.77/1.61 inference(cnf_transformation,[status(thm)],[f22])).
% 1.77/1.61 thf(f22,plain,(
% 1.77/1.61 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ Y1 @ (Y0 @ Y2 @ Y3)))))))))))),
% 1.77/1.61 inference(fool_elimination,[status(thm)],[f21])).
% 1.77/1.61 thf(f21,plain,(
% 1.77/1.61 (cGRP_ASSOC = (^[X0 : g > g > g] : (! [X1 : g,X2 : g,X3 : g] : ((X0 @ (X0 @ X3 @ X2) @ X1) = (X0 @ X3 @ (X0 @ X2 @ X1))))))),
% 1.77/1.61 inference(rectify,[status(thm)],[f1])).
% 1.77/1.61 thf(f1,axiom,(
% 1.77/1.61 (cGRP_ASSOC = (^[X0 : g > g > g] : (! [X3 : g,X2 : g,X1 : g] : ((X0 @ (X0 @ X1 @ X2) @ X3) = (X0 @ X1 @ (X0 @ X2 @ X3))))))),
% 1.77/1.61 file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_ASSOC_def)).
% 1.77/1.61 thf(f30,plain,(
% 1.77/1.61 (cGRP_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: (((Y0 @ Y2 @ Y3) = Y1) & ((Y0 @ Y3 @ Y2) = Y1))))))))))),
% 1.77/1.61 inference(cnf_transformation,[status(thm)],[f24])).
% 1.77/1.61 thf(f24,plain,(
% 1.77/1.61 (cGRP_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: (((Y0 @ Y2 @ Y3) = Y1) & ((Y0 @ Y3 @ Y2) = Y1))))))))))),
% 1.77/1.61 inference(fool_elimination,[status(thm)],[f23])).
% 1.77/1.61 thf(f23,plain,(
% 1.77/1.61 ((^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : (((X0 @ X3 @ X2) = X1) & ((X0 @ X2 @ X3) = X1)))) = cGRP_INVERSE)),
% 1.77/1.61 inference(rectify,[status(thm)],[f2])).
% 1.77/1.61 thf(f2,axiom,(
% 1.77/1.61 ((^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ? [X2 : g] : (((X0 @ X2 @ X1) = X4) & ((X0 @ X1 @ X2) = X4)))) = cGRP_INVERSE)),
% 1.77/1.61 file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_INVERSE_def)).
% 1.77/1.61 thf(f27,plain,(
% 1.77/1.61 (cGRP_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (((Y0 @ Y1 @ Y2) = Y2) & ((Y0 @ Y2 @ Y1) = Y2))))))))),
% 1.77/1.61 inference(cnf_transformation,[status(thm)],[f26])).
% 1.77/1.61 thf(f26,plain,(
% 1.77/1.61 (cGRP_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (((Y0 @ Y1 @ Y2) = Y2) & ((Y0 @ Y2 @ Y1) = Y2))))))))),
% 1.77/1.61 inference(fool_elimination,[status(thm)],[f25])).
% 1.77/1.61 thf(f25,plain,(
% 1.77/1.61 (cGRP_UNIT = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : (((X0 @ X2 @ X1) = X2) & ((X0 @ X1 @ X2) = X2)))))),
% 1.77/1.61 inference(rectify,[status(thm)],[f5])).
% 1.77/1.61 thf(f5,axiom,(
% 1.77/1.61 (cGRP_UNIT = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : (((X0 @ X1 @ X4) = X1) & ((X0 @ X4 @ X1) = X1)))))),
% 1.77/1.61 file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_UNIT_def)).
% 1.77/1.61 thf(f34,plain,(
% 1.77/1.61 (cGROUP1 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_UNIT @ Y0 @ Y1) & (cGRP_INVERSE @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))),
% 1.77/1.61 inference(cnf_transformation,[status(thm)],[f18])).
% 1.77/1.61 thf(f18,plain,(
% 1.77/1.61 (cGROUP1 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_UNIT @ Y0 @ Y1) & (cGRP_INVERSE @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))),
% 1.77/1.61 inference(fool_elimination,[status(thm)],[f17])).
% 1.77/1.61 thf(f17,plain,(
% 1.77/1.61 ((^[X0 : g > g > g, X1 : g] : ((cGRP_ASSOC @ X0) & (cGRP_INVERSE @ X0 @ X1) & (cGRP_UNIT @ X0 @ X1))) = cGROUP1)),
% 1.77/1.61 inference(rectify,[status(thm)],[f6])).
% 1.77/1.61 thf(f6,axiom,(
% 1.77/1.61 ((^[X0 : g > g > g, X4 : g] : ((cGRP_ASSOC @ X0) & (cGRP_INVERSE @ X0 @ X4) & (cGRP_UNIT @ X0 @ X4))) = cGROUP1)),
% 1.77/1.61 file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGROUP1_def)).
% 1.77/1.61 thf(f36,plain,(
% 1.77/1.61 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[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 @ Y4) @ Y5) = (Y2 @ Y3 @ (Y2 @ Y4 @ Y5)))))))))) @ Y0)) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: ((Y2 @ Y4 @ Y5) = Y3)))))))) @ Y0 @ Y1))))))),
% 1.77/1.61 inference(definition_unfolding,[status(thm)],[f33,f28,f31,f29])).
% 1.77/1.61 thf(f29,plain,(
% 1.77/1.61 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 1.77/1.61 inference(cnf_transformation,[status(thm)],[f20])).
% 1.77/1.61 thf(f20,plain,(
% 1.77/1.61 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 1.77/1.61 inference(fool_elimination,[status(thm)],[f19])).
% 1.77/1.61 thf(f19,plain,(
% 1.77/1.61 (cGRP_RIGHT_INVERSE = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : ((X0 @ X2 @ X3) = X1))))),
% 1.77/1.61 inference(rectify,[status(thm)],[f3])).
% 1.77/1.61 thf(f3,axiom,(
% 1.77/1.61 (cGRP_RIGHT_INVERSE = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ? [X2 : g] : ((X0 @ X1 @ X2) = X4))))),
% 1.77/1.61 file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_RIGHT_INVERSE_def)).
% 1.77/1.61 thf(f28,plain,(
% 1.77/1.61 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 1.77/1.61 inference(cnf_transformation,[status(thm)],[f16])).
% 1.77/1.61 thf(f16,plain,(
% 1.77/1.61 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 1.77/1.61 inference(fool_elimination,[status(thm)],[f15])).
% 1.77/1.61 thf(f15,plain,(
% 1.77/1.61 ((^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ((X0 @ X2 @ X1) = X2))) = cGRP_RIGHT_UNIT)),
% 1.77/1.61 inference(rectify,[status(thm)],[f4])).
% 1.77/1.61 thf(f4,axiom,(
% 1.77/1.61 ((^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ((X0 @ X1 @ X4) = X1))) = cGRP_RIGHT_UNIT)),
% 1.77/1.61 file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGRP_RIGHT_UNIT_def)).
% 1.77/1.61 thf(f33,plain,(
% 1.77/1.61 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_UNIT @ Y0 @ Y1) & (cGRP_ASSOC @ Y0)) & (cGRP_RIGHT_INVERSE @ Y0 @ Y1))))))),
% 1.77/1.61 inference(cnf_transformation,[status(thm)],[f12])).
% 1.77/1.61 thf(f12,plain,(
% 1.77/1.61 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_UNIT @ Y0 @ Y1) & (cGRP_ASSOC @ Y0)) & (cGRP_RIGHT_INVERSE @ Y0 @ Y1))))))),
% 1.77/1.61 inference(fool_elimination,[status(thm)],[f11])).
% 1.77/1.61 thf(f11,plain,(
% 1.77/1.61 ((^[X0 : g > g > g, X1 : g] : ((cGRP_RIGHT_INVERSE @ X0 @ X1) & (cGRP_ASSOC @ X0) & (cGRP_RIGHT_UNIT @ X0 @ X1))) = cGROUP3)),
% 1.77/1.61 inference(rectify,[status(thm)],[f7])).
% 1.77/1.61 thf(f7,axiom,(
% 1.77/1.61 ((^[X0 : g > g > g, X4 : g] : ((cGRP_RIGHT_INVERSE @ X0 @ X4) & (cGRP_ASSOC @ X0) & (cGRP_RIGHT_UNIT @ X0 @ X4))) = cGROUP3)),
% 1.77/1.61 file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cGROUP3_def)).
% 1.77/1.61 thf(f32,plain,(
% 1.77/1.61 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((cGROUP3 @ Y0 @ Y1) = (cGROUP1 @ Y0 @ Y1))))))) = $true)),
% 1.77/1.61 inference(cnf_transformation,[status(thm)],[f14])).
% 1.77/1.61 thf(f14,plain,(
% 1.77/1.61 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((cGROUP3 @ Y0 @ Y1) = (cGROUP1 @ Y0 @ Y1))))))) = $true)),
% 1.77/1.61 inference(fool_elimination,[status(thm)],[f13])).
% 1.77/1.61 thf(f13,plain,(
% 1.77/1.61 ~! [X0 : g,X1 : g > g > g] : ((cGROUP3 @ X1 @ X0) <=> (cGROUP1 @ X1 @ X0))),
% 1.77/1.61 inference(rectify,[status(thm)],[f9])).
% 1.77/1.61 thf(f9,negated_conjecture,(
% 1.77/1.61 ~! [X4 : g,X0 : g > g > g] : ((cGROUP3 @ X0 @ X4) <=> (cGROUP1 @ X0 @ X4))),
% 1.77/1.61 inference(negated_conjecture,[status(cth)],[f8])).
% 1.77/1.61 thf(f8,conjecture,(
% 1.77/1.61 ! [X4 : g,X0 : g > g > g] : ((cGROUP3 @ X0 @ X4) <=> (cGROUP1 @ X0 @ X4))),
% 1.77/1.61 file('/export/starexec/sandbox/tmp/tmp.4ds2hPo6Tn/DTF2THF_32585.p',cEQUIV_01_03)).
% 1.77/1.61 thf(f187,plain,(
% 1.77/1.61 spl0_6 | spl0_3),
% 1.77/1.61 inference(avatar_split_clause,[status(thm)],[f186,f81,f158])).
% 1.77/1.61 thf(f186,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X2 @ (sK3 @ X2)) = sK2) | ((sK1 @ X1 @ (sK4 @ X1)) = sK2)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f183])).
% 1.77/1.61 thf(f183,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ (sK4 @ X1)) = sK2) | ($true = ((sK1 @ X2 @ (sK3 @ X2)) = sK2))) )),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f181])).
% 1.77/1.61 thf(f181,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (($true = (((sK1 @ X2 @ (sK3 @ X2)) = sK2) & ((sK1 @ (sK3 @ X2) @ X2) = sK2))) | ((sK1 @ X1 @ (sK4 @ X1)) = sK2)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f180])).
% 1.77/1.61 thf(f180,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: (((sK1 @ X2 @ Y0) = sK2) & ((sK1 @ Y0 @ X2) = sK2))) @ (sK3 @ X2)) = $true) | ((sK1 @ X1 @ (sK4 @ X1)) = sK2)) )),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f179])).
% 1.77/1.61 thf(f179,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ (sK4 @ X1)) = sK2) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ X2 @ Y0) = sK2) & ((sK1 @ Y0 @ X2) = sK2)))) = $true)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f178])).
% 1.77/1.61 thf(f178,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : ((((sK1 @ X1 @ (sK4 @ X1)) = sK2) = $true) | ((?? @ g @ (^[Y0 : g]: (((sK1 @ X2 @ Y0) = sK2) & ((sK1 @ Y0 @ X2) = sK2)))) = $true)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f177])).
% 1.77/1.61 thf(f177,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : ((((sK1 @ X1 @ (sK4 @ X1)) = sK2) = $true) | (((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))) @ X2) = $true)) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f165])).
% 1.77/1.61 thf(f165,plain,(
% 1.77/1.61 ( ! [X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) | (((sK1 @ X1 @ (sK4 @ X1)) = sK2) = $true)) )),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f164])).
% 1.77/1.61 thf(f164,plain,(
% 1.77/1.61 ( ! [X1 : g] : ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $true) | (((sK1 @ X1 @ (sK4 @ X1)) = sK2) = $true)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f163])).
% 1.77/1.61 thf(f163,plain,(
% 1.77/1.61 ( ! [X1 : g] : ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $true) | (((^[Y0 : g]: ((sK1 @ X1 @ Y0) = sK2)) @ (sK4 @ X1)) = $true)) )),
% 1.77/1.61 inference(sigma_clausification,[status(thm)],[f162])).
% 1.77/1.61 thf(f162,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ X1 @ Y0) = sK2))) = $true) | (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $true)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f161])).
% 1.77/1.61 thf(f161,plain,(
% 1.77/1.61 ( ! [X1 : g] : ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $true) | (((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))) @ X1) = $true)) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f144])).
% 1.77/1.61 thf(f144,plain,(
% 1.77/1.61 ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true) | (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $true)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.77/1.61 thf(f47,plain,(
% 1.77/1.61 ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.77/1.61 thf(f45,plain,(
% 1.77/1.61 ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) = $true) | ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.77/1.61 thf(f185,plain,(
% 1.77/1.61 spl0_6 | spl0_4),
% 1.77/1.61 inference(avatar_split_clause,[status(thm)],[f184,f87,f158])).
% 1.77/1.61 thf(f184,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ (sK4 @ X1)) = sK2) | ((sK1 @ (sK3 @ X2) @ X2) = sK2)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f182])).
% 1.77/1.61 thf(f182,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ (sK4 @ X1)) = sK2) | (((sK1 @ (sK3 @ X2) @ X2) = sK2) = $true)) )),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f181])).
% 1.77/1.61 thf(f173,plain,(
% 1.77/1.61 spl0_6 | spl0_2),
% 1.77/1.61 inference(avatar_split_clause,[status(thm)],[f172,f69,f158])).
% 1.77/1.61 thf(f172,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ (sK4 @ X1)) = sK2) | ((sK1 @ sK2 @ X2) = X2)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f171])).
% 1.77/1.61 thf(f171,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ (sK4 @ X1)) = sK2) | ($true = ((sK1 @ sK2 @ X2) = X2))) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f170])).
% 1.77/1.61 thf(f170,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : ((((sK1 @ X1 @ (sK4 @ X1)) = sK2) = $true) | ($true = ((sK1 @ sK2 @ X2) = X2))) )),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f168])).
% 1.77/1.61 thf(f168,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((((sK1 @ sK2 @ X2) = X2) & ((sK1 @ X2 @ sK2) = X2)) = $true) | (((sK1 @ X1 @ (sK4 @ X1)) = sK2) = $true)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f167])).
% 1.77/1.61 thf(f167,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0))) @ X2) = $true) | (((sK1 @ X1 @ (sK4 @ X1)) = sK2) = $true)) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f166])).
% 1.77/1.61 thf(f166,plain,(
% 1.77/1.61 ( ! [X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0))))) | (((sK1 @ X1 @ (sK4 @ X1)) = sK2) = $true)) )),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f164])).
% 1.77/1.61 thf(f142,plain,(
% 1.77/1.61 spl0_5 | spl0_5),
% 1.77/1.61 inference(avatar_split_clause,[status(thm)],[f141,f101,f101])).
% 1.77/1.61 thf(f141,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g,X6 : g,X4 : g,X5 : g] : (((sK1 @ X4 @ (sK1 @ X5 @ X6)) = (sK1 @ (sK1 @ X4 @ X5) @ X6)) | ((sK1 @ X1 @ (sK1 @ X2 @ X3)) = (sK1 @ (sK1 @ X1 @ X2) @ X3))) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f140])).
% 1.77/1.61 thf(f140,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g,X6 : g,X4 : g,X5 : g] : (((sK1 @ X1 @ (sK1 @ X2 @ X3)) = (sK1 @ (sK1 @ X1 @ X2) @ X3)) | ($true = ((sK1 @ (sK1 @ X4 @ X5) @ X6) = (sK1 @ X4 @ (sK1 @ X5 @ X6))))) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f139])).
% 1.77/1.61 thf(f139,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g,X6 : g,X4 : g,X5 : g] : ((((^[Y0 : g]: ((sK1 @ (sK1 @ X4 @ X5) @ Y0) = (sK1 @ X4 @ (sK1 @ X5 @ Y0)))) @ X6) = $true) | ((sK1 @ X1 @ (sK1 @ X2 @ X3)) = (sK1 @ (sK1 @ X1 @ X2) @ X3))) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f138])).
% 1.77/1.61 thf(f138,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g,X4 : g,X5 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ X4 @ X5) @ Y0) = (sK1 @ X4 @ (sK1 @ X5 @ Y0))))) = $true) | ((sK1 @ X1 @ (sK1 @ X2 @ X3)) = (sK1 @ (sK1 @ X1 @ X2) @ X3))) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f137])).
% 1.77/1.61 thf(f137,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g,X4 : g,X5 : g] : (($true = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ X4 @ Y0) @ Y1) = (sK1 @ X4 @ (sK1 @ Y0 @ Y1)))))) @ X5)) | ((sK1 @ X1 @ (sK1 @ X2 @ X3)) = (sK1 @ (sK1 @ X1 @ X2) @ X3))) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f136])).
% 1.77/1.61 thf(f136,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ X4 @ Y0) @ Y1) = (sK1 @ X4 @ (sK1 @ Y0 @ Y1))))))) = $true) | ((sK1 @ X1 @ (sK1 @ X2 @ X3)) = (sK1 @ (sK1 @ X1 @ X2) @ X3))) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f135])).
% 1.77/1.61 thf(f135,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))) @ X4) = $true) | ((sK1 @ X1 @ (sK1 @ X2 @ X3)) = (sK1 @ (sK1 @ X1 @ X2) @ X3))) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f134])).
% 1.77/1.61 thf(f134,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2))))))))) = $true) | ((sK1 @ X1 @ (sK1 @ X2 @ X3)) = (sK1 @ (sK1 @ X1 @ X2) @ X3))) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f110])).
% 1.77/1.61 thf(f110,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK1 @ (sK1 @ X1 @ X2) @ X3) = (sK1 @ X1 @ (sK1 @ X2 @ X3))) = $true) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2))))))))) = $true)) )),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.77/1.61 thf(f109,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g] : (((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true) | (((sK1 @ (sK1 @ X1 @ X2) @ X3) = (sK1 @ X1 @ (sK1 @ X2 @ X3))) = $true)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.77/1.61 thf(f108,plain,(
% 1.77/1.61 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ (sK1 @ X1 @ X2) @ Y0) = (sK1 @ X1 @ (sK1 @ X2 @ Y0)))) @ X3)) | ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true)) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f107])).
% 1.77/1.61 thf(f107,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ (sK1 @ X1 @ X2) @ Y0) = (sK1 @ X1 @ (sK1 @ X2 @ Y0))))) = $true) | ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f106])).
% 1.77/1.61 thf(f106,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ X1 @ Y0) @ Y1) = (sK1 @ X1 @ (sK1 @ Y0 @ Y1)))))) @ X2) = $true) | ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true)) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f105])).
% 1.77/1.61 thf(f105,plain,(
% 1.77/1.61 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ (sK1 @ X1 @ Y0) @ Y1) = (sK1 @ X1 @ (sK1 @ Y0 @ Y1))))))) = $true) | ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f104])).
% 1.77/1.61 thf(f104,plain,(
% 1.77/1.61 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))) @ X1)) | ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true)) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f49])).
% 1.77/1.61 thf(f49,plain,(
% 1.77/1.61 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2))))))))) = $true) | ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.77/1.61 thf(f48,plain,(
% 1.77/1.61 (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true) | ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.77/1.61 thf(f66,plain,(
% 1.77/1.61 spl0_1 | spl0_1),
% 1.77/1.61 inference(avatar_split_clause,[status(thm)],[f62,f64,f64])).
% 1.77/1.61 thf(f62,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ sK2) = X1) | ((sK1 @ X2 @ sK2) = X2)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f60])).
% 1.77/1.61 thf(f60,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((sK1 @ X1 @ sK2) = X1) | (((sK1 @ X2 @ sK2) = X2) = $true)) )),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.77/1.61 thf(f59,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : (((((sK1 @ sK2 @ X2) = X2) & ((sK1 @ X2 @ sK2) = X2)) = $true) | ((sK1 @ X1 @ sK2) = X1)) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.77/1.61 thf(f58,plain,(
% 1.77/1.61 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0))) @ X2) = $true) | ((sK1 @ X1 @ sK2) = X1)) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f57])).
% 1.77/1.61 thf(f57,plain,(
% 1.77/1.61 ( ! [X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0))))) | ((sK1 @ X1 @ sK2) = X1)) )),
% 1.77/1.61 inference(equality_proxy_clausification,[status(thm)],[f56])).
% 1.77/1.61 thf(f56,plain,(
% 1.77/1.61 ( ! [X1 : g] : (($true = ((sK1 @ X1 @ sK2) = X1)) | ($true = (!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))))) )),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.77/1.61 thf(f54,plain,(
% 1.77/1.61 ( ! [X1 : g] : ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $true) | ($true = ((sK1 @ X1 @ sK2) = X1))) )),
% 1.77/1.61 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.77/1.61 thf(f53,plain,(
% 1.77/1.61 ( ! [X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)) @ X1)) | (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $true)) )),
% 1.77/1.61 inference(pi_clausification,[status(thm)],[f52])).
% 1.77/1.61 thf(f52,plain,(
% 1.77/1.61 ($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | (((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) = $true)),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.77/1.61 thf(f50,plain,(
% 1.77/1.61 ((((!! @ g @ (^[Y0 : g]: (((sK1 @ sK2 @ Y0) = Y0) & ((sK1 @ Y0 @ sK2) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK1 @ Y0 @ Y1) = sK2) & ((sK1 @ Y1 @ Y0) = sK2))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ Y0 @ (sK1 @ Y1 @ Y2)))))))))) = $true) | ($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))))),
% 1.77/1.61 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.77/1.61 % SZS output end Proof for DTF2THF_32585
% 1.77/1.61 % (32711)------------------------------
% 1.77/1.61 % (32711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.61 % (32711)Termination reason: Refutation
% 1.77/1.61
% 1.77/1.61 % (32711)Memory used [KB]: 5884
% 1.77/1.61 % (32711)Time elapsed: 0.038 s
% 1.77/1.61 % (32711)Instructions burned: 54 (million)
% 1.77/1.61 % (32711)------------------------------
% 1.77/1.61 % (32711)------------------------------
% 1.77/1.61 % (32683)Success in time 0.155 s
%------------------------------------------------------------------------------