%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG272^5 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:37:48 AM UTC 2026
% Result : Theorem 1.80s 1.62s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 18
% Syntax : Number of formulae : 198 ( 42 unt; 0 typ; 10 def)
% Number of atoms : 1317 ( 504 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 2927 ( 196 ~; 177 |; 196 &;1962 @)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 26 usr; 19 con; 0-2 aty)
% ( 308 !!; 75 ??; 0 @@+; 0 @@-)
% Number of variables : 577 ( 485 ^; 88 !; 4 ?; 577 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(func_def_3,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_4,type,
cGRP_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_6,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_7,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_24,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
sK2: g > g > g ).
thf(func_def_26,type,
sK3: 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 > g ).
thf(func_def_32,type,
sK9: g ).
thf(f498,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f54,f61,f65,f133,f240,f376,f387,f404,f430,f461,f472,f480,f493]) ).
thf(f493,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[status(thm)],[f492]) ).
thf(f492,plain,
( $false
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f491]) ).
thf(f491,plain,
( ( $false != $false )
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f490]) ).
thf(f490,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& $false )
!= $false )
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f489]) ).
thf(f489,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& $false )
!= ( $false
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) )
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f488]) ).
thf(f488,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& $false )
!= ( $false
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) )
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f45,f386]) ).
thf(f386,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f385]) ).
thf(f385,definition,
( spl0_10
<=> ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f45,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
!= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ^ [Y0: g] :
( ( ( !! @ g
@ ^ [Y1: g] :
( ( sK2 @ Y0 @ Y1 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK2 @ Y2 @ Y1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK2 @ ( sK2 @ Y3 @ Y2 ) @ Y1 )
= ( sK2 @ Y3 @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK2 @ ( sK2 @ Y3 @ Y2 ) @ Y1 )
= ( sK2 @ Y3 @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= Y1 )
& ( ( sK2 @ Y1 @ Y0 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( ( sK2 @ Y1 @ Y2 )
= Y0 )
& ( ( sK2 @ Y2 @ Y1 )
= Y0 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( !! @ g
@ ^ [Y0: g] :
( ( ( !! @ g
@ ^ [Y1: g] :
( ( sK2 @ Y0 @ Y1 )
= Y1 ) )
& ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( sK2 @ Y2 @ Y1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK2 @ ( sK2 @ Y3 @ Y2 ) @ Y1 )
= ( sK2 @ Y3 @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( sK2 @ ( sK2 @ Y3 @ Y2 ) @ Y1 )
= ( sK2 @ Y3 @ ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= Y1 )
& ( ( sK2 @ Y1 @ Y0 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y1: g] :
( ?? @ g
@ ^ [Y2: g] :
( ( ( sK2 @ Y1 @ Y2 )
= Y0 )
& ( ( sK2 @ Y2 @ Y1 )
= Y0 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ 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 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ 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 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( $true
= ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( ( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) )
& ( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) )
& ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= ( ( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y4 @ Y3 ) @ Y2 )
= ( Y0 @ Y4 @ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ 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 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
( $true
= ( ~ ( !! @ ( 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 @ Y5 @ Y6 )
= Y6 ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g,Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( ?? @ g
@ ^ [Y7: g] :
( ( Y4 @ Y7 @ Y6 )
= Y5 ) ) )
@ Y2
@ Y3 )
& ( ^ [Y4: g > g > g] :
( !! @ g
@ ^ [Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( !! @ g
@ ^ [Y7: g] :
( ( Y4 @ ( Y4 @ Y7 @ Y6 ) @ Y5 )
= ( Y4 @ Y7 @ ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
@ Y2 ) )
@ Y0
@ Y1 )
= ( ^ [Y2: g > g > g,Y3: g] :
( ( ^ [Y4: g > g > g] :
( !! @ g
@ ^ [Y5: g] :
( !! @ g
@ ^ [Y6: g] :
( !! @ g
@ ^ [Y7: g] :
( ( Y4 @ ( Y4 @ Y7 @ Y6 ) @ Y5 )
= ( Y4 @ Y7 @ ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
@ Y2 )
& ( ^ [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 ) )
@ Y0
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f30,f35,f34]) ).
thf(f34,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f32,f31,f28]) ).
thf(f28,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)],[f16]) ).
thf(f16,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)],[f15]) ).
thf(f15,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.dh5HRQTj7p/DTF2THF_21974.p',cGRP_INVERSE_def) ).
thf(f31,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,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)],[f13]) ).
thf(f13,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( ( X0 @ X2 @ X1 )
= X2 )
& ( ( X0 @ X1 @ X2 )
= X2 ) ) )
= cGRP_UNIT ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( ( X0 @ X1 @ X4 )
= X1 )
& ( ( X0 @ X4 @ X1 )
= X1 ) ) )
= cGRP_UNIT ),
file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGRP_UNIT_def) ).
thf(f32,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( cGRP_ASSOC
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGRP_ASSOC_def) ).
thf(f33,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( cGROUP1
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_INVERSE @ X0 @ X1 )
& ( cGRP_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( cGROUP1
= ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_INVERSE @ X0 @ X4 )
& ( cGRP_UNIT @ X0 @ X4 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGROUP1_def) ).
thf(f35,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f26,f27,f29,f32]) ).
thf(f29,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( cGRP_LEFT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X3 @ X2 )
= X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( cGRP_LEFT_INVERSE
= ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( X0 @ X2 @ X1 )
= X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGRP_LEFT_INVERSE_def) ).
thf(f27,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( cGRP_LEFT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( cGRP_LEFT_UNIT
= ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( X0 @ X4 @ X1 )
= X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGRP_LEFT_UNIT_def) ).
thf(f26,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_LEFT_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_LEFT_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_INVERSE @ X0 @ X1 )
& ( cGRP_LEFT_UNIT @ X0 @ X1 ) ) )
= cGROUP2 ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_INVERSE @ X0 @ X4 )
& ( cGRP_LEFT_UNIT @ X0 @ X4 ) ) )
= cGROUP2 ),
file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGROUP2_def) ).
thf(f30,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( cGROUP2 @ Y0 @ Y1 )
= ( cGROUP1 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ~ ( !! @ ( g > g > g )
@ ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( ( cGROUP2 @ Y0 @ Y1 )
= ( cGROUP1 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
~ ! [X0: g,X1: g > g > g] :
( ( cGROUP2 @ X1 @ X0 )
<=> ( cGROUP1 @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ! [X4: g,X0: g > g > g] :
( ( cGROUP2 @ X0 @ X4 )
<=> ( cGROUP1 @ X0 @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
! [X4: g,X0: g > g > g] :
( ( cGROUP2 @ X0 @ X4 )
<=> ( cGROUP1 @ X0 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cEQUIV_01_02) ).
thf(f480,plain,
( ~ spl0_1
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f479]) ).
thf(f479,plain,
( $false
| ~ spl0_1
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f478]) ).
thf(f478,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f477]) ).
thf(f477,plain,
( ( $true
= ( $false
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f476]) ).
thf(f476,plain,
( ( $true
= ( $false
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f50,f403]) ).
thf(f403,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f402]) ).
thf(f402,definition,
( spl0_12
<=> ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f50,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl0_1
<=> ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f472,plain,
( ~ spl0_1
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f471]) ).
thf(f471,plain,
( $false
| ~ spl0_1
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f470]) ).
thf(f470,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f469]) ).
thf(f469,plain,
( ( $true
= ( $false
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f468]) ).
thf(f468,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& $false
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f50,f400]) ).
thf(f400,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f399]) ).
thf(f399,definition,
( spl0_11
<=> ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f461,plain,
( ~ spl0_2
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f460]) ).
thf(f460,plain,
( $false
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f459]) ).
thf(f459,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f457]) ).
thf(f457,plain,
( ( $true
= ( ( ( sK2 @ sK9 @ ( sK8 @ sK9 ) )
= sK3 )
& $false ) )
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f421,f449]) ).
thf(f449,plain,
( ! [X1: g] :
( ( ( sK2 @ X1 @ sK9 )
= sK3 )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f448]) ).
thf(f448,plain,
( ! [X1: g] :
( ( ^ [Y0: g] :
( ( sK2 @ Y0 @ sK9 )
= sK3 )
@ X1 )
= $false )
| ~ spl0_11 ),
inference(pi_clausification,[status(thm)],[f442]) ).
thf(f442,plain,
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK2 @ Y0 @ sK9 )
= sK3 ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f441]) ).
thf(f441,plain,
( ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) )
@ sK9 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f400]) ).
thf(f421,plain,
( ! [X1: g] :
( $true
= ( ( ( sK2 @ X1 @ ( sK8 @ X1 ) )
= sK3 )
& ( ( sK2 @ ( sK8 @ X1 ) @ X1 )
= sK3 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f420]) ).
thf(f420,plain,
( ! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( ( sK2 @ X1 @ Y0 )
= sK3 )
& ( ( sK2 @ Y0 @ X1 )
= sK3 ) )
@ ( sK8 @ X1 ) ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f415]) ).
thf(f415,plain,
( ! [X1: g] :
( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK2 @ X1 @ Y0 )
= sK3 )
& ( ( sK2 @ Y0 @ X1 )
= sK3 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f414]) ).
thf(f414,plain,
( ! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f410]) ).
thf(f410,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl0_2
<=> ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f430,plain,
( ~ spl0_2
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f429]) ).
thf(f429,plain,
( $false
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f428]) ).
thf(f428,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f427]) ).
thf(f427,plain,
( ( ( $false
& ( ( sK2 @ sK7 @ sK3 )
= sK7 ) )
= $true )
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f423,f408]) ).
thf(f408,plain,
( ( ( ( sK2 @ sK3 @ sK7 )
= sK7 )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f407]) ).
thf(f407,plain,
( ( $false
= ( ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 )
@ sK7 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f403]) ).
thf(f423,plain,
( ! [X1: g] :
( ( ( ( sK2 @ sK3 @ X1 )
= X1 )
& ( ( sK2 @ X1 @ sK3 )
= X1 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f422]) ).
thf(f422,plain,
( ! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f419]) ).
thf(f419,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f418]) ).
thf(f418,plain,
( ( $true
= ( $true
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f413,f417]) ).
thf(f417,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f413]) ).
thf(f413,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f412]) ).
thf(f412,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f53,f410]) ).
thf(f404,plain,
( spl0_11
| spl0_12
| ~ spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f397,f382,f402,f399]) ).
thf(f382,definition,
( spl0_9
<=> ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f397,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
= $false )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f383]) ).
thf(f383,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f382]) ).
thf(f387,plain,
( spl0_9
| spl0_10
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f380,f59,f385,f382]) ).
thf(f59,definition,
( spl0_4
<=> ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f380,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f376,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[status(thm)],[f375]) ).
thf(f375,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f374]) ).
thf(f374,plain,
( ( $true = $false )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f373]) ).
thf(f373,plain,
( ( ( sK6 = sK6 )
= $false )
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f372,f351]) ).
thf(f351,plain,
( ! [X0: g] :
( ( sK2 @ X0 @ sK3 )
= X0 )
| ~ spl0_6 ),
inference(equality_proxy_clausification,[status(thm)],[f343]) ).
thf(f343,plain,
( ! [X0: g] :
( $true
= ( X0
= ( sK2 @ X0 @ sK3 ) ) )
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f325,f338]) ).
thf(f338,plain,
( ! [X0: g,X1: g] :
( ( sK2 @ ( sK4 @ ( sK4 @ X0 ) ) @ X1 )
= ( sK2 @ X0 @ X1 ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f324,f324]) ).
thf(f324,plain,
( ! [X0: g,X1: g] :
( ( sK2 @ ( sK4 @ X0 ) @ ( sK2 @ X0 @ X1 ) )
= X1 )
| ~ spl0_6 ),
inference(equality_proxy_clausification,[status(thm)],[f320]) ).
thf(f320,plain,
( ! [X0: g,X1: g] :
( $true
= ( X1
= ( sK2 @ ( sK4 @ X0 ) @ ( sK2 @ X0 @ X1 ) ) ) )
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f305,f288]) ).
thf(f288,plain,
( ! [X1: g] :
( ( sK2 @ sK3 @ X1 )
= X1 )
| ~ spl0_6 ),
inference(equality_proxy_clausification,[status(thm)],[f287]) ).
thf(f287,plain,
( ! [X1: g] :
( ( ( sK2 @ sK3 @ X1 )
= X1 )
= $true )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f286]) ).
thf(f286,plain,
( ! [X1: g] :
( ( ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 )
@ X1 )
= $true )
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f273]) ).
thf(f273,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f261]) ).
thf(f261,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
!= $false )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f258]) ).
thf(f258,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& $true )
!= $false )
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f250,f256]) ).
thf(f256,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f250]) ).
thf(f250,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
!= $false )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f249]) ).
thf(f249,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
!= ( $false
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
!= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& $false
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) )
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f45,f132]) ).
thf(f132,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f131]) ).
thf(f131,definition,
( spl0_6
<=> ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f305,plain,
( ! [X0: g,X1: g] :
( $true
= ( ( sK2 @ sK3 @ X1 )
= ( sK2 @ ( sK4 @ X0 ) @ ( sK2 @ X0 @ X1 ) ) ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f299,f283]) ).
thf(f283,plain,
( ! [X1: g] :
( ( sK2 @ ( sK4 @ X1 ) @ X1 )
= sK3 )
| ~ spl0_6 ),
inference(equality_proxy_clausification,[status(thm)],[f282]) ).
thf(f282,plain,
( ! [X1: g] :
( ( ( sK2 @ ( sK4 @ X1 ) @ X1 )
= sK3 )
= $true )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f281]) ).
thf(f281,plain,
( ! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK2 @ Y0 @ X1 )
= sK3 )
@ ( sK4 @ X1 ) ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f280]) ).
thf(f280,plain,
( ! [X1: g] :
( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK2 @ Y0 @ X1 )
= sK3 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f279]) ).
thf(f279,plain,
( ! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) )
@ X1 ) )
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f276]) ).
thf(f276,plain,
( ( $false
!= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f275]) ).
thf(f275,plain,
( ( $false
!= ( $true
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) )
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f261,f273]) ).
thf(f299,plain,
( ! [X2: g,X3: g,X1: g] :
( $true
= ( ( sK2 @ ( sK2 @ X3 @ X2 ) @ X1 )
= ( sK2 @ X3 @ ( sK2 @ X2 @ X1 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f298]) ).
thf(f298,plain,
( ! [X2: g,X3: g,X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK2 @ ( sK2 @ Y0 @ X2 ) @ X1 )
= ( sK2 @ Y0 @ ( sK2 @ X2 @ X1 ) ) )
@ X3 ) )
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f297]) ).
thf(f297,plain,
( ! [X2: g,X1: g] :
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ ( sK2 @ Y0 @ X2 ) @ X1 )
= ( sK2 @ Y0 @ ( sK2 @ X2 @ X1 ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f296]) ).
thf(f296,plain,
( ! [X2: g,X1: g] :
( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK2 @ ( sK2 @ Y1 @ Y0 ) @ X1 )
= ( sK2 @ Y1 @ ( sK2 @ Y0 @ X1 ) ) ) )
@ X2 ) )
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f295]) ).
thf(f295,plain,
( ! [X1: g] :
( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK2 @ ( sK2 @ Y1 @ Y0 ) @ X1 )
= ( sK2 @ Y1 @ ( sK2 @ Y0 @ X1 ) ) ) ) )
= $true )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f294]) ).
thf(f294,plain,
( ! [X1: g] :
( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_6 ),
inference(pi_clausification,[status(thm)],[f256]) ).
thf(f325,plain,
( ! [X0: g] :
( $true
= ( X0
= ( sK2 @ ( sK4 @ ( sK4 @ X0 ) ) @ sK3 ) ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f320,f283]) ).
thf(f372,plain,
( ( ( ( sK2 @ sK6 @ sK3 )
= sK6 )
= $false )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f371]) ).
thf(f371,plain,
( ( ( $true
& ( ( sK2 @ sK6 @ sK3 )
= sK6 ) )
= $false )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f370]) ).
thf(f370,plain,
( ( ( ( sK6 = sK6 )
& ( ( sK2 @ sK6 @ sK3 )
= sK6 ) )
= $false )
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f255,f288]) ).
thf(f255,plain,
( ( ( ( ( sK2 @ sK3 @ sK6 )
= sK6 )
& ( ( sK2 @ sK6 @ sK3 )
= sK6 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f254]) ).
thf(f254,plain,
( ( $false
= ( ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) )
@ sK6 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f132]) ).
thf(f240,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f239]) ).
thf(f239,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f238]) ).
thf(f238,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f237]) ).
thf(f237,plain,
( ( ( sK3 = sK3 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f168,f223]) ).
thf(f223,plain,
( ! [X0: g] :
( ( sK2 @ X0 @ ( sK4 @ X0 ) )
= sK3 )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f112,f123]) ).
thf(f123,plain,
( ! [X0: g,X1: g] :
( ( sK2 @ ( sK4 @ ( sK4 @ X0 ) ) @ X1 )
= ( sK2 @ X0 @ X1 ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f116,f116]) ).
thf(f116,plain,
( ! [X0: g,X1: g] :
( ( sK2 @ ( sK4 @ X0 ) @ ( sK2 @ X0 @ X1 ) )
= X1 )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f115,f85]) ).
thf(f85,plain,
( ! [X1: g] :
( ( sK2 @ sK3 @ X1 )
= X1 )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ! [X1: g] :
( ( ( sK2 @ sK3 @ X1 )
= X1 )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
( ! [X1: g] :
( ( ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
!= $false )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f45,f57]) ).
thf(f57,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl0_3
<=> ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f115,plain,
( ! [X0: g,X1: g] :
( ( sK2 @ sK3 @ X1 )
= ( sK2 @ ( sK4 @ X0 ) @ ( sK2 @ X0 @ X1 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f90,f112]) ).
thf(f90,plain,
( ! [X2: g,X3: g,X1: g] :
( ( sK2 @ X3 @ ( sK2 @ X2 @ X1 ) )
= ( sK2 @ ( sK2 @ X3 @ X2 ) @ X1 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ! [X2: g,X3: g,X1: g] :
( $true
= ( ( sK2 @ ( sK2 @ X3 @ X2 ) @ X1 )
= ( sK2 @ X3 @ ( sK2 @ X2 @ X1 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
( ! [X2: g,X3: g,X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK2 @ ( sK2 @ Y0 @ X2 ) @ X1 )
= ( sK2 @ Y0 @ ( sK2 @ X2 @ X1 ) ) )
@ X3 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ! [X2: g,X1: g] :
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ ( sK2 @ Y0 @ X2 ) @ X1 )
= ( sK2 @ Y0 @ ( sK2 @ X2 @ X1 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X2: g,X1: g] :
( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK2 @ ( sK2 @ Y1 @ Y0 ) @ X1 )
= ( sK2 @ Y1 @ ( sK2 @ Y0 @ X1 ) ) ) )
@ X2 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ! [X1: g] :
( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK2 @ ( sK2 @ Y1 @ Y0 ) @ X1 )
= ( sK2 @ Y1 @ ( sK2 @ Y0 @ X1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
( ! [X1: g] :
( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
!= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ( $true
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
!= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f66,f68]) ).
thf(f112,plain,
( ! [X1: g] :
( ( sK2 @ ( sK4 @ X1 ) @ X1 )
= sK3 )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
( ! [X1: g] :
( ( ( sK2 @ ( sK4 @ X1 ) @ X1 )
= sK3 )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f110]) ).
thf(f110,plain,
( ! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK2 @ Y0 @ X1 )
= sK3 )
@ ( sK4 @ X1 ) ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
( ! [X1: g] :
( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK2 @ Y0 @ X1 )
= sK3 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
( ! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true
= ( $true
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f68,f76]) ).
thf(f168,plain,
( ( ( ( sK2 @ sK5 @ ( sK4 @ sK5 ) )
= sK3 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f167]) ).
thf(f167,plain,
( ( ( ( ( sK2 @ sK5 @ ( sK4 @ sK5 ) )
= sK3 )
& $true )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f165]) ).
thf(f165,plain,
( ( ( ( ( sK2 @ sK5 @ ( sK4 @ sK5 ) )
= sK3 )
& ( sK3 = sK3 ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f146,f112]) ).
thf(f146,plain,
( ! [X1: g] :
( ( ( ( sK2 @ sK5 @ X1 )
= sK3 )
& ( ( sK2 @ X1 @ sK5 )
= sK3 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f145]) ).
thf(f145,plain,
( ! [X1: g] :
( ( ^ [Y0: g] :
( ( ( sK2 @ sK5 @ Y0 )
= sK3 )
& ( ( sK2 @ Y0 @ sK5 )
= sK3 ) )
@ X1 )
= $false )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK5 @ Y0 )
= sK3 )
& ( ( sK2 @ Y0 @ sK5 )
= sK3 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f140]) ).
thf(f140,plain,
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
@ sK5 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f128]) ).
thf(f128,definition,
( spl0_5
<=> ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f133,plain,
( spl0_5
| spl0_6
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f126,f56,f49,f131,f128]) ).
thf(f126,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
= $false )
| ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $false
= ( $true
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f57,f72]) ).
thf(f72,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( $true
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f50,f68]) ).
thf(f65,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f53,f57]) ).
thf(f61,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f47,f59,f56]) ).
thf(f47,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f54,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f46,f52,f49]) ).
thf(f46,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK2 @ sK3 @ Y0 )
= Y0 )
& ( ( sK2 @ Y0 @ sK3 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK2 @ Y0 @ Y1 )
= sK3 )
& ( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK2 @ sK3 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK2 @ Y1 @ Y0 )
= sK3 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK2 @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ Y2 @ ( sK2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15 % Problem : ALG272^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.12/0.16 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.37 % Computer : n008.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Tue Feb 24 03:42:54 EST 2026
% 0.17/0.37 % CPUTime :
% 0.17/0.37 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.54 ---- Original DTF file ---
% 0.28/0.54 thf(spec,logic,$$dhol).
% 0.28/0.54 %------------------------------------------------------------------------------
% 0.28/0.54 % File : ALG272^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.28/0.54 % Domain : General Algebra
% 0.28/0.54 % Problem : TPS problem EQUIV-01-02
% 0.28/0.54 % Version : Especial.
% 0.28/0.54 % English :
% 0.28/0.54
% 0.28/0.54 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.54 % Source : [Bro09]
% 0.28/0.54 % Names : tps_0531 [Bro09]
% 0.28/0.54 % : EQUIV-01-02 [TPS]
% 0.28/0.54
% 0.28/0.54 % Status : Theorem
% 0.28/0.54 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0, 0.36 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, 0.71 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% 0.28/0.54 % Syntax : Number of formulae : 16 ( 7 unt; 8 typ; 7 def)
% 0.28/0.54 % Number of atoms : 29 ( 14 equ; 0 cnn)
% 0.28/0.54 % Maximal formula atoms : 2 ( 3 avg)
% 0.28/0.54 % Number of connectives : 41 ( 0 ~; 0 |; 6 &; 34 @)
% 0.28/0.54 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.54 % Maximal formula depth : 6 ( 2 avg)
% 0.28/0.54 % Number of types : 2 ( 1 usr)
% 0.28/0.54 % Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% 0.28/0.54 % Number of symbols : 8 ( 7 usr; 0 con; 1-2 aty)
% 0.28/0.54 % Number of variables : 24 ( 13 ^; 9 !; 2 ?; 24 :)
% 0.28/0.54 % SPC : TH0_THM_EQU_NAR
% 0.28/0.54
% 0.28/0.54 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.54 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.54 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.54 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.54 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.28/0.54 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.28/0.54 %------------------------------------------------------------------------------
% 0.28/0.54 thf(g_type,type,
% 0.28/0.54 g: $tType ).
% 0.28/0.54
% 0.28/0.54 thf(cGROUP1_type,type,
% 0.28/0.54 cGROUP1: ( g > g > g ) > g > $o ).
% 0.28/0.54
% 0.28/0.54 thf(cGROUP2_type,type,
% 0.28/0.54 cGROUP2: ( g > g > g ) > g > $o ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_ASSOC_type,type,
% 0.28/0.54 cGRP_ASSOC: ( g > g > g ) > $o ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_INVERSE_type,type,
% 0.28/0.54 cGRP_INVERSE: ( g > g > g ) > g > $o ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_LEFT_INVERSE_type,type,
% 0.28/0.54 cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_LEFT_UNIT_type,type,
% 0.28/0.54 cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_UNIT_type,type,
% 0.28/0.54 cGRP_UNIT: ( g > g > g ) > g > $o ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_ASSOC_def,definition,
% 0.28/0.54 ( cGRP_ASSOC
% 0.28/0.54 = ( ^ [Xf: g > g > g] :
% 0.28/0.54 ! [Xa: g,Xb: g,Xc: g] :
% 0.28/0.54 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 0.28/0.54 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_INVERSE_def,definition,
% 0.28/0.54 ( cGRP_INVERSE
% 0.28/0.54 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.28/0.54 ! [Xa: g] :
% 0.28/0.54 ? [Xb: g] :
% 0.28/0.54 ( ( ( Xf @ Xa @ Xb )
% 0.28/0.54 = Xe )
% 0.28/0.54 & ( ( Xf @ Xb @ Xa )
% 0.28/0.54 = Xe ) ) ) ) ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_LEFT_INVERSE_def,definition,
% 0.28/0.54 ( cGRP_LEFT_INVERSE
% 0.28/0.54 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.28/0.54 ! [Xa: g] :
% 0.28/0.54 ? [Xb: g] :
% 0.28/0.54 ( ( Xf @ Xb @ Xa )
% 0.28/0.54 = Xe ) ) ) ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_LEFT_UNIT_def,definition,
% 0.28/0.54 ( cGRP_LEFT_UNIT
% 0.28/0.54 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.28/0.54 ! [Xa: g] :
% 0.28/0.54 ( ( Xf @ Xe @ Xa )
% 0.28/0.54 = Xa ) ) ) ).
% 0.28/0.54
% 0.28/0.54 thf(cGRP_UNIT_def,definition,
% 0.28/0.54 ( cGRP_UNIT
% 0.28/0.54 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.28/0.54 ! [Xa: g] :
% 0.28/0.54 ( ( ( Xf @ Xe @ Xa )
% 0.28/0.54 = Xa )
% 0.28/0.54 & ( ( Xf @ Xa @ Xe )
% 0.28/0.54 = Xa ) ) ) ) ).
% 0.28/0.54
% 0.28/0.54 thf(cGROUP1_def,definition,
% 0.28/0.54 ( cGROUP1
% 0.28/0.54 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.28/0.54 ( ( cGRP_ASSOC @ Xf )
% 0.28/0.54 & ( cGRP_UNIT @ Xf @ Xe )
% 0.28/0.54 & ( cGRP_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.28/0.54
% 0.28/0.54 thf(cGROUP2_def,definition,
% 0.28/0.54 ( cGROUP2
% 0.28/0.54 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.28/0.54 ( ( cGRP_ASSOC @ Xf )
% 0.28/0.54 & ( cGRP_LEFT_UNIT @ Xf @ Xe )
% 0.28/0.54 & ( cGRP_LEFT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.28/0.54
% 0.28/0.54 thf(cEQUIV_01_02,conjecture,
% 0.28/0.54 ! [Xf: g > g > g,Xe: g] :
% 0.28/0.54 ( ( cGROUP1 @ Xf @ Xe )
% 0.28/0.54 <=> ( cGROUP2 @ Xf @ Xe ) ) ).
% 0.28/0.54
% 0.28/0.54 %------------------------------------------------------------------------------
% 0.28/0.54 ------------------------
% 0.35/1.50 ---- Embedded in THF ---
% 0.35/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.35/1.50 %%% Generated on Tue Feb 24 03:42:55 EST 2026
% 0.35/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.35/1.50 %%% Logic specification used:
% 0.35/1.50 %%% thf(spec, logic, $$dhol).
% 0.35/1.50
% 0.35/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2DTF21974.p
% See solution above
% 0.35/1.50 ------------------------
% 0.35/1.51 ---- Cleaned THF ---
% 0.35/1.51 thf(g_type,type,
% 0.35/1.51 g: $tType ).
% 0.35/1.51
% 0.35/1.51 thf(cGROUP1_type,type,
% 0.35/1.51 cGROUP1: ( g > g > g ) > g > $o ).
% 0.35/1.51
% 0.35/1.51 thf(cGROUP2_type,type,
% 0.35/1.51 cGROUP2: ( g > g > g ) > g > $o ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_ASSOC_type,type,
% 0.35/1.51 cGRP_ASSOC: ( g > g > g ) > $o ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_INVERSE_type,type,
% 0.35/1.51 cGRP_INVERSE: ( g > g > g ) > g > $o ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_LEFT_INVERSE_type,type,
% 0.35/1.51 cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_LEFT_UNIT_type,type,
% 0.35/1.51 cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_UNIT_type,type,
% 0.35/1.51 cGRP_UNIT: ( g > g > g ) > g > $o ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_ASSOC_def,definition,
% 0.35/1.51 ( cGRP_ASSOC
% 0.35/1.51 = ( ^ [Xf: g > g > g] :
% 0.35/1.51 ! [Xa: g,Xb: g,Xc: g] :
% 0.35/1.51 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 0.35/1.51 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_INVERSE_def,definition,
% 0.35/1.51 ( cGRP_INVERSE
% 0.35/1.51 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.35/1.51 ! [Xa: g] :
% 0.35/1.51 ? [Xb: g] :
% 0.35/1.51 ( ( ( Xf @ Xa @ Xb )
% 0.35/1.51 = Xe )
% 0.35/1.51 & ( ( Xf @ Xb @ Xa )
% 0.35/1.51 = Xe ) ) ) ) ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_LEFT_INVERSE_def,definition,
% 0.35/1.51 ( cGRP_LEFT_INVERSE
% 0.35/1.51 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.35/1.51 ! [Xa: g] :
% 0.35/1.51 ? [Xb: g] :
% 0.35/1.51 ( ( Xf @ Xb @ Xa )
% 0.35/1.51 = Xe ) ) ) ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_LEFT_UNIT_def,definition,
% 0.35/1.51 ( cGRP_LEFT_UNIT
% 0.35/1.51 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.35/1.51 ! [Xa: g] :
% 0.35/1.51 ( ( Xf @ Xe @ Xa )
% 0.35/1.51 = Xa ) ) ) ).
% 0.35/1.51
% 0.35/1.51 thf(cGRP_UNIT_def,definition,
% 0.35/1.51 ( cGRP_UNIT
% 0.35/1.51 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.35/1.51 ! [Xa: g] :
% 0.35/1.51 ( ( ( Xf @ Xe @ Xa )
% 0.35/1.51 = Xa )
% 0.35/1.51 & ( ( Xf @ Xa @ Xe )
% 0.35/1.51 = Xa ) ) ) ) ).
% 0.35/1.51
% 0.35/1.51 thf(cGROUP1_def,definition,
% 0.35/1.51 ( cGROUP1
% 0.35/1.51 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.35/1.51 ( ( cGRP_ASSOC @ Xf )
% 0.35/1.51 & ( cGRP_UNIT @ Xf @ Xe )
% 0.35/1.51 & ( cGRP_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.35/1.51
% 0.35/1.51 thf(cGROUP2_def,definition,
% 0.35/1.51 ( cGROUP2
% 0.35/1.51 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.35/1.51 ( ( cGRP_ASSOC @ Xf )
% 0.35/1.51 & ( cGRP_LEFT_UNIT @ Xf @ Xe )
% 0.35/1.51 & ( cGRP_LEFT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.35/1.51
% 0.35/1.51 thf(cEQUIV_01_02,conjecture,
% 0.35/1.51 ! [Xf: g > g > g,Xe: g] :
% 0.35/1.51 ( ( cGROUP1 @ Xf @ Xe )
% 0.35/1.51 <=> ( cGROUP2 @ Xf @ Xe ) ) ).
% 0.35/1.51 ------------------------
% 0.35/1.53 % (22078)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/183Mi)
% 0.35/1.53 % (22081)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/2Mi)
% 0.35/1.53 % (22079)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_21974 for (2999ds/4Mi)
% 0.35/1.53 % (22080)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_21974 for (2999ds/27Mi)
% 0.35/1.53 % (22082)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_21974 for (2999ds/2Mi)
% 0.35/1.53 % (22083)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_21974 for (2999ds/275Mi)
% 0.35/1.53 % (22084)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/18Mi)
% 0.35/1.53 % (22081)Instruction limit reached!
% 0.35/1.53 % (22081)------------------------------
% 0.35/1.53 % (22081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.53 % (22081)Termination reason: Unknown
% 0.35/1.53 % (22081)Termination phase: shuffling
% 0.35/1.53
% 0.35/1.53 % (22081)Memory used [KB]: 895
% 0.35/1.53 % (22081)Time elapsed: 0.002 s
% 0.35/1.53 % (22081)Instructions burned: 2 (million)
% 0.35/1.53 % (22081)------------------------------
% 0.35/1.53 % (22081)------------------------------
% 0.35/1.53 % (22082)Instruction limit reached!
% 0.35/1.53 % (22082)------------------------------
% 0.35/1.53 % (22082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.53 % (22082)Termination reason: Unknown
% 0.35/1.53 % (22082)Termination phase: Function definition elimination
% 0.35/1.53
% 0.35/1.53 % (22082)Memory used [KB]: 1023
% 0.35/1.53 % (22082)Time elapsed: 0.003 s
% 0.35/1.53 % (22082)Instructions burned: 3 (million)
% 0.35/1.53 % (22082)------------------------------
% 0.35/1.53 % (22082)------------------------------
% 0.35/1.53 % (22079)Instruction limit reached!
% 0.35/1.53 % (22079)------------------------------
% 0.35/1.53 % (22079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.53 % (22079)Termination reason: Unknown
% 0.35/1.53 % (22079)Termination phase: Saturation
% 0.35/1.53
% 0.35/1.53 % (22079)Memory used [KB]: 5500
% 0.35/1.53 % (22079)Time elapsed: 0.004 s
% 0.35/1.53 % (22079)Instructions burned: 5 (million)
% 0.35/1.53 % (22079)------------------------------
% 0.35/1.53 % (22079)------------------------------
% 0.35/1.54 % (22084)Instruction limit reached!
% 0.35/1.54 % (22084)------------------------------
% 0.35/1.54 % (22084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.54 % (22084)Termination reason: Unknown
% 0.35/1.54 % (22084)Termination phase: Saturation
% 0.35/1.54
% 0.35/1.54 % (22084)Memory used [KB]: 5500
% 0.35/1.54 % (22084)Time elapsed: 0.010 s
% 0.35/1.54 % (22084)Instructions burned: 18 (million)
% 0.35/1.54 % (22084)------------------------------
% 0.35/1.54 % (22084)------------------------------
% 0.35/1.55 % (22080)Instruction limit reached!
% 0.35/1.55 % (22080)------------------------------
% 0.35/1.55 % (22080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.55 % (22080)Termination reason: Unknown
% 0.35/1.55 % (22080)Termination phase: Saturation
% 0.35/1.55
% 0.35/1.55 % (22080)Memory used [KB]: 5756
% 0.35/1.55 % (22080)Time elapsed: 0.016 s
% 0.35/1.55 % (22080)Instructions burned: 28 (million)
% 0.35/1.55 % (22080)------------------------------
% 0.35/1.55 % (22080)------------------------------
% 0.35/1.55 % (22086)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_21974 for (2999ds/37Mi)
% 0.35/1.55 % (22085)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/3Mi)
% 0.35/1.55 % (22087)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_21974 for (2999ds/15Mi)
% 0.35/1.55 % (22085)Instruction limit reached!
% 0.35/1.55 % (22085)------------------------------
% 0.35/1.55 % (22085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.55 % (22085)Termination reason: Unknown
% 0.35/1.55 % (22085)Termination phase: Property scanning
% 0.35/1.55
% 0.35/1.55 % (22085)Memory used [KB]: 1023
% 0.35/1.55 % (22085)Time elapsed: 0.003 s
% 0.35/1.55 % (22085)Instructions burned: 4 (million)
% 0.35/1.55 % (22085)------------------------------
% 0.35/1.55 % (22085)------------------------------
% 0.35/1.56 % (22087)Instruction limit reached!
% 0.35/1.56 % (22087)------------------------------
% 0.35/1.56 % (22087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.56 % (22088)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_21974 for (2999ds/3Mi)
% 0.35/1.56 % (22087)Termination reason: Unknown
% 0.35/1.56 % (22087)Termination phase: Saturation
% 0.35/1.56
% 0.35/1.56 % (22087)Memory used [KB]: 5500
% 0.35/1.56 % (22087)Time elapsed: 0.008 s
% 0.35/1.56 % (22087)Instructions burned: 15 (million)
% 0.35/1.56 % (22087)------------------------------
% 0.35/1.56 % (22087)------------------------------
% 0.35/1.56 % (22088)Instruction limit reached!
% 0.35/1.56 % (22088)------------------------------
% 0.35/1.56 % (22088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.56 % (22088)Termination reason: Unknown
% 0.35/1.56 % (22088)Termination phase: Function definition elimination
% 0.35/1.56
% 0.35/1.56 % (22088)Memory used [KB]: 1023
% 0.35/1.56 % (22088)Time elapsed: 0.003 s
% 0.35/1.56 % (22088)Instructions burned: 3 (million)
% 0.35/1.56 % (22088)------------------------------
% 0.35/1.56 % (22088)------------------------------
% 0.35/1.56 % (22089)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_21974 for (2999ds/1041Mi)
% 0.35/1.57 % (22090)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/7Mi)
% 0.35/1.57 % (22086)Instruction limit reached!
% 0.35/1.57 % (22086)------------------------------
% 0.35/1.57 % (22086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.57 % (22086)Termination reason: Unknown
% 0.35/1.57 % (22086)Termination phase: Saturation
% 0.35/1.57
% 0.35/1.57 % (22086)Memory used [KB]: 5628
% 0.35/1.57 % (22086)Time elapsed: 0.020 s
% 0.35/1.57 % (22086)Instructions burned: 38 (million)
% 0.35/1.57 % (22086)------------------------------
% 0.35/1.57 % (22086)------------------------------
% 0.35/1.57 % (22090)Instruction limit reached!
% 0.35/1.57 % (22090)------------------------------
% 0.35/1.57 % (22090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.57 % (22090)Termination reason: Unknown
% 0.35/1.57 % (22090)Termination phase: Saturation
% 0.35/1.57
% 0.35/1.57 % (22090)Memory used [KB]: 1023
% 0.35/1.57 % (22090)Time elapsed: 0.005 s
% 0.35/1.57 % (22090)Instructions burned: 8 (million)
% 0.35/1.57 % (22090)------------------------------
% 0.35/1.57 % (22090)------------------------------
% 0.35/1.57 % (22091)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/16Mi)
% 0.35/1.57 % (22092)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_21974 for (2999ds/3Mi)
% 0.35/1.57 % (22092)Instruction limit reached!
% 0.35/1.57 % (22092)------------------------------
% 0.35/1.57 % (22092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.57 % (22092)Termination reason: Unknown
% 0.35/1.57 % (22092)Termination phase: Function definition elimination
% 0.35/1.57
% 0.35/1.57 % (22092)Memory used [KB]: 1023
% 0.35/1.57 % (22092)Time elapsed: 0.003 s
% 0.35/1.57 % (22092)Instructions burned: 3 (million)
% 0.35/1.57 % (22092)------------------------------
% 0.35/1.57 % (22092)------------------------------
% 0.35/1.58 % (22091)Instruction limit reached!
% 0.35/1.58 % (22091)------------------------------
% 0.35/1.58 % (22091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.58 % (22091)Termination reason: Unknown
% 0.35/1.58 % (22091)Termination phase: Saturation
% 0.35/1.58
% 0.35/1.58 % (22091)Memory used [KB]: 5756
% 0.35/1.58 % (22091)Time elapsed: 0.010 s
% 0.35/1.58 % (22091)Instructions burned: 16 (million)
% 0.35/1.58 % (22091)------------------------------
% 0.35/1.58 % (22091)------------------------------
% 0.35/1.58 % (22093)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_21974 for (2999ds/3Mi)
% 0.35/1.58 % (22093)Instruction limit reached!
% 0.35/1.58 % (22093)------------------------------
% 0.35/1.58 % (22093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.58 % (22093)Termination reason: Unknown
% 0.35/1.58 % (22093)Termination phase: Equality resolution with deletion
% 0.35/1.58
% 0.35/1.58 % (22093)Memory used [KB]: 1023
% 0.35/1.58 % (22093)Time elapsed: 0.003 s
% 0.35/1.58 % (22093)Instructions burned: 4 (million)
% 0.35/1.58 % (22093)------------------------------
% 0.35/1.58 % (22093)------------------------------
% 0.35/1.59 % (22094)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/7Mi)
% 0.35/1.59 % (22094)Instruction limit reached!
% 0.35/1.59 % (22094)------------------------------
% 0.35/1.59 % (22094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.59 % (22094)Termination reason: Unknown
% 0.35/1.59 % (22094)Termination phase: Saturation
% 0.35/1.59
% 0.35/1.59 % (22094)Memory used [KB]: 5500
% 0.35/1.59 % (22094)Time elapsed: 0.005 s
% 0.35/1.59 % (22094)Instructions burned: 8 (million)
% 0.35/1.59 % (22094)------------------------------
% 0.35/1.59 % (22094)------------------------------
% 0.35/1.59 % (22095)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/3Mi)
% 0.35/1.59 % (22095)Instruction limit reached!
% 0.35/1.59 % (22095)------------------------------
% 0.35/1.59 % (22095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.59 % (22095)Termination reason: Unknown
% 0.35/1.59 % (22095)Termination phase: Property scanning
% 0.35/1.59
% 0.35/1.59 % (22095)Memory used [KB]: 1023
% 0.35/1.59 % (22095)Time elapsed: 0.003 s
% 0.35/1.59 % (22095)Instructions burned: 3 (million)
% 0.35/1.59 % (22095)------------------------------
% 0.35/1.59 % (22095)------------------------------
% 1.80/1.60 % (22096)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/4Mi)
% 1.80/1.60 % (22096)Instruction limit reached!
% 1.80/1.60 % (22096)------------------------------
% 1.80/1.60 % (22096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.60 % (22096)Termination reason: Unknown
% 1.80/1.60 % (22096)Termination phase: Property scanning
% 1.80/1.60
% 1.80/1.60 % (22096)Memory used [KB]: 1023
% 1.80/1.60 % (22096)Time elapsed: 0.003 s
% 1.80/1.60 % (22096)Instructions burned: 4 (million)
% 1.80/1.60 % (22096)------------------------------
% 1.80/1.60 % (22096)------------------------------
% 1.80/1.60 % (22097)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/18Mi)
% 1.80/1.61 % (22098)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/710Mi)
% 1.80/1.61 % (22099)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21974 for (2999ds/6Mi)
% 1.80/1.61 % (22097)Instruction limit reached!
% 1.80/1.61 % (22097)------------------------------
% 1.80/1.61 % (22097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.61 % (22097)Termination reason: Unknown
% 1.80/1.61 % (22097)Termination phase: Saturation
% 1.80/1.61
% 1.80/1.61 % (22097)Memory used [KB]: 5628
% 1.80/1.61 % (22097)Time elapsed: 0.011 s
% 1.80/1.61 % (22097)Instructions burned: 19 (million)
% 1.80/1.61 % (22097)------------------------------
% 1.80/1.61 % (22097)------------------------------
% 1.80/1.61 % (22099)Instruction limit reached!
% 1.80/1.61 % (22099)------------------------------
% 1.80/1.61 % (22099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.61 % (22099)Termination reason: Unknown
% 1.80/1.61 % (22099)Termination phase: Saturation
% 1.80/1.61
% 1.80/1.61 % (22099)Memory used [KB]: 5500
% 1.80/1.61 % (22099)Time elapsed: 0.005 s
% 1.80/1.61 % (22099)Instructions burned: 8 (million)
% 1.80/1.61 % (22099)------------------------------
% 1.80/1.61 % (22099)------------------------------
% 1.80/1.61 % (22100)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_21974 for (2999ds/902Mi)
% 1.80/1.61 % (22089)First to succeed.
% 1.80/1.62 % (22078)Instruction limit reached!
% 1.80/1.62 % (22078)------------------------------
% 1.80/1.62 % (22078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.62 % (22078)Termination reason: Unknown
% 1.80/1.62 % (22078)Termination phase: Saturation
% 1.80/1.62
% 1.80/1.62 % (22078)Memory used [KB]: 6780
% 1.80/1.62 % (22078)Time elapsed: 0.091 s
% 1.80/1.62 % (22078)Instructions burned: 184 (million)
% 1.80/1.62 % (22078)------------------------------
% 1.80/1.62 % (22078)------------------------------
% 1.80/1.62 % (22100)Refutation not found, incomplete strategy
% 1.80/1.62 % (22100)------------------------------
% 1.80/1.62 % (22100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.62 % (22100)Termination reason: Refutation not found, incomplete strategy
% 1.80/1.62
% 1.80/1.62
% 1.80/1.62 % (22100)Memory used [KB]: 5500
% 1.80/1.62 % (22100)Time elapsed: 0.003 s
% 1.80/1.62 % (22100)Instructions burned: 3 (million)
% 1.80/1.62 % (22100)------------------------------
% 1.80/1.62 % (22100)------------------------------
% 1.80/1.62 % (22089)Refutation found. Thanks to Tanya!
% 1.80/1.62 % SZS status Theorem for DTF2THF_21974
% 1.80/1.62 % SZS output start Proof for DTF2THF_21974
% 1.80/1.62 thf(type_def_5, type, g: $tType).
% 1.80/1.62 thf(func_def_0, type, g: $tType).
% 1.80/1.62 thf(func_def_1, type, cGROUP1: (g > g > g) > g > $o).
% 1.80/1.62 thf(func_def_2, type, cGROUP2: (g > g > g) > g > $o).
% 1.80/1.62 thf(func_def_3, type, cGRP_ASSOC: (g > g > g) > $o).
% 1.80/1.62 thf(func_def_4, type, cGRP_INVERSE: (g > g > g) > g > $o).
% 1.80/1.62 thf(func_def_5, type, cGRP_LEFT_INVERSE: (g > g > g) > g > $o).
% 1.80/1.62 thf(func_def_6, type, cGRP_LEFT_UNIT: (g > g > g) > g > $o).
% 1.80/1.62 thf(func_def_7, type, cGRP_UNIT: (g > g > g) > g > $o).
% 1.80/1.62 thf(func_def_24, type, ph1: !>[X0: $tType]:(X0)).
% 1.80/1.62 thf(func_def_25, type, sK2: g > g > g).
% 1.80/1.62 thf(func_def_26, type, sK3: g).
% 1.80/1.62 thf(func_def_27, type, sK4: g > g).
% 1.80/1.62 thf(func_def_28, type, sK5: g).
% 1.80/1.62 thf(func_def_29, type, sK6: g).
% 1.80/1.62 thf(func_def_30, type, sK7: g).
% 1.80/1.62 thf(func_def_31, type, sK8: g > g).
% 1.80/1.62 thf(func_def_32, type, sK9: g).
% 1.80/1.62 thf(f498,plain,(
% 1.80/1.62 $false),
% 1.80/1.62 inference(avatar_sat_refutation,[status(thm)],[f54,f61,f65,f133,f240,f376,f387,f404,f430,f461,f472,f480,f493])).
% 1.80/1.62 thf(f493,plain,(
% 1.80/1.62 ~spl0_10),
% 1.80/1.62 inference(avatar_contradiction_clause,[status(thm)],[f492])).
% 1.80/1.62 thf(f492,plain,(
% 1.80/1.62 $false | ~spl0_10),
% 1.80/1.62 inference(trivial_inequality_removal,[status(thm)],[f491])).
% 1.80/1.62 thf(f491,plain,(
% 1.80/1.62 ($false != $false) | ~spl0_10),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f490])).
% 1.80/1.62 thf(f490,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & $false) != $false) | ~spl0_10),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f489])).
% 1.80/1.62 thf(f489,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & $false) != ($false & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))))) | ~spl0_10),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f488])).
% 1.80/1.62 thf(f488,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & $false) != (($false & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))))) | ~spl0_10),
% 1.80/1.62 inference(forward_demodulation,[status(thm)],[f45,f386])).
% 1.80/1.62 thf(f386,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) = $false) | ~spl0_10),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f385])).
% 1.80/1.62 thf(f385,definition,(
% 1.80/1.62 spl0_10 <=> ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) = $false)),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.80/1.62 thf(f45,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) != (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3))))))))),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.80/1.62 thf(f44,plain,(
% 1.80/1.62 (((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))))) = $false)),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.80/1.62 thf(f43,plain,(
% 1.80/1.62 (((^[Y0 : g]: ((((!! @ g @ (^[Y1 : g]: ((sK2 @ Y0 @ Y1) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK2 @ Y2 @ Y1) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK2 @ (sK2 @ Y3 @ Y2) @ Y1) = (sK2 @ Y3 @ (sK2 @ Y2 @ Y1)))))))))) = (((!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK2 @ (sK2 @ Y3 @ Y2) @ Y1) = (sK2 @ Y3 @ (sK2 @ Y2 @ Y1))))))))) & (!! @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = Y1) & ((sK2 @ Y1 @ Y0) = Y1))))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: (((sK2 @ Y1 @ Y2) = Y0) & ((sK2 @ Y2 @ Y1) = Y0))))))))) @ sK3) = $false)),
% 1.80/1.62 inference(sigma_clausification,[status(thm)],[f42])).
% 1.80/1.62 thf(f42,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: ((((!! @ g @ (^[Y1 : g]: ((sK2 @ Y0 @ Y1) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK2 @ Y2 @ Y1) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK2 @ (sK2 @ Y3 @ Y2) @ Y1) = (sK2 @ Y3 @ (sK2 @ Y2 @ Y1)))))))))) = (((!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK2 @ (sK2 @ Y3 @ Y2) @ Y1) = (sK2 @ Y3 @ (sK2 @ Y2 @ Y1))))))))) & (!! @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = Y1) & ((sK2 @ Y1 @ Y0) = Y1))))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: (((sK2 @ Y1 @ Y2) = Y0) & ((sK2 @ Y2 @ Y1) = Y0)))))))))) = $false)),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.80/1.62 thf(f41,plain,(
% 1.80/1.62 (((^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((((!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1)))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) = (((!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2))))))))) & (!! @ 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))))))))))) @ sK2) = $false)),
% 1.80/1.62 inference(sigma_clausification,[status(thm)],[f38])).
% 1.80/1.62 thf(f38,plain,(
% 1.80/1.62 ((!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((((!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1)))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) = (((!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2))))))))) & (!! @ 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)))))))))))) = $false)),
% 1.80/1.62 inference(not_proxy_clausification,[status(thm)],[f37])).
% 1.80/1.62 thf(f37,plain,(
% 1.80/1.62 ($true = (~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((((!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1)))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2)))))))))) = (((!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ (Y0 @ Y4 @ Y3) @ Y2) = (Y0 @ Y4 @ (Y0 @ Y3 @ Y2))))))))) & (!! @ 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))))))))))))))),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.80/1.62 thf(f36,plain,(
% 1.80/1.62 ($true = (~ (!! @ (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 @ Y5 @ Y6) = Y6)))))) @ Y2 @ Y3) & ((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (?? @ g @ (^[Y7 : g]: ((Y4 @ Y7 @ Y6) = Y5)))))))) @ Y2 @ Y3)) & ((^[Y4 : g > g > g]: (!! @ g @ (^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (!! @ g @ (^[Y7 : g]: ((Y4 @ (Y4 @ Y7 @ Y6) @ Y5) = (Y4 @ Y7 @ (Y4 @ Y6 @ Y5)))))))))) @ Y2))))) @ Y0 @ Y1) = ((^[Y2 : g > g > g]: ((^[Y3 : g]: ((((^[Y4 : g > g > g]: (!! @ g @ (^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (!! @ g @ (^[Y7 : g]: ((Y4 @ (Y4 @ Y7 @ Y6) @ Y5) = (Y4 @ Y7 @ (Y4 @ Y6 @ Y5)))))))))) @ Y2) & ((^[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))))) @ Y0 @ Y1))))))))),
% 1.80/1.62 inference(definition_unfolding,[status(thm)],[f30,f35,f34])).
% 1.80/1.62 thf(f34,plain,(
% 1.80/1.62 (cGROUP1 = (^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ Y5 @ (Y2 @ Y4 @ Y3)))))))))) @ Y0) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (((Y2 @ Y3 @ Y4) = Y4) & ((Y2 @ Y4 @ Y3) = Y4))))))) @ Y0 @ Y1)) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: (((Y2 @ Y4 @ Y5) = Y3) & ((Y2 @ Y5 @ Y4) = Y3))))))))) @ Y0 @ Y1))))))),
% 1.80/1.62 inference(definition_unfolding,[status(thm)],[f33,f32,f31,f28])).
% 1.80/1.62 thf(f28,plain,(
% 1.80/1.62 (cGRP_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: (((Y0 @ Y2 @ Y3) = Y1) & ((Y0 @ Y3 @ Y2) = Y1))))))))))),
% 1.80/1.62 inference(cnf_transformation,[status(thm)],[f16])).
% 1.80/1.62 thf(f16,plain,(
% 1.80/1.62 (cGRP_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: (((Y0 @ Y2 @ Y3) = Y1) & ((Y0 @ Y3 @ Y2) = Y1))))))))))),
% 1.80/1.62 inference(fool_elimination,[status(thm)],[f15])).
% 1.80/1.62 thf(f15,plain,(
% 1.80/1.62 ((^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : (((X0 @ X3 @ X2) = X1) & ((X0 @ X2 @ X3) = X1)))) = cGRP_INVERSE)),
% 1.80/1.62 inference(rectify,[status(thm)],[f2])).
% 1.80/1.62 thf(f2,axiom,(
% 1.80/1.62 ((^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ? [X2 : g] : (((X0 @ X2 @ X1) = X4) & ((X0 @ X1 @ X2) = X4)))) = cGRP_INVERSE)),
% 1.80/1.62 file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGRP_INVERSE_def)).
% 1.80/1.62 thf(f31,plain,(
% 1.80/1.62 (cGRP_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (((Y0 @ Y1 @ Y2) = Y2) & ((Y0 @ Y2 @ Y1) = Y2))))))))),
% 1.80/1.62 inference(cnf_transformation,[status(thm)],[f14])).
% 1.80/1.62 thf(f14,plain,(
% 1.80/1.62 (cGRP_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (((Y0 @ Y1 @ Y2) = Y2) & ((Y0 @ Y2 @ Y1) = Y2))))))))),
% 1.80/1.62 inference(fool_elimination,[status(thm)],[f13])).
% 1.80/1.62 thf(f13,plain,(
% 1.80/1.62 ((^[X0 : g > g > g, X1 : g] : (! [X2 : g] : (((X0 @ X2 @ X1) = X2) & ((X0 @ X1 @ X2) = X2)))) = cGRP_UNIT)),
% 1.80/1.62 inference(rectify,[status(thm)],[f5])).
% 1.80/1.62 thf(f5,axiom,(
% 1.80/1.62 ((^[X0 : g > g > g, X4 : g] : (! [X1 : g] : (((X0 @ X1 @ X4) = X1) & ((X0 @ X4 @ X1) = X1)))) = cGRP_UNIT)),
% 1.80/1.62 file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGRP_UNIT_def)).
% 1.80/1.62 thf(f32,plain,(
% 1.80/1.62 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ Y3 @ (Y0 @ Y2 @ Y1)))))))))))),
% 1.80/1.62 inference(cnf_transformation,[status(thm)],[f19])).
% 1.80/1.62 thf(f19,plain,(
% 1.80/1.62 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ Y3 @ (Y0 @ Y2 @ Y1)))))))))))),
% 1.80/1.62 inference(fool_elimination,[status(thm)],[f1])).
% 1.80/1.62 thf(f1,axiom,(
% 1.80/1.62 (cGRP_ASSOC = (^[X0 : g > g > g] : (! [X1 : g,X2 : g,X3 : g] : ((X0 @ (X0 @ X1 @ X2) @ X3) = (X0 @ X1 @ (X0 @ X2 @ X3))))))),
% 1.80/1.62 file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGRP_ASSOC_def)).
% 1.80/1.62 thf(f33,plain,(
% 1.80/1.62 (cGROUP1 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_ASSOC @ Y0) & (cGRP_UNIT @ Y0 @ Y1)) & (cGRP_INVERSE @ Y0 @ Y1))))))),
% 1.80/1.62 inference(cnf_transformation,[status(thm)],[f23])).
% 1.80/1.62 thf(f23,plain,(
% 1.80/1.62 (cGROUP1 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_ASSOC @ Y0) & (cGRP_UNIT @ Y0 @ Y1)) & (cGRP_INVERSE @ Y0 @ Y1))))))),
% 1.80/1.62 inference(fool_elimination,[status(thm)],[f22])).
% 1.80/1.62 thf(f22,plain,(
% 1.80/1.62 (cGROUP1 = (^[X0 : g > g > g, X1 : g] : ((cGRP_INVERSE @ X0 @ X1) & (cGRP_UNIT @ X0 @ X1) & (cGRP_ASSOC @ X0))))),
% 1.80/1.62 inference(rectify,[status(thm)],[f6])).
% 1.80/1.62 thf(f6,axiom,(
% 1.80/1.62 (cGROUP1 = (^[X0 : g > g > g, X4 : g] : ((cGRP_INVERSE @ X0 @ X4) & (cGRP_UNIT @ X0 @ X4) & (cGRP_ASSOC @ X0))))),
% 1.80/1.62 file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGROUP1_def)).
% 1.80/1.62 thf(f35,plain,(
% 1.80/1.62 (cGROUP2 = (^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y2 @ Y3 @ Y4) = Y4)))))) @ Y0 @ Y1) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: ((Y2 @ Y5 @ Y4) = Y3)))))))) @ Y0 @ Y1)) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ Y5 @ (Y2 @ Y4 @ Y3)))))))))) @ Y0))))))),
% 1.80/1.62 inference(definition_unfolding,[status(thm)],[f26,f27,f29,f32])).
% 1.80/1.62 thf(f29,plain,(
% 1.80/1.62 (cGRP_LEFT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1)))))))))),
% 1.80/1.62 inference(cnf_transformation,[status(thm)],[f12])).
% 1.80/1.62 thf(f12,plain,(
% 1.80/1.62 (cGRP_LEFT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1)))))))))),
% 1.80/1.62 inference(fool_elimination,[status(thm)],[f11])).
% 1.80/1.62 thf(f11,plain,(
% 1.80/1.62 (cGRP_LEFT_INVERSE = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : ((X0 @ X3 @ X2) = X1))))),
% 1.80/1.62 inference(rectify,[status(thm)],[f3])).
% 1.80/1.62 thf(f3,axiom,(
% 1.80/1.62 (cGRP_LEFT_INVERSE = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ? [X2 : g] : ((X0 @ X2 @ X1) = X4))))),
% 1.80/1.62 file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGRP_LEFT_INVERSE_def)).
% 1.80/1.62 thf(f27,plain,(
% 1.80/1.62 (cGRP_LEFT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2)))))))),
% 1.80/1.62 inference(cnf_transformation,[status(thm)],[f18])).
% 1.80/1.62 thf(f18,plain,(
% 1.80/1.62 (cGRP_LEFT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y1 @ Y2) = Y2)))))))),
% 1.80/1.62 inference(fool_elimination,[status(thm)],[f17])).
% 1.80/1.62 thf(f17,plain,(
% 1.80/1.62 (cGRP_LEFT_UNIT = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ((X0 @ X1 @ X2) = X2))))),
% 1.80/1.62 inference(rectify,[status(thm)],[f4])).
% 1.80/1.62 thf(f4,axiom,(
% 1.80/1.62 (cGRP_LEFT_UNIT = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ((X0 @ X4 @ X1) = X1))))),
% 1.80/1.62 file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGRP_LEFT_UNIT_def)).
% 1.80/1.62 thf(f26,plain,(
% 1.80/1.62 (cGROUP2 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_LEFT_UNIT @ Y0 @ Y1) & (cGRP_LEFT_INVERSE @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))),
% 1.80/1.62 inference(cnf_transformation,[status(thm)],[f25])).
% 1.80/1.62 thf(f25,plain,(
% 1.80/1.62 (cGROUP2 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_LEFT_UNIT @ Y0 @ Y1) & (cGRP_LEFT_INVERSE @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))),
% 1.80/1.62 inference(fool_elimination,[status(thm)],[f24])).
% 1.80/1.62 thf(f24,plain,(
% 1.80/1.62 ((^[X0 : g > g > g, X1 : g] : ((cGRP_ASSOC @ X0) & (cGRP_LEFT_INVERSE @ X0 @ X1) & (cGRP_LEFT_UNIT @ X0 @ X1))) = cGROUP2)),
% 1.80/1.62 inference(rectify,[status(thm)],[f7])).
% 1.80/1.62 thf(f7,axiom,(
% 1.80/1.62 ((^[X0 : g > g > g, X4 : g] : ((cGRP_ASSOC @ X0) & (cGRP_LEFT_INVERSE @ X0 @ X4) & (cGRP_LEFT_UNIT @ X0 @ X4))) = cGROUP2)),
% 1.80/1.62 file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cGROUP2_def)).
% 1.80/1.62 thf(f30,plain,(
% 1.80/1.62 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((cGROUP2 @ Y0 @ Y1) = (cGROUP1 @ Y0 @ Y1))))))) = $true)),
% 1.80/1.62 inference(cnf_transformation,[status(thm)],[f21])).
% 1.80/1.62 thf(f21,plain,(
% 1.80/1.62 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: ((cGROUP2 @ Y0 @ Y1) = (cGROUP1 @ Y0 @ Y1))))))) = $true)),
% 1.80/1.62 inference(fool_elimination,[status(thm)],[f20])).
% 1.80/1.62 thf(f20,plain,(
% 1.80/1.62 ~! [X0 : g,X1 : g > g > g] : ((cGROUP2 @ X1 @ X0) <=> (cGROUP1 @ X1 @ X0))),
% 1.80/1.62 inference(rectify,[status(thm)],[f9])).
% 1.80/1.62 thf(f9,negated_conjecture,(
% 1.80/1.62 ~! [X4 : g,X0 : g > g > g] : ((cGROUP2 @ X0 @ X4) <=> (cGROUP1 @ X0 @ X4))),
% 1.80/1.62 inference(negated_conjecture,[status(cth)],[f8])).
% 1.80/1.62 thf(f8,conjecture,(
% 1.80/1.62 ! [X4 : g,X0 : g > g > g] : ((cGROUP2 @ X0 @ X4) <=> (cGROUP1 @ X0 @ X4))),
% 1.80/1.62 file('/export/starexec/sandbox/tmp/tmp.dh5HRQTj7p/DTF2THF_21974.p',cEQUIV_01_02)).
% 1.80/1.62 thf(f480,plain,(
% 1.80/1.62 ~spl0_1 | ~spl0_12),
% 1.80/1.62 inference(avatar_contradiction_clause,[status(thm)],[f479])).
% 1.80/1.62 thf(f479,plain,(
% 1.80/1.62 $false | (~spl0_1 | ~spl0_12)),
% 1.80/1.62 inference(trivial_inequality_removal,[status(thm)],[f478])).
% 1.80/1.62 thf(f478,plain,(
% 1.80/1.62 ($true = $false) | (~spl0_1 | ~spl0_12)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f477])).
% 1.80/1.62 thf(f477,plain,(
% 1.80/1.62 ($true = ($false & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))))) | (~spl0_1 | ~spl0_12)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f476])).
% 1.80/1.62 thf(f476,plain,(
% 1.80/1.62 ($true = (($false & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))))) | (~spl0_1 | ~spl0_12)),
% 1.80/1.62 inference(forward_demodulation,[status(thm)],[f50,f403])).
% 1.80/1.62 thf(f403,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) = $false) | ~spl0_12),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f402])).
% 1.80/1.62 thf(f402,definition,(
% 1.80/1.62 spl0_12 <=> ((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) = $false)),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.80/1.62 thf(f50,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = $true) | ~spl0_1),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.80/1.62 thf(f49,definition,(
% 1.80/1.62 spl0_1 <=> ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = $true)),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.80/1.62 thf(f472,plain,(
% 1.80/1.62 ~spl0_1 | ~spl0_11),
% 1.80/1.62 inference(avatar_contradiction_clause,[status(thm)],[f471])).
% 1.80/1.62 thf(f471,plain,(
% 1.80/1.62 $false | (~spl0_1 | ~spl0_11)),
% 1.80/1.62 inference(trivial_inequality_removal,[status(thm)],[f470])).
% 1.80/1.62 thf(f470,plain,(
% 1.80/1.62 ($true = $false) | (~spl0_1 | ~spl0_11)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f469])).
% 1.80/1.62 thf(f469,plain,(
% 1.80/1.62 ($true = ($false & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))))) | (~spl0_1 | ~spl0_11)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f468])).
% 1.80/1.62 thf(f468,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & $false) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = $true) | (~spl0_1 | ~spl0_11)),
% 1.80/1.62 inference(forward_demodulation,[status(thm)],[f50,f400])).
% 1.80/1.62 thf(f400,plain,(
% 1.80/1.62 ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) | ~spl0_11),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f399])).
% 1.80/1.62 thf(f399,definition,(
% 1.80/1.62 spl0_11 <=> ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3))))))),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.80/1.62 thf(f461,plain,(
% 1.80/1.62 ~spl0_2 | ~spl0_11),
% 1.80/1.62 inference(avatar_contradiction_clause,[status(thm)],[f460])).
% 1.80/1.62 thf(f460,plain,(
% 1.80/1.62 $false | (~spl0_2 | ~spl0_11)),
% 1.80/1.62 inference(trivial_inequality_removal,[status(thm)],[f459])).
% 1.80/1.62 thf(f459,plain,(
% 1.80/1.62 ($true = $false) | (~spl0_2 | ~spl0_11)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f457])).
% 1.80/1.62 thf(f457,plain,(
% 1.80/1.62 ($true = (((sK2 @ sK9 @ (sK8 @ sK9)) = sK3) & $false)) | (~spl0_2 | ~spl0_11)),
% 1.80/1.62 inference(superposition,[status(thm)],[f421,f449])).
% 1.80/1.62 thf(f449,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((sK2 @ X1 @ sK9) = sK3) = $false)) ) | ~spl0_11),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f448])).
% 1.80/1.62 thf(f448,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((^[Y0 : g]: ((sK2 @ Y0 @ sK9) = sK3)) @ X1) = $false)) ) | ~spl0_11),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f442])).
% 1.80/1.62 thf(f442,plain,(
% 1.80/1.62 ((?? @ g @ (^[Y0 : g]: ((sK2 @ Y0 @ sK9) = sK3))) = $false) | ~spl0_11),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f441])).
% 1.80/1.62 thf(f441,plain,(
% 1.80/1.62 ($false = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))) @ sK9)) | ~spl0_11),
% 1.80/1.62 inference(sigma_clausification,[status(thm)],[f400])).
% 1.80/1.62 thf(f421,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = (((sK2 @ X1 @ (sK8 @ X1)) = sK3) & ((sK2 @ (sK8 @ X1) @ X1) = sK3)))) ) | ~spl0_2),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f420])).
% 1.80/1.62 thf(f420,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (((sK2 @ X1 @ Y0) = sK3) & ((sK2 @ Y0 @ X1) = sK3))) @ (sK8 @ X1)))) ) | ~spl0_2),
% 1.80/1.62 inference(sigma_clausification,[status(thm)],[f415])).
% 1.80/1.62 thf(f415,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = (?? @ g @ (^[Y0 : g]: (((sK2 @ X1 @ Y0) = sK3) & ((sK2 @ Y0 @ X1) = sK3)))))) ) | ~spl0_2),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f414])).
% 1.80/1.62 thf(f414,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3))))) @ X1))) ) | ~spl0_2),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f410])).
% 1.80/1.62 thf(f410,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))) = $true) | ~spl0_2),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.80/1.62 thf(f53,plain,(
% 1.80/1.62 ($true = (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))))) | ~spl0_2),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.80/1.62 thf(f52,definition,(
% 1.80/1.62 spl0_2 <=> ($true = (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3))))))))),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.80/1.62 thf(f430,plain,(
% 1.80/1.62 ~spl0_2 | ~spl0_12),
% 1.80/1.62 inference(avatar_contradiction_clause,[status(thm)],[f429])).
% 1.80/1.62 thf(f429,plain,(
% 1.80/1.62 $false | (~spl0_2 | ~spl0_12)),
% 1.80/1.62 inference(trivial_inequality_removal,[status(thm)],[f428])).
% 1.80/1.62 thf(f428,plain,(
% 1.80/1.62 ($true = $false) | (~spl0_2 | ~spl0_12)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f427])).
% 1.80/1.62 thf(f427,plain,(
% 1.80/1.62 (($false & ((sK2 @ sK7 @ sK3) = sK7)) = $true) | (~spl0_2 | ~spl0_12)),
% 1.80/1.62 inference(superposition,[status(thm)],[f423,f408])).
% 1.80/1.62 thf(f408,plain,(
% 1.80/1.62 (((sK2 @ sK3 @ sK7) = sK7) = $false) | ~spl0_12),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f407])).
% 1.80/1.62 thf(f407,plain,(
% 1.80/1.62 ($false = ((^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0)) @ sK7)) | ~spl0_12),
% 1.80/1.62 inference(sigma_clausification,[status(thm)],[f403])).
% 1.80/1.62 thf(f423,plain,(
% 1.80/1.62 ( ! [X1 : g] : (((((sK2 @ sK3 @ X1) = X1) & ((sK2 @ X1 @ sK3) = X1)) = $true)) ) | ~spl0_2),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f422])).
% 1.80/1.62 thf(f422,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))) @ X1))) ) | ~spl0_2),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f419])).
% 1.80/1.62 thf(f419,plain,(
% 1.80/1.62 ($true = (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) | ~spl0_2),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f418])).
% 1.80/1.62 thf(f418,plain,(
% 1.80/1.62 ($true = ($true & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0)))))) | ~spl0_2),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f413,f417])).
% 1.80/1.62 thf(f417,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) = $true) | ~spl0_2),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f413])).
% 1.80/1.62 thf(f413,plain,(
% 1.80/1.62 (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) = $true) | ~spl0_2),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f412])).
% 1.80/1.62 thf(f412,plain,(
% 1.80/1.62 ($true = (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & $true)) | ~spl0_2),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f53,f410])).
% 1.80/1.62 thf(f404,plain,(
% 1.80/1.62 spl0_11 | spl0_12 | ~spl0_9),
% 1.80/1.62 inference(avatar_split_clause,[status(thm)],[f397,f382,f402,f399])).
% 1.80/1.62 thf(f382,definition,(
% 1.80/1.62 spl0_9 <=> (((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) = $false)),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.80/1.62 thf(f397,plain,(
% 1.80/1.62 ($false = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) | ((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) = $false) | ~spl0_9),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f383])).
% 1.80/1.62 thf(f383,plain,(
% 1.80/1.62 (((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) = $false) | ~spl0_9),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f382])).
% 1.80/1.62 thf(f387,plain,(
% 1.80/1.62 spl0_9 | spl0_10 | ~spl0_4),
% 1.80/1.62 inference(avatar_split_clause,[status(thm)],[f380,f59,f385,f382])).
% 1.80/1.62 thf(f59,definition,(
% 1.80/1.62 spl0_4 <=> ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = $false)),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.80/1.62 thf(f380,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) = $false) | (((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) = $false) | ~spl0_4),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.80/1.62 thf(f60,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = $false) | ~spl0_4),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.80/1.62 thf(f376,plain,(
% 1.80/1.62 ~spl0_6),
% 1.80/1.62 inference(avatar_contradiction_clause,[status(thm)],[f375])).
% 1.80/1.62 thf(f375,plain,(
% 1.80/1.62 $false | ~spl0_6),
% 1.80/1.62 inference(trivial_inequality_removal,[status(thm)],[f374])).
% 1.80/1.62 thf(f374,plain,(
% 1.80/1.62 ($true = $false) | ~spl0_6),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f373])).
% 1.80/1.62 thf(f373,plain,(
% 1.80/1.62 ((sK6 = sK6) = $false) | ~spl0_6),
% 1.80/1.62 inference(forward_demodulation,[status(thm)],[f372,f351])).
% 1.80/1.62 thf(f351,plain,(
% 1.80/1.62 ( ! [X0 : g] : (((sK2 @ X0 @ sK3) = X0)) ) | ~spl0_6),
% 1.80/1.62 inference(equality_proxy_clausification,[status(thm)],[f343])).
% 1.80/1.62 thf(f343,plain,(
% 1.80/1.62 ( ! [X0 : g] : (($true = (X0 = (sK2 @ X0 @ sK3)))) ) | ~spl0_6),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f325,f338])).
% 1.80/1.62 thf(f338,plain,(
% 1.80/1.62 ( ! [X0 : g,X1 : g] : (((sK2 @ (sK4 @ (sK4 @ X0)) @ X1) = (sK2 @ X0 @ X1))) ) | ~spl0_6),
% 1.80/1.62 inference(superposition,[status(thm)],[f324,f324])).
% 1.80/1.62 thf(f324,plain,(
% 1.80/1.62 ( ! [X0 : g,X1 : g] : (((sK2 @ (sK4 @ X0) @ (sK2 @ X0 @ X1)) = X1)) ) | ~spl0_6),
% 1.80/1.62 inference(equality_proxy_clausification,[status(thm)],[f320])).
% 1.80/1.62 thf(f320,plain,(
% 1.80/1.62 ( ! [X0 : g,X1 : g] : (($true = (X1 = (sK2 @ (sK4 @ X0) @ (sK2 @ X0 @ X1))))) ) | ~spl0_6),
% 1.80/1.62 inference(forward_demodulation,[status(thm)],[f305,f288])).
% 1.80/1.62 thf(f288,plain,(
% 1.80/1.62 ( ! [X1 : g] : (((sK2 @ sK3 @ X1) = X1)) ) | ~spl0_6),
% 1.80/1.62 inference(equality_proxy_clausification,[status(thm)],[f287])).
% 1.80/1.62 thf(f287,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((sK2 @ sK3 @ X1) = X1) = $true)) ) | ~spl0_6),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f286])).
% 1.80/1.62 thf(f286,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0)) @ X1) = $true)) ) | ~spl0_6),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f273])).
% 1.80/1.62 thf(f273,plain,(
% 1.80/1.62 ($true = (!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0)))) | ~spl0_6),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f261])).
% 1.80/1.62 thf(f261,plain,(
% 1.80/1.62 (((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) != $false) | ~spl0_6),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f258])).
% 1.80/1.62 thf(f258,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & $true) != $false) | ~spl0_6),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f250,f256])).
% 1.80/1.62 thf(f256,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) = $true) | ~spl0_6),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f250])).
% 1.80/1.62 thf(f250,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) != $false) | ~spl0_6),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f249])).
% 1.80/1.62 thf(f249,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) != ($false & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))))) | ~spl0_6),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f248])).
% 1.80/1.62 thf(f248,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) != (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & $false) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))))) | ~spl0_6),
% 1.80/1.62 inference(forward_demodulation,[status(thm)],[f45,f132])).
% 1.80/1.62 thf(f132,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0)))) = $false) | ~spl0_6),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f131])).
% 1.80/1.62 thf(f131,definition,(
% 1.80/1.62 spl0_6 <=> ((!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0)))) = $false)),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.80/1.62 thf(f305,plain,(
% 1.80/1.62 ( ! [X0 : g,X1 : g] : (($true = ((sK2 @ sK3 @ X1) = (sK2 @ (sK4 @ X0) @ (sK2 @ X0 @ X1))))) ) | ~spl0_6),
% 1.80/1.62 inference(superposition,[status(thm)],[f299,f283])).
% 1.80/1.62 thf(f283,plain,(
% 1.80/1.62 ( ! [X1 : g] : (((sK2 @ (sK4 @ X1) @ X1) = sK3)) ) | ~spl0_6),
% 1.80/1.62 inference(equality_proxy_clausification,[status(thm)],[f282])).
% 1.80/1.62 thf(f282,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((sK2 @ (sK4 @ X1) @ X1) = sK3) = $true)) ) | ~spl0_6),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f281])).
% 1.80/1.62 thf(f281,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = ((^[Y0 : g]: ((sK2 @ Y0 @ X1) = sK3)) @ (sK4 @ X1)))) ) | ~spl0_6),
% 1.80/1.62 inference(sigma_clausification,[status(thm)],[f280])).
% 1.80/1.62 thf(f280,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = (?? @ g @ (^[Y0 : g]: ((sK2 @ Y0 @ X1) = sK3))))) ) | ~spl0_6),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f279])).
% 1.80/1.62 thf(f279,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))) @ X1))) ) | ~spl0_6),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f276])).
% 1.80/1.62 thf(f276,plain,(
% 1.80/1.62 ($false != (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) | ~spl0_6),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f275])).
% 1.80/1.62 thf(f275,plain,(
% 1.80/1.62 ($false != ($true & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3))))))) | ~spl0_6),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f261,f273])).
% 1.80/1.62 thf(f299,plain,(
% 1.80/1.62 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK2 @ (sK2 @ X3 @ X2) @ X1) = (sK2 @ X3 @ (sK2 @ X2 @ X1))))) ) | ~spl0_6),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f298])).
% 1.80/1.62 thf(f298,plain,(
% 1.80/1.62 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: ((sK2 @ (sK2 @ Y0 @ X2) @ X1) = (sK2 @ Y0 @ (sK2 @ X2 @ X1)))) @ X3))) ) | ~spl0_6),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f297])).
% 1.80/1.62 thf(f297,plain,(
% 1.80/1.62 ( ! [X2 : g,X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: ((sK2 @ (sK2 @ Y0 @ X2) @ X1) = (sK2 @ Y0 @ (sK2 @ X2 @ X1))))))) ) | ~spl0_6),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f296])).
% 1.80/1.62 thf(f296,plain,(
% 1.80/1.62 ( ! [X2 : g,X1 : g] : (($true = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK2 @ (sK2 @ Y1 @ Y0) @ X1) = (sK2 @ Y1 @ (sK2 @ Y0 @ X1)))))) @ X2))) ) | ~spl0_6),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f295])).
% 1.80/1.62 thf(f295,plain,(
% 1.80/1.62 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK2 @ (sK2 @ Y1 @ Y0) @ X1) = (sK2 @ Y1 @ (sK2 @ Y0 @ X1))))))) = $true)) ) | ~spl0_6),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f294])).
% 1.80/1.62 thf(f294,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))) @ X1) = $true)) ) | ~spl0_6),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f256])).
% 1.80/1.62 thf(f325,plain,(
% 1.80/1.62 ( ! [X0 : g] : (($true = (X0 = (sK2 @ (sK4 @ (sK4 @ X0)) @ sK3)))) ) | ~spl0_6),
% 1.80/1.62 inference(superposition,[status(thm)],[f320,f283])).
% 1.80/1.62 thf(f372,plain,(
% 1.80/1.62 (((sK2 @ sK6 @ sK3) = sK6) = $false) | ~spl0_6),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f371])).
% 1.80/1.62 thf(f371,plain,(
% 1.80/1.62 (($true & ((sK2 @ sK6 @ sK3) = sK6)) = $false) | ~spl0_6),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f370])).
% 1.80/1.62 thf(f370,plain,(
% 1.80/1.62 (((sK6 = sK6) & ((sK2 @ sK6 @ sK3) = sK6)) = $false) | ~spl0_6),
% 1.80/1.62 inference(forward_demodulation,[status(thm)],[f255,f288])).
% 1.80/1.62 thf(f255,plain,(
% 1.80/1.62 ((((sK2 @ sK3 @ sK6) = sK6) & ((sK2 @ sK6 @ sK3) = sK6)) = $false) | ~spl0_6),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f254])).
% 1.80/1.62 thf(f254,plain,(
% 1.80/1.62 ($false = ((^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))) @ sK6)) | ~spl0_6),
% 1.80/1.62 inference(sigma_clausification,[status(thm)],[f132])).
% 1.80/1.62 thf(f240,plain,(
% 1.80/1.62 ~spl0_3 | ~spl0_5),
% 1.80/1.62 inference(avatar_contradiction_clause,[status(thm)],[f239])).
% 1.80/1.62 thf(f239,plain,(
% 1.80/1.62 $false | (~spl0_3 | ~spl0_5)),
% 1.80/1.62 inference(trivial_inequality_removal,[status(thm)],[f238])).
% 1.80/1.62 thf(f238,plain,(
% 1.80/1.62 ($true = $false) | (~spl0_3 | ~spl0_5)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f237])).
% 1.80/1.62 thf(f237,plain,(
% 1.80/1.62 ((sK3 = sK3) = $false) | (~spl0_3 | ~spl0_5)),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f168,f223])).
% 1.80/1.62 thf(f223,plain,(
% 1.80/1.62 ( ! [X0 : g] : (((sK2 @ X0 @ (sK4 @ X0)) = sK3)) ) | ~spl0_3),
% 1.80/1.62 inference(superposition,[status(thm)],[f112,f123])).
% 1.80/1.62 thf(f123,plain,(
% 1.80/1.62 ( ! [X0 : g,X1 : g] : (((sK2 @ (sK4 @ (sK4 @ X0)) @ X1) = (sK2 @ X0 @ X1))) ) | ~spl0_3),
% 1.80/1.62 inference(superposition,[status(thm)],[f116,f116])).
% 1.80/1.62 thf(f116,plain,(
% 1.80/1.62 ( ! [X0 : g,X1 : g] : (((sK2 @ (sK4 @ X0) @ (sK2 @ X0 @ X1)) = X1)) ) | ~spl0_3),
% 1.80/1.62 inference(forward_demodulation,[status(thm)],[f115,f85])).
% 1.80/1.62 thf(f85,plain,(
% 1.80/1.62 ( ! [X1 : g] : (((sK2 @ sK3 @ X1) = X1)) ) | ~spl0_3),
% 1.80/1.62 inference(equality_proxy_clausification,[status(thm)],[f82])).
% 1.80/1.62 thf(f82,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((sK2 @ sK3 @ X1) = X1) = $true)) ) | ~spl0_3),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.80/1.62 thf(f81,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0)) @ X1) = $true)) ) | ~spl0_3),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f76])).
% 1.80/1.62 thf(f76,plain,(
% 1.80/1.62 ($true = (!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0)))) | ~spl0_3),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 1.80/1.62 thf(f68,plain,(
% 1.80/1.62 ($true = ((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3))))))) | ~spl0_3),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.80/1.62 thf(f66,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) != $false) | ~spl0_3),
% 1.80/1.62 inference(forward_demodulation,[status(thm)],[f45,f57])).
% 1.80/1.62 thf(f57,plain,(
% 1.80/1.62 ($false = (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))))) | ~spl0_3),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.80/1.62 thf(f56,definition,(
% 1.80/1.62 spl0_3 <=> ($false = (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3))))))))),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.80/1.62 thf(f115,plain,(
% 1.80/1.62 ( ! [X0 : g,X1 : g] : (((sK2 @ sK3 @ X1) = (sK2 @ (sK4 @ X0) @ (sK2 @ X0 @ X1)))) ) | ~spl0_3),
% 1.80/1.62 inference(superposition,[status(thm)],[f90,f112])).
% 1.80/1.62 thf(f90,plain,(
% 1.80/1.62 ( ! [X2 : g,X3 : g,X1 : g] : (((sK2 @ X3 @ (sK2 @ X2 @ X1)) = (sK2 @ (sK2 @ X3 @ X2) @ X1))) ) | ~spl0_3),
% 1.80/1.62 inference(equality_proxy_clausification,[status(thm)],[f89])).
% 1.80/1.62 thf(f89,plain,(
% 1.80/1.62 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK2 @ (sK2 @ X3 @ X2) @ X1) = (sK2 @ X3 @ (sK2 @ X2 @ X1))))) ) | ~spl0_3),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.80/1.62 thf(f88,plain,(
% 1.80/1.62 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: ((sK2 @ (sK2 @ Y0 @ X2) @ X1) = (sK2 @ Y0 @ (sK2 @ X2 @ X1)))) @ X3))) ) | ~spl0_3),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f84])).
% 1.80/1.62 thf(f84,plain,(
% 1.80/1.62 ( ! [X2 : g,X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: ((sK2 @ (sK2 @ Y0 @ X2) @ X1) = (sK2 @ Y0 @ (sK2 @ X2 @ X1))))))) ) | ~spl0_3),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.80/1.62 thf(f83,plain,(
% 1.80/1.62 ( ! [X2 : g,X1 : g] : (($true = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK2 @ (sK2 @ Y1 @ Y0) @ X1) = (sK2 @ Y1 @ (sK2 @ Y0 @ X1)))))) @ X2))) ) | ~spl0_3),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f80])).
% 1.80/1.62 thf(f80,plain,(
% 1.80/1.62 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK2 @ (sK2 @ Y1 @ Y0) @ X1) = (sK2 @ Y1 @ (sK2 @ Y0 @ X1))))))) = $true)) ) | ~spl0_3),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.80/1.62 thf(f79,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))) @ X1) = $true)) ) | ~spl0_3),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f71])).
% 1.80/1.62 thf(f71,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) != $false) | ~spl0_3),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f69])).
% 1.80/1.62 thf(f69,plain,(
% 1.80/1.62 (($true & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) != $false) | ~spl0_3),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f66,f68])).
% 1.80/1.62 thf(f112,plain,(
% 1.80/1.62 ( ! [X1 : g] : (((sK2 @ (sK4 @ X1) @ X1) = sK3)) ) | ~spl0_3),
% 1.80/1.62 inference(equality_proxy_clausification,[status(thm)],[f111])).
% 1.80/1.62 thf(f111,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((sK2 @ (sK4 @ X1) @ X1) = sK3) = $true)) ) | ~spl0_3),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f110])).
% 1.80/1.62 thf(f110,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = ((^[Y0 : g]: ((sK2 @ Y0 @ X1) = sK3)) @ (sK4 @ X1)))) ) | ~spl0_3),
% 1.80/1.62 inference(sigma_clausification,[status(thm)],[f109])).
% 1.80/1.62 thf(f109,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = (?? @ g @ (^[Y0 : g]: ((sK2 @ Y0 @ X1) = sK3))))) ) | ~spl0_3),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.80/1.62 thf(f108,plain,(
% 1.80/1.62 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))) @ X1))) ) | ~spl0_3),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f78])).
% 1.80/1.62 thf(f78,plain,(
% 1.80/1.62 ($true = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) | ~spl0_3),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f77])).
% 1.80/1.62 thf(f77,plain,(
% 1.80/1.62 ($true = ($true & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3))))))) | ~spl0_3),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f68,f76])).
% 1.80/1.62 thf(f168,plain,(
% 1.80/1.62 (((sK2 @ sK5 @ (sK4 @ sK5)) = sK3) = $false) | (~spl0_3 | ~spl0_5)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f167])).
% 1.80/1.62 thf(f167,plain,(
% 1.80/1.62 ((((sK2 @ sK5 @ (sK4 @ sK5)) = sK3) & $true) = $false) | (~spl0_3 | ~spl0_5)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f165])).
% 1.80/1.62 thf(f165,plain,(
% 1.80/1.62 ((((sK2 @ sK5 @ (sK4 @ sK5)) = sK3) & (sK3 = sK3)) = $false) | (~spl0_3 | ~spl0_5)),
% 1.80/1.62 inference(superposition,[status(thm)],[f146,f112])).
% 1.80/1.62 thf(f146,plain,(
% 1.80/1.62 ( ! [X1 : g] : (((((sK2 @ sK5 @ X1) = sK3) & ((sK2 @ X1 @ sK5) = sK3)) = $false)) ) | ~spl0_5),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f145])).
% 1.80/1.62 thf(f145,plain,(
% 1.80/1.62 ( ! [X1 : g] : ((((^[Y0 : g]: (((sK2 @ sK5 @ Y0) = sK3) & ((sK2 @ Y0 @ sK5) = sK3))) @ X1) = $false)) ) | ~spl0_5),
% 1.80/1.62 inference(pi_clausification,[status(thm)],[f141])).
% 1.80/1.62 thf(f141,plain,(
% 1.80/1.62 ((?? @ g @ (^[Y0 : g]: (((sK2 @ sK5 @ Y0) = sK3) & ((sK2 @ Y0 @ sK5) = sK3)))) = $false) | ~spl0_5),
% 1.80/1.62 inference(beta_eta_normalization,[status(thm)],[f140])).
% 1.80/1.62 thf(f140,plain,(
% 1.80/1.62 (((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3))))) @ sK5) = $false) | ~spl0_5),
% 1.80/1.62 inference(sigma_clausification,[status(thm)],[f129])).
% 1.80/1.62 thf(f129,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))) = $false) | ~spl0_5),
% 1.80/1.62 inference(avatar_component_clause,[status(thm)],[f128])).
% 1.80/1.62 thf(f128,definition,(
% 1.80/1.62 spl0_5 <=> ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))) = $false)),
% 1.80/1.62 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.80/1.62 thf(f133,plain,(
% 1.80/1.62 spl0_5 | spl0_6 | ~spl0_1 | ~spl0_3),
% 1.80/1.62 inference(avatar_split_clause,[status(thm)],[f126,f56,f49,f131,f128])).
% 1.80/1.62 thf(f126,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0)))) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))) = $false) | (~spl0_1 | ~spl0_3)),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.80/1.62 thf(f74,plain,(
% 1.80/1.62 (((!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0)))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3))))))) = $false) | (~spl0_1 | ~spl0_3)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f73])).
% 1.80/1.62 thf(f73,plain,(
% 1.80/1.62 ($false = (($true & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))))) | (~spl0_1 | ~spl0_3)),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f57,f72])).
% 1.80/1.62 thf(f72,plain,(
% 1.80/1.62 ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) = $true) | (~spl0_1 | ~spl0_3)),
% 1.80/1.62 inference(boolean_simplification,[status(thm)],[f70])).
% 1.80/1.62 thf(f70,plain,(
% 1.80/1.62 (($true & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = $true) | (~spl0_1 | ~spl0_3)),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f50,f68])).
% 1.80/1.62 thf(f65,plain,(
% 1.80/1.62 ~spl0_2 | ~spl0_3),
% 1.80/1.62 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.80/1.62 thf(f64,plain,(
% 1.80/1.62 $false | (~spl0_2 | ~spl0_3)),
% 1.80/1.62 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.80/1.62 thf(f63,plain,(
% 1.80/1.62 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.80/1.62 inference(backward_demodulation,[status(thm)],[f53,f57])).
% 1.80/1.62 thf(f61,plain,(
% 1.80/1.62 spl0_3 | spl0_4),
% 1.80/1.62 inference(avatar_split_clause,[status(thm)],[f47,f59,f56])).
% 1.80/1.62 thf(f47,plain,(
% 1.80/1.62 ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = $false) | ($false = (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3))))))))),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.80/1.62 thf(f54,plain,(
% 1.80/1.62 spl0_1 | spl0_2),
% 1.80/1.62 inference(avatar_split_clause,[status(thm)],[f46,f52,f49])).
% 1.80/1.62 thf(f46,plain,(
% 1.80/1.62 ($true = (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0))))))))) & (!! @ g @ (^[Y0 : g]: (((sK2 @ sK3 @ Y0) = Y0) & ((sK2 @ Y0 @ sK3) = Y0))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: (((sK2 @ Y0 @ Y1) = sK3) & ((sK2 @ Y1 @ Y0) = sK3)))))))) | ((((!! @ g @ (^[Y0 : g]: ((sK2 @ sK3 @ Y0) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK2 @ Y1 @ Y0) = sK3)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK2 @ (sK2 @ Y2 @ Y1) @ Y0) = (sK2 @ Y2 @ (sK2 @ Y1 @ Y0)))))))))) = $true)),
% 1.80/1.62 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.80/1.62 % SZS output end Proof for DTF2THF_21974
% 1.80/1.62 % (22089)------------------------------
% 1.80/1.62 % (22089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.62 % (22089)Termination reason: Refutation
% 1.80/1.62
% 1.80/1.62 % (22089)Memory used [KB]: 5884
% 1.80/1.62 % (22089)Time elapsed: 0.061 s
% 1.80/1.62 % (22089)Instructions burned: 103 (million)
% 1.80/1.62 % (22089)------------------------------
% 1.80/1.62 % (22089)------------------------------
% 1.80/1.62 % (22077)Success in time 0.094 s
%------------------------------------------------------------------------------