%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG277^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.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 08:37:49 AM UTC 2026
% Result : Theorem 1.67s 1.45s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 213 ( 102 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 478 ( 11 ~; 0 |; 19 &; 394 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 8 usr; 6 con; 0-2 aty)
% ( 40 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 161 ( 96 ^; 55 !; 10 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_3,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_4,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_17,type,
sK0: g ).
thf(func_def_18,type,
sK1: g > g > g ).
thf(func_def_19,type,
sK2: g ).
thf(func_def_21,type,
sK4: g > g ).
thf(f340,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f324]) ).
thf(f324,plain,
sK2 != sK2,
inference(superposition,[status(thm)],[f26,f295]) ).
thf(f295,plain,
! [X0: g] :
( ( sK1 @ sK0 @ X0 )
= X0 ),
inference(superposition,[status(thm)],[f37,f173]) ).
thf(f173,plain,
! [X0: g] :
( ( sK1 @ sK0 @ X0 )
= ( sK1 @ X0 @ sK0 ) ),
inference(superposition,[status(thm)],[f51,f159]) ).
thf(f159,plain,
! [X0: g] :
( sK0
= ( sK1 @ ( sK4 @ X0 ) @ X0 ) ),
inference(superposition,[status(thm)],[f155,f37]) ).
thf(f155,plain,
! [X0: g] :
( sK0
= ( sK1 @ ( sK4 @ X0 ) @ ( sK1 @ X0 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f91,f73]) ).
thf(f73,plain,
! [X0: g] :
( ( sK1 @ X0 @ sK0 )
= ( sK1 @ sK0 @ ( sK4 @ ( sK4 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f51,f49]) ).
thf(f49,plain,
! [X1: g] :
( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK0 ),
inference(equality_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: g] :
( ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK0 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK0 )
@ ( sK4 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: g] :
( ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y3 @ ( Y2 @ Y5 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y3 @ Y5 ) @ Y4 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) )
@ sK1
@ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f25,f28]) ).
thf(f28,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y3 @ ( Y2 @ Y5 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y3 @ Y5 ) @ Y4 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f27,f22,f24]) ).
thf(f24,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) )
= cGRP_RIGHT_INVERSE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( X0 @ X1 @ X2 )
= X4 ) )
= cGRP_RIGHT_INVERSE ),
file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cGRP_RIGHT_INVERSE_def) ).
thf(f22,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ X3 @ ( X0 @ X1 @ X2 ) )
= ( X0 @ ( X0 @ X3 @ X1 ) @ X2 ) ) )
= cGRP_ASSOC ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: g > g > g] :
! [X2: g,X3: g,X1: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) )
= cGRP_ASSOC ),
file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cGRP_ASSOC_def) ).
thf(f27,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( cGRP_RIGHT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( X0 @ X1 @ X4 )
= X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cGRP_RIGHT_UNIT_def) ).
thf(f23,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 ) ) )
= cGROUP3 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_RIGHT_INVERSE @ X0 @ X4 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_UNIT @ X0 @ X4 ) ) )
= cGROUP3 ),
file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cGROUP3_def) ).
thf(f25,plain,
( ( cGROUP3 @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( sK1 @ sK0 @ sK2 )
!= sK2 )
& ( ( cGROUP3 @ sK1 @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f20,f19]) ).
thf(f19,plain,
( ? [X0: g,X1: g > g > g] :
( ? [X2: g] :
( ( X1 @ X0 @ X2 )
!= X2 )
& ( $true
= ( cGROUP3 @ X1 @ X0 ) ) )
=> ( ? [X2: g] :
( ( sK1 @ sK0 @ X2 )
!= X2 )
& ( ( cGROUP3 @ sK1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X2: g] :
( ( sK1 @ sK0 @ X2 )
!= X2 )
=> ( ( sK1 @ sK0 @ sK2 )
!= sK2 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
? [X0: g,X1: g > g > g] :
( ? [X2: g] :
( ( X1 @ X0 @ X2 )
!= X2 )
& ( $true
= ( cGROUP3 @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ! [X0: g,X1: g > g > g] :
( ( $true
= ( cGROUP3 @ X1 @ X0 ) )
=> ! [X2: g] :
( ( X1 @ X0 @ X2 )
= X2 ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ! [X0: g,X1: g > g > g] :
( ( cGROUP3 @ X1 @ X0 )
=> ! [X2: g] :
( ( X1 @ X0 @ X2 )
= X2 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X4: g,X0: g > g > g] :
( ( cGROUP3 @ X0 @ X4 )
=> ! [X1: g] :
( ( X0 @ X4 @ X1 )
= X1 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X4: g,X0: g > g > g] :
( ( cGROUP3 @ X0 @ X4 )
=> ! [X1: g] :
( ( X0 @ X4 @ X1 )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cE13A2) ).
thf(f91,plain,
! [X0: g] :
( ( sK1 @ X0 @ ( sK1 @ sK0 @ ( sK4 @ X0 ) ) )
= sK0 ),
inference(superposition,[status(thm)],[f56,f37]) ).
thf(f56,plain,
! [X0: g,X1: g] :
( sK0
= ( sK1 @ X0 @ ( sK1 @ X1 @ ( sK4 @ ( sK1 @ X0 @ X1 ) ) ) ) ),
inference(superposition,[status(thm)],[f49,f44]) ).
thf(f44,plain,
! [X2: g,X3: g,X1: g] :
( ( sK1 @ X1 @ ( sK1 @ X3 @ X2 ) )
= ( sK1 @ ( sK1 @ X1 @ X3 ) @ X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK1 @ X1 @ ( sK1 @ X3 @ X2 ) )
= ( sK1 @ ( sK1 @ X1 @ X3 ) @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: g,X3: g,X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK1 @ X1 @ ( sK1 @ Y0 @ X2 ) )
= ( sK1 @ ( sK1 @ X1 @ Y0 ) @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: g,X1: g] :
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ ( sK1 @ Y0 @ X2 ) )
= ( sK1 @ ( sK1 @ X1 @ Y0 ) @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: g,X1: g] :
( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ X1 @ ( sK1 @ Y1 @ Y0 ) )
= ( sK1 @ ( sK1 @ X1 @ Y1 ) @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: g] :
( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK1 @ X1 @ ( sK1 @ Y1 @ Y0 ) )
= ( sK1 @ ( sK1 @ X1 @ Y1 ) @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: g] :
( ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK1 @ Y0 @ ( sK1 @ Y2 @ Y1 ) )
= ( sK1 @ ( sK1 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f51,plain,
! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ ( sK4 @ X0 ) @ X1 ) )
= ( sK1 @ sK0 @ X1 ) ),
inference(superposition,[status(thm)],[f44,f49]) ).
thf(f37,plain,
! [X1: g] :
( ( sK1 @ X1 @ sK0 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: g] :
( ( ( sK1 @ X1 @ sK0 )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: g] :
( ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK0 )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f26,plain,
( ( sK1 @ sK0 @ sK2 )
!= sK2 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG277^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.00/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.36 % Computer : n029.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Tue Feb 24 03:42:44 EST 2026
% 0.18/0.36 % CPUTime :
% 0.18/0.36 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : ALG277^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.29/0.46 % Domain : General Algebra
% 0.29/0.46 % Problem : TPS problem from GRP-THMS
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0701 [Bro09]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.40 v5.3.0
% 0.29/0.46 % Syntax : Number of formulae : 10 ( 4 unt; 5 typ; 4 def)
% 0.29/0.46 % Number of atoms : 16 ( 8 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 2 ( 3 avg)
% 0.29/0.46 % Number of connectives : 24 ( 0 ~; 0 |; 2 &; 21 @)
% 0.29/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 6 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.29/0.46 % Number of variables : 16 ( 7 ^; 8 !; 1 ?; 16 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.29/0.46 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(g_type,type,
% 0.29/0.46 g: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cGROUP3_type,type,
% 0.29/0.46 cGROUP3: ( g > g > g ) > g > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cGRP_ASSOC_type,type,
% 0.29/0.46 cGRP_ASSOC: ( g > g > g ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cGRP_RIGHT_INVERSE_type,type,
% 0.29/0.46 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cGRP_RIGHT_UNIT_type,type,
% 0.29/0.46 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 0.29/0.46
% 0.29/0.46 thf(cGRP_ASSOC_def,definition,
% 0.29/0.46 ( cGRP_ASSOC
% 0.29/0.46 = ( ^ [Xf: g > g > g] :
% 0.29/0.46 ! [Xa: g,Xb: g,Xc: g] :
% 0.29/0.46 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 0.29/0.46 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cGRP_RIGHT_INVERSE_def,definition,
% 0.29/0.46 ( cGRP_RIGHT_INVERSE
% 0.29/0.46 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.29/0.46 ! [Xa: g] :
% 0.29/0.46 ? [Xb: g] :
% 0.29/0.46 ( ( Xf @ Xa @ Xb )
% 0.29/0.46 = Xe ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cGRP_RIGHT_UNIT_def,definition,
% 0.29/0.46 ( cGRP_RIGHT_UNIT
% 0.29/0.46 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.29/0.46 ! [Xa: g] :
% 0.29/0.46 ( ( Xf @ Xa @ Xe )
% 0.29/0.46 = Xa ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cGROUP3_def,definition,
% 0.29/0.46 ( cGROUP3
% 0.29/0.46 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.29/0.46 ( ( cGRP_ASSOC @ Xf )
% 0.29/0.46 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 0.29/0.46 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cE13A2,conjecture,
% 0.29/0.46 ! [Xf: g > g > g,Xe: g] :
% 0.29/0.46 ( ( cGROUP3 @ Xf @ Xe )
% 0.29/0.46 => ! [Xa: g] :
% 0.29/0.46 ( ( Xf @ Xe @ Xa )
% 0.29/0.46 = Xa ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.49/1.39 ---- Embedded in THF ---
% 1.49/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.39 %%% Generated on Tue Feb 24 03:42:45 EST 2026
% 1.49/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.39 %%% Logic specification used:
% 1.49/1.39 %%% thf(spec, logic, $$dhol).
% 1.49/1.39
% 1.49/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2DTF8127.p
% See solution above
% 1.49/1.39 ------------------------
% 1.49/1.40 ---- Cleaned THF ---
% 1.49/1.40 thf(g_type,type,
% 1.49/1.40 g: $tType ).
% 1.49/1.40
% 1.49/1.40 thf(cGROUP3_type,type,
% 1.49/1.40 cGROUP3: ( g > g > g ) > g > $o ).
% 1.49/1.40
% 1.49/1.40 thf(cGRP_ASSOC_type,type,
% 1.49/1.40 cGRP_ASSOC: ( g > g > g ) > $o ).
% 1.49/1.40
% 1.49/1.40 thf(cGRP_RIGHT_INVERSE_type,type,
% 1.49/1.40 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 1.49/1.40
% 1.49/1.40 thf(cGRP_RIGHT_UNIT_type,type,
% 1.49/1.40 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 1.49/1.40
% 1.49/1.40 thf(cGRP_ASSOC_def,definition,
% 1.49/1.40 ( cGRP_ASSOC
% 1.49/1.40 = ( ^ [Xf: g > g > g] :
% 1.49/1.40 ! [Xa: g,Xb: g,Xc: g] :
% 1.49/1.40 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 1.49/1.40 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 1.49/1.40
% 1.49/1.40 thf(cGRP_RIGHT_INVERSE_def,definition,
% 1.49/1.40 ( cGRP_RIGHT_INVERSE
% 1.49/1.40 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.49/1.40 ! [Xa: g] :
% 1.49/1.40 ? [Xb: g] :
% 1.49/1.40 ( ( Xf @ Xa @ Xb )
% 1.49/1.40 = Xe ) ) ) ).
% 1.49/1.40
% 1.49/1.40 thf(cGRP_RIGHT_UNIT_def,definition,
% 1.49/1.40 ( cGRP_RIGHT_UNIT
% 1.49/1.40 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.49/1.40 ! [Xa: g] :
% 1.49/1.40 ( ( Xf @ Xa @ Xe )
% 1.49/1.40 = Xa ) ) ) ).
% 1.49/1.40
% 1.49/1.40 thf(cGROUP3_def,definition,
% 1.49/1.40 ( cGROUP3
% 1.49/1.40 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.49/1.40 ( ( cGRP_ASSOC @ Xf )
% 1.49/1.40 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 1.49/1.40 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 1.49/1.40
% 1.49/1.40 thf(cE13A2,conjecture,
% 1.49/1.40 ! [Xf: g > g > g,Xe: g] :
% 1.49/1.40 ( ( cGROUP3 @ Xf @ Xe )
% 1.49/1.40 => ! [Xa: g] :
% 1.49/1.40 ( ( Xf @ Xe @ Xa )
% 1.49/1.40 = Xa ) ) ).
% 1.49/1.40 ------------------------
% 1.67/1.42 % (8226)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_8127 for (2999ds/27Mi)
% 1.67/1.42 % (8225)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_8127 for (2999ds/4Mi)
% 1.67/1.42 % (8227)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8127 for (2999ds/2Mi)
% 1.67/1.42 % (8228)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_8127 for (2999ds/2Mi)
% 1.67/1.42 % (8224)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8127 for (2999ds/183Mi)
% 1.67/1.42 % (8230)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8127 for (2999ds/18Mi)
% 1.67/1.42 % (8229)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_8127 for (2999ds/275Mi)
% 1.67/1.42 % (8227)Instruction limit reached!
% 1.67/1.42 % (8227)------------------------------
% 1.67/1.42 % (8227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (8227)Termination reason: Unknown
% 1.67/1.42 % (8228)Instruction limit reached!
% 1.67/1.42 % (8228)------------------------------
% 1.67/1.42 % (8228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (8228)Termination reason: Unknown
% 1.67/1.42 % (8228)Termination phase: Saturation
% 1.67/1.42
% 1.67/1.42 % (8228)Memory used [KB]: 1023
% 1.67/1.42 % (8228)Time elapsed: 0.003 s
% 1.67/1.42 % (8228)Instructions burned: 3 (million)
% 1.67/1.42 % (8228)------------------------------
% 1.67/1.42 % (8228)------------------------------
% 1.67/1.42 % (8227)Termination phase: Saturation
% 1.67/1.42
% 1.67/1.42 % (8227)Memory used [KB]: 1023
% 1.67/1.42 % (8227)Time elapsed: 0.003 s
% 1.67/1.42 % (8227)Instructions burned: 3 (million)
% 1.67/1.42 % (8227)------------------------------
% 1.67/1.42 % (8227)------------------------------
% 1.67/1.42 % (8229)Refutation not found, incomplete strategy
% 1.67/1.42 % (8229)------------------------------
% 1.67/1.42 % (8229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (8229)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.42
% 1.67/1.42
% 1.67/1.42 % (8229)Memory used [KB]: 5500
% 1.67/1.42 % (8229)Time elapsed: 0.003 s
% 1.67/1.42 % (8229)Instructions burned: 2 (million)
% 1.67/1.42 % (8229)------------------------------
% 1.67/1.42 % (8229)------------------------------
% 1.67/1.42 % (8225)Instruction limit reached!
% 1.67/1.42 % (8225)------------------------------
% 1.67/1.42 % (8225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (8225)Termination reason: Unknown
% 1.67/1.42 % (8225)Termination phase: Saturation
% 1.67/1.42
% 1.67/1.42 % (8225)Memory used [KB]: 5500
% 1.67/1.42 % (8225)Time elapsed: 0.004 s
% 1.67/1.42 % (8225)Instructions burned: 4 (million)
% 1.67/1.42 % (8225)------------------------------
% 1.67/1.42 % (8225)------------------------------
% 1.67/1.43 % (8230)Instruction limit reached!
% 1.67/1.43 % (8230)------------------------------
% 1.67/1.43 % (8230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (8230)Termination reason: Unknown
% 1.67/1.43 % (8230)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.43 % (8230)Memory used [KB]: 5628
% 1.67/1.43 % (8230)Time elapsed: 0.011 s
% 1.67/1.43 % (8230)Instructions burned: 18 (million)
% 1.67/1.43 % (8230)------------------------------
% 1.67/1.43 % (8230)------------------------------
% 1.67/1.43 % (8226)Instruction limit reached!
% 1.67/1.43 % (8226)------------------------------
% 1.67/1.43 % (8226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (8226)Termination reason: Unknown
% 1.67/1.43 % (8226)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.43 % (8226)Memory used [KB]: 5628
% 1.67/1.43 % (8226)Time elapsed: 0.016 s
% 1.67/1.43 % (8226)Instructions burned: 28 (million)
% 1.67/1.43 % (8226)------------------------------
% 1.67/1.43 % (8226)------------------------------
% 1.67/1.43 % (8231)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8127 for (2999ds/3Mi)
% 1.67/1.43 % (8232)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_8127 for (2999ds/37Mi)
% 1.67/1.43 % (8233)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_8127 for (2999ds/15Mi)
% 1.67/1.43 % (8234)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_8127 for (2999ds/3Mi)
% 1.67/1.43 % (8231)Instruction limit reached!
% 1.67/1.43 % (8231)------------------------------
% 1.67/1.43 % (8231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (8231)Termination reason: Unknown
% 1.67/1.43 % (8231)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.44 % (8231)Memory used [KB]: 5500
% 1.67/1.44 % (8231)Time elapsed: 0.003 s
% 1.67/1.44 % (8231)Instructions burned: 3 (million)
% 1.67/1.44 % (8231)------------------------------
% 1.67/1.44 % (8231)------------------------------
% 1.67/1.44 % (8234)Instruction limit reached!
% 1.67/1.44 % (8234)------------------------------
% 1.67/1.44 % (8234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (8234)Termination reason: Unknown
% 1.67/1.44 % (8234)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (8234)Memory used [KB]: 5500
% 1.67/1.44 % (8234)Time elapsed: 0.003 s
% 1.67/1.44 % (8234)Instructions burned: 3 (million)
% 1.67/1.44 % (8234)------------------------------
% 1.67/1.44 % (8234)------------------------------
% 1.67/1.44 % (8235)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_8127 for (2999ds/1041Mi)
% 1.67/1.44 % (8233)Instruction limit reached!
% 1.67/1.44 % (8233)------------------------------
% 1.67/1.44 % (8233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (8233)Termination reason: Unknown
% 1.67/1.44 % (8233)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (8233)Memory used [KB]: 5628
% 1.67/1.44 % (8233)Time elapsed: 0.010 s
% 1.67/1.44 % (8233)Instructions burned: 16 (million)
% 1.67/1.44 % (8233)------------------------------
% 1.67/1.44 % (8233)------------------------------
% 1.67/1.45 % (8236)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8127 for (2999ds/7Mi)
% 1.67/1.45 % (8236)Instruction limit reached!
% 1.67/1.45 % (8236)------------------------------
% 1.67/1.45 % (8236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (8236)Termination reason: Unknown
% 1.67/1.45 % (8236)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (8236)Memory used [KB]: 1023
% 1.67/1.45 % (8236)Time elapsed: 0.005 s
% 1.67/1.45 % (8236)Instructions burned: 7 (million)
% 1.67/1.45 % (8236)------------------------------
% 1.67/1.45 % (8236)------------------------------
% 1.67/1.45 % (8224)First to succeed.
% 1.67/1.45 % (8237)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8127 for (2999ds/16Mi)
% 1.67/1.45 % (8238)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_8127 for (2999ds/3Mi)
% 1.67/1.45 % (8232)Also succeeded, but the first one will report.
% 1.67/1.45 % (8224)Refutation found. Thanks to Tanya!
% 1.67/1.45 % SZS status Theorem for DTF2THF_8127
% 1.67/1.45 % SZS output start Proof for DTF2THF_8127
% 1.67/1.45 thf(type_def_5, type, g: $tType).
% 1.67/1.45 thf(func_def_0, type, g: $tType).
% 1.67/1.45 thf(func_def_1, type, cGROUP3: (g > g > g) > g > $o).
% 1.67/1.45 thf(func_def_2, type, cGRP_ASSOC: (g > g > g) > $o).
% 1.67/1.45 thf(func_def_3, type, cGRP_RIGHT_INVERSE: (g > g > g) > g > $o).
% 1.67/1.45 thf(func_def_4, type, cGRP_RIGHT_UNIT: (g > g > g) > g > $o).
% 1.67/1.45 thf(func_def_17, type, sK0: g).
% 1.67/1.45 thf(func_def_18, type, sK1: g > g > g).
% 1.67/1.45 thf(func_def_19, type, sK2: g).
% 1.67/1.45 thf(func_def_21, type, sK4: g > g).
% 1.67/1.45 thf(f340,plain,(
% 1.67/1.45 $false),
% 1.67/1.45 inference(trivial_inequality_removal,[status(thm)],[f324])).
% 1.67/1.45 thf(f324,plain,(
% 1.67/1.45 (sK2 != sK2)),
% 1.67/1.45 inference(superposition,[status(thm)],[f26,f295])).
% 1.67/1.45 thf(f295,plain,(
% 1.67/1.45 ( ! [X0 : g] : (((sK1 @ sK0 @ X0) = X0)) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f37,f173])).
% 1.67/1.45 thf(f173,plain,(
% 1.67/1.45 ( ! [X0 : g] : (((sK1 @ sK0 @ X0) = (sK1 @ X0 @ sK0))) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f51,f159])).
% 1.67/1.45 thf(f159,plain,(
% 1.67/1.45 ( ! [X0 : g] : ((sK0 = (sK1 @ (sK4 @ X0) @ X0))) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f155,f37])).
% 1.67/1.45 thf(f155,plain,(
% 1.67/1.45 ( ! [X0 : g] : ((sK0 = (sK1 @ (sK4 @ X0) @ (sK1 @ X0 @ sK0)))) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f91,f73])).
% 1.67/1.45 thf(f73,plain,(
% 1.67/1.45 ( ! [X0 : g] : (((sK1 @ X0 @ sK0) = (sK1 @ sK0 @ (sK4 @ (sK4 @ X0))))) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f51,f49])).
% 1.67/1.45 thf(f49,plain,(
% 1.67/1.45 ( ! [X1 : g] : (((sK1 @ X1 @ (sK4 @ X1)) = sK0)) )),
% 1.67/1.45 inference(equality_proxy_clausification,[status(thm)],[f48])).
% 1.67/1.45 thf(f48,plain,(
% 1.67/1.45 ( ! [X1 : g] : ((((sK1 @ X1 @ (sK4 @ X1)) = sK0) = $true)) )),
% 1.67/1.45 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.67/1.45 thf(f47,plain,(
% 1.67/1.45 ( ! [X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ X1 @ Y0) = sK0)) @ (sK4 @ X1)))) )),
% 1.67/1.45 inference(sigma_clausification,[status(thm)],[f46])).
% 1.67/1.45 thf(f46,plain,(
% 1.67/1.45 ( ! [X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ X1 @ Y0) = sK0))) = $true)) )),
% 1.67/1.45 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.67/1.45 thf(f45,plain,(
% 1.67/1.45 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK0)))) @ X1))) )),
% 1.67/1.45 inference(pi_clausification,[status(thm)],[f31])).
% 1.67/1.45 thf(f31,plain,(
% 1.67/1.45 ($true = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK0))))))),
% 1.67/1.45 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.67/1.45 thf(f30,plain,(
% 1.67/1.45 ($true = (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK0) = Y0))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y2 @ Y1)) = (sK1 @ (sK1 @ Y0 @ Y2) @ Y1))))))))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK0)))))))),
% 1.67/1.45 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.67/1.45 thf(f29,plain,(
% 1.67/1.45 (((^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y2 @ Y4 @ Y3) = Y4)))))) @ Y0 @ Y1) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ Y3 @ (Y2 @ Y5 @ Y4)) = (Y2 @ (Y2 @ Y3 @ Y5) @ Y4))))))))) @ Y0)) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: ((Y2 @ Y4 @ Y5) = Y3)))))))) @ Y0 @ Y1))))) @ sK1 @ sK0) = $true)),
% 1.67/1.45 inference(definition_unfolding,[status(thm)],[f25,f28])).
% 1.67/1.45 thf(f28,plain,(
% 1.67/1.45 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y2 @ Y4 @ Y3) = Y4)))))) @ Y0 @ Y1) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ Y3 @ (Y2 @ Y5 @ Y4)) = (Y2 @ (Y2 @ Y3 @ Y5) @ Y4))))))))) @ Y0)) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: ((Y2 @ Y4 @ Y5) = Y3)))))))) @ Y0 @ Y1))))))),
% 1.67/1.45 inference(definition_unfolding,[status(thm)],[f23,f27,f22,f24])).
% 1.67/1.45 thf(f24,plain,(
% 1.67/1.45 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f9])).
% 1.67/1.45 thf(f9,plain,(
% 1.67/1.45 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f8])).
% 1.67/1.45 thf(f8,plain,(
% 1.67/1.45 ((^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : ((X0 @ X2 @ X3) = X1))) = cGRP_RIGHT_INVERSE)),
% 1.67/1.45 inference(rectify,[status(thm)],[f2])).
% 1.67/1.45 thf(f2,axiom,(
% 1.67/1.45 ((^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ? [X2 : g] : ((X0 @ X1 @ X2) = X4))) = cGRP_RIGHT_INVERSE)),
% 1.67/1.45 file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cGRP_RIGHT_INVERSE_def)).
% 1.67/1.45 thf(f22,plain,(
% 1.67/1.45 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ (Y0 @ Y3 @ Y2)) = (Y0 @ (Y0 @ Y1 @ Y3) @ Y2))))))))))),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f11])).
% 1.67/1.45 thf(f11,plain,(
% 1.67/1.45 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ (Y0 @ Y3 @ Y2)) = (Y0 @ (Y0 @ Y1 @ Y3) @ Y2))))))))))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.45 thf(f10,plain,(
% 1.67/1.45 ((^[X0 : g > g > g] : (! [X1 : g,X2 : g,X3 : g] : ((X0 @ X3 @ (X0 @ X1 @ X2)) = (X0 @ (X0 @ X3 @ X1) @ X2)))) = cGRP_ASSOC)),
% 1.67/1.45 inference(rectify,[status(thm)],[f1])).
% 1.67/1.45 thf(f1,axiom,(
% 1.67/1.45 ((^[X0 : g > g > g] : (! [X2 : g,X3 : g,X1 : g] : ((X0 @ (X0 @ X1 @ X2) @ X3) = (X0 @ X1 @ (X0 @ X2 @ X3))))) = cGRP_ASSOC)),
% 1.67/1.45 file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cGRP_ASSOC_def)).
% 1.67/1.45 thf(f27,plain,(
% 1.67/1.45 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.67/1.45 thf(f15,plain,(
% 1.67/1.45 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f14])).
% 1.67/1.45 thf(f14,plain,(
% 1.67/1.45 (cGRP_RIGHT_UNIT = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ((X0 @ X2 @ X1) = X2))))),
% 1.67/1.45 inference(rectify,[status(thm)],[f3])).
% 1.67/1.45 thf(f3,axiom,(
% 1.67/1.45 (cGRP_RIGHT_UNIT = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ((X0 @ X1 @ X4) = X1))))),
% 1.67/1.45 file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cGRP_RIGHT_UNIT_def)).
% 1.67/1.45 thf(f23,plain,(
% 1.67/1.45 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_UNIT @ Y0 @ Y1) & (cGRP_ASSOC @ Y0)) & (cGRP_RIGHT_INVERSE @ Y0 @ Y1))))))),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f17])).
% 1.67/1.45 thf(f17,plain,(
% 1.67/1.45 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_UNIT @ Y0 @ Y1) & (cGRP_ASSOC @ Y0)) & (cGRP_RIGHT_INVERSE @ Y0 @ Y1))))))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f16])).
% 1.67/1.45 thf(f16,plain,(
% 1.67/1.45 ((^[X0 : g > g > g, X1 : g] : ((cGRP_RIGHT_INVERSE @ X0 @ X1) & (cGRP_ASSOC @ X0) & (cGRP_RIGHT_UNIT @ X0 @ X1))) = cGROUP3)),
% 1.67/1.45 inference(rectify,[status(thm)],[f4])).
% 1.67/1.45 thf(f4,axiom,(
% 1.67/1.45 ((^[X0 : g > g > g, X4 : g] : ((cGRP_RIGHT_INVERSE @ X0 @ X4) & (cGRP_ASSOC @ X0) & (cGRP_RIGHT_UNIT @ X0 @ X4))) = cGROUP3)),
% 1.67/1.45 file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cGROUP3_def)).
% 1.67/1.45 thf(f25,plain,(
% 1.67/1.45 ((cGROUP3 @ sK1 @ sK0) = $true)),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f21])).
% 1.67/1.45 thf(f21,plain,(
% 1.67/1.45 ((sK1 @ sK0 @ sK2) != sK2) & ((cGROUP3 @ sK1 @ sK0) = $true)),
% 1.67/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f20,f19])).
% 1.67/1.45 thf(f19,plain,(
% 1.67/1.45 ? [X0 : g,X1 : g > g > g] : (? [X2 : g] : ((X1 @ X0 @ X2) != X2) & ($true = (cGROUP3 @ X1 @ X0))) => (? [X2 : g] : ((sK1 @ sK0 @ X2) != X2) & ((cGROUP3 @ sK1 @ sK0) = $true))),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f20,plain,(
% 1.67/1.45 ? [X2 : g] : ((sK1 @ sK0 @ X2) != X2) => ((sK1 @ sK0 @ sK2) != sK2)),
% 1.67/1.45 introduced(definition,[],[choice_axiom])).
% 1.67/1.45 thf(f18,plain,(
% 1.67/1.45 ? [X0 : g,X1 : g > g > g] : (? [X2 : g] : ((X1 @ X0 @ X2) != X2) & ($true = (cGROUP3 @ X1 @ X0)))),
% 1.67/1.45 inference(ennf_transformation,[status(thm)],[f13])).
% 1.67/1.45 thf(f13,plain,(
% 1.67/1.45 ~! [X0 : g,X1 : g > g > g] : (($true = (cGROUP3 @ X1 @ X0)) => ! [X2 : g] : ((X1 @ X0 @ X2) = X2))),
% 1.67/1.45 inference(fool_elimination,[status(thm)],[f12])).
% 1.67/1.45 thf(f12,plain,(
% 1.67/1.45 ~! [X0 : g,X1 : g > g > g] : ((cGROUP3 @ X1 @ X0) => ! [X2 : g] : ((X1 @ X0 @ X2) = X2))),
% 1.67/1.45 inference(rectify,[status(thm)],[f6])).
% 1.67/1.45 thf(f6,negated_conjecture,(
% 1.67/1.45 ~! [X4 : g,X0 : g > g > g] : ((cGROUP3 @ X0 @ X4) => ! [X1 : g] : ((X0 @ X4 @ X1) = X1))),
% 1.67/1.45 inference(negated_conjecture,[status(cth)],[f5])).
% 1.67/1.45 thf(f5,conjecture,(
% 1.67/1.45 ! [X4 : g,X0 : g > g > g] : ((cGROUP3 @ X0 @ X4) => ! [X1 : g] : ((X0 @ X4 @ X1) = X1))),
% 1.67/1.45 file('/export/starexec/sandbox2/tmp/tmp.deaDMYXAV6/DTF2THF_8127.p',cE13A2)).
% 1.67/1.45 thf(f91,plain,(
% 1.67/1.45 ( ! [X0 : g] : (((sK1 @ X0 @ (sK1 @ sK0 @ (sK4 @ X0))) = sK0)) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f56,f37])).
% 1.67/1.45 thf(f56,plain,(
% 1.67/1.45 ( ! [X0 : g,X1 : g] : ((sK0 = (sK1 @ X0 @ (sK1 @ X1 @ (sK4 @ (sK1 @ X0 @ X1)))))) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f49,f44])).
% 1.67/1.45 thf(f44,plain,(
% 1.67/1.45 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X1 @ (sK1 @ X3 @ X2)) = (sK1 @ (sK1 @ X1 @ X3) @ X2))) )),
% 1.67/1.45 inference(equality_proxy_clausification,[status(thm)],[f43])).
% 1.67/1.45 thf(f43,plain,(
% 1.67/1.45 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK1 @ X1 @ (sK1 @ X3 @ X2)) = (sK1 @ (sK1 @ X1 @ X3) @ X2)) = $true)) )),
% 1.67/1.45 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.67/1.45 thf(f42,plain,(
% 1.67/1.45 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ X1 @ (sK1 @ Y0 @ X2)) = (sK1 @ (sK1 @ X1 @ Y0) @ X2))) @ X3))) )),
% 1.67/1.45 inference(pi_clausification,[status(thm)],[f41])).
% 1.67/1.45 thf(f41,plain,(
% 1.67/1.45 ( ! [X2 : g,X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ X1 @ (sK1 @ Y0 @ X2)) = (sK1 @ (sK1 @ X1 @ Y0) @ X2)))))) )),
% 1.67/1.45 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.67/1.45 thf(f40,plain,(
% 1.67/1.45 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X1 @ (sK1 @ Y1 @ Y0)) = (sK1 @ (sK1 @ X1 @ Y1) @ Y0))))) @ X2) = $true)) )),
% 1.67/1.45 inference(pi_clausification,[status(thm)],[f39])).
% 1.67/1.45 thf(f39,plain,(
% 1.67/1.45 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X1 @ (sK1 @ Y1 @ Y0)) = (sK1 @ (sK1 @ X1 @ Y1) @ Y0)))))) = $true)) )),
% 1.67/1.45 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.67/1.45 thf(f38,plain,(
% 1.67/1.45 ( ! [X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y2 @ Y1)) = (sK1 @ (sK1 @ Y0 @ Y2) @ Y1))))))) @ X1) = $true)) )),
% 1.67/1.45 inference(pi_clausification,[status(thm)],[f33])).
% 1.67/1.45 thf(f33,plain,(
% 1.67/1.45 ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y2 @ Y1)) = (sK1 @ (sK1 @ Y0 @ Y2) @ Y1)))))))))),
% 1.67/1.45 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.67/1.45 thf(f32,plain,(
% 1.67/1.45 ($true = ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK0) = Y0))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y2 @ Y1)) = (sK1 @ (sK1 @ Y0 @ Y2) @ Y1))))))))))),
% 1.67/1.45 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.67/1.45 thf(f51,plain,(
% 1.67/1.45 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ (sK4 @ X0) @ X1)) = (sK1 @ sK0 @ X1))) )),
% 1.67/1.45 inference(superposition,[status(thm)],[f44,f49])).
% 1.67/1.45 thf(f37,plain,(
% 1.67/1.45 ( ! [X1 : g] : (((sK1 @ X1 @ sK0) = X1)) )),
% 1.67/1.45 inference(equality_proxy_clausification,[status(thm)],[f36])).
% 1.67/1.45 thf(f36,plain,(
% 1.67/1.45 ( ! [X1 : g] : ((((sK1 @ X1 @ sK0) = X1) = $true)) )),
% 1.67/1.45 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.67/1.45 thf(f35,plain,(
% 1.67/1.45 ( ! [X1 : g] : ((((^[Y0 : g]: ((sK1 @ Y0 @ sK0) = Y0)) @ X1) = $true)) )),
% 1.67/1.45 inference(pi_clausification,[status(thm)],[f34])).
% 1.67/1.45 thf(f34,plain,(
% 1.67/1.45 ($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK0) = Y0))))),
% 1.67/1.45 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.67/1.45 thf(f26,plain,(
% 1.67/1.45 ((sK1 @ sK0 @ sK2) != sK2)),
% 1.67/1.45 inference(cnf_transformation,[status(thm)],[f21])).
% 1.67/1.45 % SZS output end Proof for DTF2THF_8127
% 1.67/1.45 % (8224)------------------------------
% 1.67/1.45 % (8224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (8224)Termination reason: Refutation
% 1.67/1.45
% 1.67/1.45 % (8224)Memory used [KB]: 6012
% 1.67/1.45 % (8224)Time elapsed: 0.037 s
% 1.67/1.45 % (8224)Instructions burned: 66 (million)
% 1.67/1.45 % (8224)------------------------------
% 1.67/1.45 % (8224)------------------------------
% 1.67/1.45 % (8223)Success in time 0.048 s
%------------------------------------------------------------------------------