%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG279^5 : 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 : n028.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 1.65s 1.45s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 153 ( 84 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 336 ( 13 ~; 0 |; 26 &; 277 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 6 usr; 6 con; 0-2 aty)
% ( 8 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 115 ( 33 ^; 67 !; 15 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_14,type,
sK0: g ).
thf(func_def_15,type,
sK1: g > g > g ).
thf(func_def_16,type,
sK2: g ).
thf(func_def_18,type,
sK4: g > g ).
thf(f324,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f308]) ).
thf(f308,plain,
sK2 != sK2,
inference(superposition,[status(thm)],[f19,f275]) ).
thf(f275,plain,
! [X0: g] :
( ( sK1 @ sK0 @ X0 )
= X0 ),
inference(superposition,[status(thm)],[f27,f227]) ).
thf(f227,plain,
! [X0: g] :
( ( sK1 @ X0 @ sK0 )
= ( sK1 @ sK0 @ X0 ) ),
inference(superposition,[status(thm)],[f35,f149]) ).
thf(f149,plain,
! [X0: g] :
( sK0
= ( sK1 @ ( sK4 @ X0 ) @ X0 ) ),
inference(superposition,[status(thm)],[f39,f139]) ).
thf(f139,plain,
! [X0: g] :
( ( sK1 @ ( sK4 @ X0 ) @ ( sK1 @ X0 @ sK0 ) )
= sK0 ),
inference(superposition,[status(thm)],[f75,f57]) ).
thf(f57,plain,
! [X0: g] :
( ( sK1 @ X0 @ sK0 )
= ( sK1 @ sK0 @ ( sK4 @ ( sK4 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f35,f33]) ).
thf(f33,plain,
! [X1: g] :
( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK0 ),
inference(equality_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: g] :
( $true
= ( ( sK1 @ X1 @ ( sK4 @ X1 ) )
= sK0 ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK0 )
@ ( sK4 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: g] :
( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK1 @ X1 @ Y0 )
= sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK1 @ Y0 @ Y1 )
= sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f20,f16]) ).
thf(f16,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)],[f8]) ).
thf(f8,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)],[f1]) ).
thf(f1,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Fe6bS95qwX/DTF2THF_21744.p',cGRP_RIGHT_INVERSE_def) ).
thf(f20,plain,
( $true
= ( cGRP_RIGHT_INVERSE @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( cGRP_RIGHT_INVERSE @ sK1 @ sK0 ) )
& ( sK2
!= ( sK1 @ sK0 @ sK2 ) )
& ( $true
= ( cGRP_RIGHT_UNIT @ sK1 @ sK0 ) )
& ! [X3: g,X4: g,X5: g] :
( ( sK1 @ ( sK1 @ X4 @ X5 ) @ X3 )
= ( sK1 @ X4 @ ( sK1 @ X5 @ X3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f14,f13]) ).
thf(f13,plain,
( ? [X0: g,X1: g > g > g] :
( ( $true
= ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) )
& ? [X2: g] :
( ( X1 @ X0 @ X2 )
!= X2 )
& ( $true
= ( cGRP_RIGHT_UNIT @ X1 @ X0 ) )
& ! [X3: g,X4: g,X5: g] :
( ( X1 @ ( X1 @ X4 @ X5 ) @ X3 )
= ( X1 @ X4 @ ( X1 @ X5 @ X3 ) ) ) )
=> ( ( $true
= ( cGRP_RIGHT_INVERSE @ sK1 @ sK0 ) )
& ? [X2: g] :
( ( sK1 @ sK0 @ X2 )
!= X2 )
& ( $true
= ( cGRP_RIGHT_UNIT @ sK1 @ sK0 ) )
& ! [X5: g,X4: g,X3: g] :
( ( sK1 @ ( sK1 @ X4 @ X5 ) @ X3 )
= ( sK1 @ X4 @ ( sK1 @ X5 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X2: g] :
( ( sK1 @ sK0 @ X2 )
!= X2 )
=> ( sK2
!= ( sK1 @ sK0 @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: g,X1: g > g > g] :
( ( $true
= ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) )
& ? [X2: g] :
( ( X1 @ X0 @ X2 )
!= X2 )
& ( $true
= ( cGRP_RIGHT_UNIT @ X1 @ X0 ) )
& ! [X3: g,X4: g,X5: g] :
( ( X1 @ ( X1 @ X4 @ X5 ) @ X3 )
= ( X1 @ X4 @ ( X1 @ X5 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
? [X0: g,X1: g > g > g] :
( ( $true
= ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) )
& ? [X5: g] :
( ( X1 @ X0 @ X5 )
!= X5 )
& ( $true
= ( cGRP_RIGHT_UNIT @ X1 @ X0 ) )
& ! [X2: g,X3: g,X4: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X2 )
= ( X1 @ X3 @ ( X1 @ X4 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
? [X0: g,X1: g > g > g] :
( ? [X5: g] :
( ( X1 @ X0 @ X5 )
!= X5 )
& ( $true
= ( cGRP_RIGHT_UNIT @ X1 @ X0 ) )
& ! [X2: g,X3: g,X4: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X2 )
= ( X1 @ X3 @ ( X1 @ X4 @ X2 ) ) )
& ( $true
= ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: g,X1: g > g > g] :
( ( ( $true
= ( cGRP_RIGHT_UNIT @ X1 @ X0 ) )
& ! [X2: g,X3: g,X4: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X2 )
= ( X1 @ X3 @ ( X1 @ X4 @ X2 ) ) )
& ( $true
= ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) ) )
=> ! [X5: g] :
( ( X1 @ X0 @ X5 )
= X5 ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: g,X1: g > g > g] :
( ( ( cGRP_RIGHT_UNIT @ X1 @ X0 )
& ( cGRP_RIGHT_INVERSE @ X1 @ X0 )
& ! [X2: g,X3: g,X4: g] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X2 )
= ( X1 @ X3 @ ( X1 @ X4 @ X2 ) ) ) )
=> ! [X5: g] :
( ( X1 @ X0 @ X5 )
= X5 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X1: g,X0: g > g > g] :
( ( ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ! [X4: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) ) )
=> ! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X1: g,X0: g > g > g] :
( ( ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ! [X4: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) ) )
=> ! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Fe6bS95qwX/DTF2THF_21744.p',cE13A2A) ).
thf(f75,plain,
! [X0: g] :
( ( sK1 @ X0 @ ( sK1 @ sK0 @ ( sK4 @ X0 ) ) )
= sK0 ),
inference(superposition,[status(thm)],[f38,f27]) ).
thf(f38,plain,
! [X0: g,X1: g] :
( sK0
= ( sK1 @ X0 @ ( sK1 @ X1 @ ( sK4 @ ( sK1 @ X0 @ X1 ) ) ) ) ),
inference(superposition,[status(thm)],[f17,f33]) ).
thf(f17,plain,
! [X3: g,X4: g,X5: g] :
( ( sK1 @ ( sK1 @ X4 @ X5 ) @ X3 )
= ( sK1 @ X4 @ ( sK1 @ X5 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f39,plain,
! [X0: g,X1: g] :
( ( sK1 @ X0 @ ( sK1 @ X1 @ sK0 ) )
= ( sK1 @ X0 @ X1 ) ),
inference(superposition,[status(thm)],[f27,f17]) ).
thf(f35,plain,
! [X0: g,X1: g] :
( ( sK1 @ sK0 @ X1 )
= ( sK1 @ X0 @ ( sK1 @ ( sK4 @ X0 ) @ X1 ) ) ),
inference(superposition,[status(thm)],[f17,f33]) ).
thf(f27,plain,
! [X1: g] :
( ( sK1 @ X1 @ sK0 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: g] :
( $true
= ( ( sK1 @ X1 @ sK0 )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK1 @ Y0 @ sK0 )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK1 @ Y0 @ sK0 )
= Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f18,f21]) ).
thf(f21,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Fe6bS95qwX/DTF2THF_21744.p',cGRP_RIGHT_UNIT_def) ).
thf(f18,plain,
( $true
= ( cGRP_RIGHT_UNIT @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f19,plain,
( sK2
!= ( sK1 @ sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG279^5 : 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
% 0.19/0.36 % Computer : n028.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Tue Feb 24 03:42:42 EST 2026
% 0.19/0.37 % CPUTime :
% 0.19/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : ALG279^5 : TPTP v9.2.1. Bugfixed v5.3.0.
% 0.26/0.47 % Domain : General Algebra
% 0.26/0.47 % Problem : TPS problem from GRP-THMS
% 0.26/0.47 % Version : Especial.
% 0.26/0.47 % English :
% 0.26/0.47
% 0.26/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.47 % Source : [Bro09]
% 0.26/0.47 % Names : tps_0879 [Bro09]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % 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, 0.25 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.40 v5.3.0
% 0.26/0.47 % Syntax : Number of formulae : 6 ( 2 unt; 3 typ; 2 def)
% 0.26/0.47 % Number of atoms : 10 ( 6 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 4 ( 3 avg)
% 0.26/0.47 % Number of connectives : 21 ( 0 ~; 0 |; 2 &; 18 @)
% 0.26/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 8 ( 3 avg)
% 0.26/0.47 % Number of types : 2 ( 1 usr)
% 0.26/0.47 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 3 ( 2 usr; 0 con; 2-2 aty)
% 0.26/0.47 % Number of variables : 13 ( 4 ^; 8 !; 1 ?; 13 :)
% 0.26/0.47 % SPC : TH0_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.47 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.26/0.47 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf(g_type,type,
% 0.26/0.47 g: $tType ).
% 0.26/0.47
% 0.26/0.47 thf(cGRP_RIGHT_INVERSE_type,type,
% 0.26/0.47 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 0.26/0.47
% 0.26/0.47 thf(cGRP_RIGHT_UNIT_type,type,
% 0.26/0.47 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 0.26/0.47
% 0.26/0.47 thf(cGRP_RIGHT_INVERSE_def,definition,
% 0.26/0.47 ( cGRP_RIGHT_INVERSE
% 0.26/0.47 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.26/0.47 ! [Xa: g] :
% 0.26/0.47 ? [Xb: g] :
% 0.26/0.47 ( ( Xf @ Xa @ Xb )
% 0.26/0.47 = Xe ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cGRP_RIGHT_UNIT_def,definition,
% 0.26/0.47 ( cGRP_RIGHT_UNIT
% 0.26/0.47 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.26/0.47 ! [Xa: g] :
% 0.26/0.47 ( ( Xf @ Xa @ Xe )
% 0.26/0.47 = Xa ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cE13A2A,conjecture,
% 0.26/0.47 ! [Xf: g > g > g,Xe: g] :
% 0.26/0.47 ( ( ! [Xb: g,Xc: g,Xa: g] :
% 0.26/0.47 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 0.26/0.47 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) )
% 0.26/0.47 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 0.26/0.47 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) )
% 0.26/0.47 => ! [Xa: g] :
% 0.26/0.47 ( ( Xf @ Xe @ Xa )
% 0.26/0.47 = Xa ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 1.46/1.39 ---- Embedded in THF ---
% 1.46/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.39 %%% Generated on Tue Feb 24 03:42:43 EST 2026
% 1.46/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.39 %%% Logic specification used:
% 1.46/1.39 %%% thf(spec, logic, $$dhol).
% 1.46/1.39
% 1.46/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Fe6bS95qwX/DTF2DTF21744.p
% See solution above
% 1.46/1.39 ------------------------
% 1.46/1.40 ---- Cleaned THF ---
% 1.65/1.40 thf(g_type,type,
% 1.65/1.40 g: $tType ).
% 1.65/1.40
% 1.65/1.40 thf(cGRP_RIGHT_INVERSE_type,type,
% 1.65/1.40 cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
% 1.65/1.40
% 1.65/1.40 thf(cGRP_RIGHT_UNIT_type,type,
% 1.65/1.40 cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
% 1.65/1.40
% 1.65/1.40 thf(cGRP_RIGHT_INVERSE_def,definition,
% 1.65/1.40 ( cGRP_RIGHT_INVERSE
% 1.65/1.40 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.65/1.40 ! [Xa: g] :
% 1.65/1.40 ? [Xb: g] :
% 1.65/1.40 ( ( Xf @ Xa @ Xb )
% 1.65/1.40 = Xe ) ) ) ).
% 1.65/1.40
% 1.65/1.40 thf(cGRP_RIGHT_UNIT_def,definition,
% 1.65/1.40 ( cGRP_RIGHT_UNIT
% 1.65/1.40 = ( ^ [Xf: g > g > g,Xe: g] :
% 1.65/1.40 ! [Xa: g] :
% 1.65/1.40 ( ( Xf @ Xa @ Xe )
% 1.65/1.40 = Xa ) ) ) ).
% 1.65/1.40
% 1.65/1.40 thf(cE13A2A,conjecture,
% 1.65/1.40 ! [Xf: g > g > g,Xe: g] :
% 1.65/1.40 ( ( ! [Xb: g,Xc: g,Xa: g] :
% 1.65/1.40 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 1.65/1.40 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) )
% 1.65/1.40 & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
% 1.65/1.40 & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) )
% 1.65/1.40 => ! [Xa: g] :
% 1.65/1.40 ( ( Xf @ Xe @ Xa )
% 1.65/1.40 = Xa ) ) ).
% 1.65/1.40 ------------------------
% 1.65/1.42 % (21842)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21744 for (2999ds/183Mi)
% 1.65/1.42 % (21843)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_21744 for (2999ds/4Mi)
% 1.65/1.42 % (21844)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_21744 for (2999ds/27Mi)
% 1.65/1.42 % (21845)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21744 for (2999ds/2Mi)
% 1.65/1.42 % (21846)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_21744 for (2999ds/2Mi)
% 1.65/1.42 % (21847)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_21744 for (2999ds/275Mi)
% 1.65/1.42 % (21848)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21744 for (2999ds/18Mi)
% 1.65/1.42 % (21845)Instruction limit reached!
% 1.65/1.42 % (21845)------------------------------
% 1.65/1.42 % (21845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (21845)Termination reason: Unknown
% 1.65/1.42 % (21845)Termination phase: Saturation
% 1.65/1.42
% 1.65/1.42 % (21845)Memory used [KB]: 5500
% 1.65/1.42 % (21845)Time elapsed: 0.003 s
% 1.65/1.42 % (21845)Instructions burned: 3 (million)
% 1.65/1.42 % (21845)------------------------------
% 1.65/1.42 % (21845)------------------------------
% 1.65/1.42 % (21846)Instruction limit reached!
% 1.65/1.42 % (21846)------------------------------
% 1.65/1.42 % (21846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (21846)Termination reason: Unknown
% 1.65/1.42 % (21846)Termination phase: Saturation
% 1.65/1.42
% 1.65/1.42 % (21846)Memory used [KB]: 5500
% 1.65/1.42 % (21846)Time elapsed: 0.003 s
% 1.65/1.42 % (21846)Instructions burned: 3 (million)
% 1.65/1.42 % (21846)------------------------------
% 1.65/1.42 % (21846)------------------------------
% 1.65/1.42 % (21843)Instruction limit reached!
% 1.65/1.42 % (21843)------------------------------
% 1.65/1.42 % (21843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (21843)Termination reason: Unknown
% 1.65/1.42 % (21843)Termination phase: Saturation
% 1.65/1.42
% 1.65/1.42 % (21843)Memory used [KB]: 5500
% 1.65/1.42 % (21843)Time elapsed: 0.004 s
% 1.65/1.42 % (21843)Instructions burned: 4 (million)
% 1.65/1.42 % (21843)------------------------------
% 1.65/1.42 % (21843)------------------------------
% 1.65/1.42 % (21847)Refutation not found, incomplete strategy
% 1.65/1.42 % (21847)------------------------------
% 1.65/1.42 % (21847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (21847)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.42
% 1.65/1.42
% 1.65/1.42 % (21847)Memory used [KB]: 5500
% 1.65/1.42 % (21847)Time elapsed: 0.004 s
% 1.65/1.42 % (21847)Instructions burned: 4 (million)
% 1.65/1.42 % (21847)------------------------------
% 1.65/1.42 % (21847)------------------------------
% 1.65/1.43 % (21848)Instruction limit reached!
% 1.65/1.43 % (21848)------------------------------
% 1.65/1.43 % (21848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.43 % (21848)Termination reason: Unknown
% 1.65/1.43 % (21848)Termination phase: Saturation
% 1.65/1.43
% 1.65/1.43 % (21848)Memory used [KB]: 5500
% 1.65/1.43 % (21848)Time elapsed: 0.011 s
% 1.65/1.43 % (21848)Instructions burned: 18 (million)
% 1.65/1.43 % (21848)------------------------------
% 1.65/1.43 % (21848)------------------------------
% 1.65/1.43 % (21844)Instruction limit reached!
% 1.65/1.43 % (21844)------------------------------
% 1.65/1.43 % (21844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.43 % (21844)Termination reason: Unknown
% 1.65/1.43 % (21844)Termination phase: Saturation
% 1.65/1.43
% 1.65/1.43 % (21844)Memory used [KB]: 5628
% 1.65/1.43 % (21844)Time elapsed: 0.016 s
% 1.65/1.43 % (21844)Instructions burned: 29 (million)
% 1.65/1.43 % (21844)------------------------------
% 1.65/1.43 % (21844)------------------------------
% 1.65/1.43 % (21849)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21744 for (2999ds/3Mi)
% 1.65/1.43 % (21850)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_21744 for (2999ds/37Mi)
% 1.65/1.43 % (21851)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_21744 for (2999ds/15Mi)
% 1.65/1.44 % (21849)Instruction limit reached!
% 1.65/1.44 % (21849)------------------------------
% 1.65/1.44 % (21849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.44 % (21849)Termination reason: Unknown
% 1.65/1.44 % (21849)Termination phase: Saturation
% 1.65/1.44
% 1.65/1.44 % (21849)Memory used [KB]: 5500
% 1.65/1.44 % (21849)Time elapsed: 0.003 s
% 1.65/1.44 % (21849)Instructions burned: 3 (million)
% 1.65/1.44 % (21849)------------------------------
% 1.65/1.44 % (21849)------------------------------
% 1.65/1.44 % (21852)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_21744 for (2999ds/3Mi)
% 1.65/1.44 % (21852)Instruction limit reached!
% 1.65/1.44 % (21852)------------------------------
% 1.65/1.44 % (21852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.44 % (21852)Termination reason: Unknown
% 1.65/1.44 % (21852)Termination phase: Saturation
% 1.65/1.44
% 1.65/1.44 % (21852)Memory used [KB]: 5500
% 1.65/1.44 % (21852)Time elapsed: 0.003 s
% 1.65/1.44 % (21852)Instructions burned: 3 (million)
% 1.65/1.44 % (21852)------------------------------
% 1.65/1.44 % (21852)------------------------------
% 1.65/1.44 % (21853)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_21744 for (2999ds/1041Mi)
% 1.65/1.44 % (21851)Instruction limit reached!
% 1.65/1.44 % (21851)------------------------------
% 1.65/1.44 % (21851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.44 % (21851)Termination reason: Unknown
% 1.65/1.44 % (21851)Termination phase: Saturation
% 1.65/1.44
% 1.65/1.44 % (21851)Memory used [KB]: 5500
% 1.65/1.44 % (21851)Time elapsed: 0.009 s
% 1.65/1.44 % (21851)Instructions burned: 15 (million)
% 1.65/1.44 % (21851)------------------------------
% 1.65/1.44 % (21851)------------------------------
% 1.65/1.45 % (21854)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21744 for (2999ds/7Mi)
% 1.65/1.45 % (21854)Instruction limit reached!
% 1.65/1.45 % (21854)------------------------------
% 1.65/1.45 % (21854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (21854)Termination reason: Unknown
% 1.65/1.45 % (21854)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (21854)Memory used [KB]: 1023
% 1.65/1.45 % (21854)Time elapsed: 0.005 s
% 1.65/1.45 % (21854)Instructions burned: 7 (million)
% 1.65/1.45 % (21854)------------------------------
% 1.65/1.45 % (21854)------------------------------
% 1.65/1.45 % (21842)First to succeed.
% 1.65/1.45 % (21855)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21744 for (2999ds/16Mi)
% 1.65/1.45 % (21850)Also succeeded, but the first one will report.
% 1.65/1.45 % (21842)Refutation found. Thanks to Tanya!
% 1.65/1.45 % SZS status Theorem for DTF2THF_21744
% 1.65/1.45 % SZS output start Proof for DTF2THF_21744
% 1.65/1.45 thf(type_def_5, type, g: $tType).
% 1.65/1.45 thf(func_def_0, type, g: $tType).
% 1.65/1.45 thf(func_def_1, type, cGRP_RIGHT_INVERSE: (g > g > g) > g > $o).
% 1.65/1.45 thf(func_def_2, type, cGRP_RIGHT_UNIT: (g > g > g) > g > $o).
% 1.65/1.45 thf(func_def_14, type, sK0: g).
% 1.65/1.45 thf(func_def_15, type, sK1: g > g > g).
% 1.65/1.45 thf(func_def_16, type, sK2: g).
% 1.65/1.45 thf(func_def_18, type, sK4: g > g).
% 1.65/1.45 thf(f324,plain,(
% 1.65/1.45 $false),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f308])).
% 1.65/1.45 thf(f308,plain,(
% 1.65/1.45 (sK2 != sK2)),
% 1.65/1.45 inference(superposition,[status(thm)],[f19,f275])).
% 1.65/1.45 thf(f275,plain,(
% 1.65/1.45 ( ! [X0 : g] : (((sK1 @ sK0 @ X0) = X0)) )),
% 1.65/1.45 inference(superposition,[status(thm)],[f27,f227])).
% 1.65/1.45 thf(f227,plain,(
% 1.65/1.45 ( ! [X0 : g] : (((sK1 @ X0 @ sK0) = (sK1 @ sK0 @ X0))) )),
% 1.65/1.45 inference(superposition,[status(thm)],[f35,f149])).
% 1.65/1.45 thf(f149,plain,(
% 1.65/1.45 ( ! [X0 : g] : ((sK0 = (sK1 @ (sK4 @ X0) @ X0))) )),
% 1.65/1.45 inference(superposition,[status(thm)],[f39,f139])).
% 1.65/1.45 thf(f139,plain,(
% 1.65/1.45 ( ! [X0 : g] : (((sK1 @ (sK4 @ X0) @ (sK1 @ X0 @ sK0)) = sK0)) )),
% 1.65/1.45 inference(superposition,[status(thm)],[f75,f57])).
% 1.65/1.45 thf(f57,plain,(
% 1.65/1.45 ( ! [X0 : g] : (((sK1 @ X0 @ sK0) = (sK1 @ sK0 @ (sK4 @ (sK4 @ X0))))) )),
% 1.65/1.45 inference(superposition,[status(thm)],[f35,f33])).
% 1.65/1.45 thf(f33,plain,(
% 1.65/1.45 ( ! [X1 : g] : (((sK1 @ X1 @ (sK4 @ X1)) = sK0)) )),
% 1.65/1.45 inference(equality_proxy_clausification,[status(thm)],[f32])).
% 1.65/1.45 thf(f32,plain,(
% 1.65/1.45 ( ! [X1 : g] : (($true = ((sK1 @ X1 @ (sK4 @ X1)) = sK0))) )),
% 1.65/1.45 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.65/1.45 thf(f31,plain,(
% 1.65/1.45 ( ! [X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ X1 @ Y0) = sK0)) @ (sK4 @ X1)))) )),
% 1.65/1.45 inference(sigma_clausification,[status(thm)],[f30])).
% 1.65/1.45 thf(f30,plain,(
% 1.65/1.45 ( ! [X1 : g] : (($true = (?? @ g @ (^[Y0 : g]: ((sK1 @ X1 @ Y0) = sK0))))) )),
% 1.65/1.45 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.65/1.45 thf(f29,plain,(
% 1.65/1.45 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK0)))) @ X1))) )),
% 1.65/1.45 inference(pi_clausification,[status(thm)],[f28])).
% 1.65/1.45 thf(f28,plain,(
% 1.65/1.45 ($true = (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK0))))))),
% 1.65/1.45 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.65/1.45 thf(f22,plain,(
% 1.65/1.45 ($true = ((^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))) @ sK1 @ sK0))),
% 1.65/1.45 inference(definition_unfolding,[status(thm)],[f20,f16])).
% 1.65/1.45 thf(f16,plain,(
% 1.65/1.45 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f8])).
% 1.65/1.45 thf(f8,plain,(
% 1.65/1.45 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
% 1.65/1.45 inference(fool_elimination,[status(thm)],[f1])).
% 1.65/1.45 thf(f1,axiom,(
% 1.65/1.45 (cGRP_RIGHT_INVERSE = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : ((X0 @ X2 @ X3) = X1))))),
% 1.65/1.45 file('/export/starexec/sandbox2/tmp/tmp.Fe6bS95qwX/DTF2THF_21744.p',cGRP_RIGHT_INVERSE_def)).
% 1.65/1.45 thf(f20,plain,(
% 1.65/1.45 ($true = (cGRP_RIGHT_INVERSE @ sK1 @ sK0))),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.45 thf(f15,plain,(
% 1.65/1.45 ($true = (cGRP_RIGHT_INVERSE @ sK1 @ sK0)) & (sK2 != (sK1 @ sK0 @ sK2)) & ($true = (cGRP_RIGHT_UNIT @ sK1 @ sK0)) & ! [X3 : g,X4 : g,X5 : g] : ((sK1 @ (sK1 @ X4 @ X5) @ X3) = (sK1 @ X4 @ (sK1 @ X5 @ X3)))),
% 1.65/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f14,f13])).
% 1.65/1.45 thf(f13,plain,(
% 1.65/1.45 ? [X0 : g,X1 : g > g > g] : (($true = (cGRP_RIGHT_INVERSE @ X1 @ X0)) & ? [X2 : g] : ((X1 @ X0 @ X2) != X2) & ($true = (cGRP_RIGHT_UNIT @ X1 @ X0)) & ! [X3 : g,X4 : g,X5 : g] : ((X1 @ (X1 @ X4 @ X5) @ X3) = (X1 @ X4 @ (X1 @ X5 @ X3)))) => (($true = (cGRP_RIGHT_INVERSE @ sK1 @ sK0)) & ? [X2 : g] : ((sK1 @ sK0 @ X2) != X2) & ($true = (cGRP_RIGHT_UNIT @ sK1 @ sK0)) & ! [X5 : g,X4 : g,X3 : g] : ((sK1 @ (sK1 @ X4 @ X5) @ X3) = (sK1 @ X4 @ (sK1 @ X5 @ X3))))),
% 1.65/1.45 introduced(definition,[],[choice_axiom])).
% 1.65/1.45 thf(f14,plain,(
% 1.65/1.45 ? [X2 : g] : ((sK1 @ sK0 @ X2) != X2) => (sK2 != (sK1 @ sK0 @ sK2))),
% 1.65/1.45 introduced(definition,[],[choice_axiom])).
% 1.65/1.45 thf(f12,plain,(
% 1.65/1.45 ? [X0 : g,X1 : g > g > g] : (($true = (cGRP_RIGHT_INVERSE @ X1 @ X0)) & ? [X2 : g] : ((X1 @ X0 @ X2) != X2) & ($true = (cGRP_RIGHT_UNIT @ X1 @ X0)) & ! [X3 : g,X4 : g,X5 : g] : ((X1 @ (X1 @ X4 @ X5) @ X3) = (X1 @ X4 @ (X1 @ X5 @ X3))))),
% 1.65/1.45 inference(rectify,[status(thm)],[f11])).
% 1.65/1.45 thf(f11,plain,(
% 1.65/1.45 ? [X0 : g,X1 : g > g > g] : (($true = (cGRP_RIGHT_INVERSE @ X1 @ X0)) & ? [X5 : g] : ((X1 @ X0 @ X5) != X5) & ($true = (cGRP_RIGHT_UNIT @ X1 @ X0)) & ! [X2 : g,X3 : g,X4 : g] : ((X1 @ (X1 @ X3 @ X4) @ X2) = (X1 @ X3 @ (X1 @ X4 @ X2))))),
% 1.65/1.45 inference(flattening,[status(thm)],[f10])).
% 1.65/1.45 thf(f10,plain,(
% 1.65/1.45 ? [X0 : g,X1 : g > g > g] : (? [X5 : g] : ((X1 @ X0 @ X5) != X5) & (($true = (cGRP_RIGHT_UNIT @ X1 @ X0)) & ! [X2 : g,X3 : g,X4 : g] : ((X1 @ (X1 @ X3 @ X4) @ X2) = (X1 @ X3 @ (X1 @ X4 @ X2))) & ($true = (cGRP_RIGHT_INVERSE @ X1 @ X0))))),
% 1.65/1.45 inference(ennf_transformation,[status(thm)],[f7])).
% 1.65/1.45 thf(f7,plain,(
% 1.65/1.45 ~! [X0 : g,X1 : g > g > g] : ((($true = (cGRP_RIGHT_UNIT @ X1 @ X0)) & ! [X2 : g,X3 : g,X4 : g] : ((X1 @ (X1 @ X3 @ X4) @ X2) = (X1 @ X3 @ (X1 @ X4 @ X2))) & ($true = (cGRP_RIGHT_INVERSE @ X1 @ X0))) => ! [X5 : g] : ((X1 @ X0 @ X5) = X5))),
% 1.65/1.45 inference(fool_elimination,[status(thm)],[f6])).
% 1.65/1.45 thf(f6,plain,(
% 1.65/1.45 ~! [X0 : g,X1 : g > g > g] : (((cGRP_RIGHT_UNIT @ X1 @ X0) & (cGRP_RIGHT_INVERSE @ X1 @ X0) & ! [X2 : g,X3 : g,X4 : g] : ((X1 @ (X1 @ X3 @ X4) @ X2) = (X1 @ X3 @ (X1 @ X4 @ X2)))) => ! [X5 : g] : ((X1 @ X0 @ X5) = X5))),
% 1.65/1.45 inference(rectify,[status(thm)],[f4])).
% 1.65/1.45 thf(f4,negated_conjecture,(
% 1.65/1.45 ~! [X1 : g,X0 : g > g > g] : (((cGRP_RIGHT_UNIT @ X0 @ X1) & (cGRP_RIGHT_INVERSE @ X0 @ X1) & ! [X4 : g,X2 : g,X3 : g] : ((X0 @ (X0 @ X2 @ X3) @ X4) = (X0 @ X2 @ (X0 @ X3 @ X4)))) => ! [X2 : g] : ((X0 @ X1 @ X2) = X2))),
% 1.65/1.45 inference(negated_conjecture,[status(cth)],[f3])).
% 1.65/1.45 thf(f3,conjecture,(
% 1.65/1.45 ! [X1 : g,X0 : g > g > g] : (((cGRP_RIGHT_UNIT @ X0 @ X1) & (cGRP_RIGHT_INVERSE @ X0 @ X1) & ! [X4 : g,X2 : g,X3 : g] : ((X0 @ (X0 @ X2 @ X3) @ X4) = (X0 @ X2 @ (X0 @ X3 @ X4)))) => ! [X2 : g] : ((X0 @ X1 @ X2) = X2))),
% 1.65/1.45 file('/export/starexec/sandbox2/tmp/tmp.Fe6bS95qwX/DTF2THF_21744.p',cE13A2A)).
% 1.65/1.45 thf(f75,plain,(
% 1.65/1.45 ( ! [X0 : g] : (((sK1 @ X0 @ (sK1 @ sK0 @ (sK4 @ X0))) = sK0)) )),
% 1.65/1.45 inference(superposition,[status(thm)],[f38,f27])).
% 1.65/1.45 thf(f38,plain,(
% 1.65/1.45 ( ! [X0 : g,X1 : g] : ((sK0 = (sK1 @ X0 @ (sK1 @ X1 @ (sK4 @ (sK1 @ X0 @ X1)))))) )),
% 1.65/1.45 inference(superposition,[status(thm)],[f17,f33])).
% 1.65/1.45 thf(f17,plain,(
% 1.65/1.45 ( ! [X3 : g,X4 : g,X5 : g] : (((sK1 @ (sK1 @ X4 @ X5) @ X3) = (sK1 @ X4 @ (sK1 @ X5 @ X3)))) )),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.45 thf(f39,plain,(
% 1.65/1.45 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ X1 @ sK0)) = (sK1 @ X0 @ X1))) )),
% 1.65/1.45 inference(superposition,[status(thm)],[f27,f17])).
% 1.65/1.45 thf(f35,plain,(
% 1.65/1.45 ( ! [X0 : g,X1 : g] : (((sK1 @ sK0 @ X1) = (sK1 @ X0 @ (sK1 @ (sK4 @ X0) @ X1)))) )),
% 1.65/1.45 inference(superposition,[status(thm)],[f17,f33])).
% 1.65/1.45 thf(f27,plain,(
% 1.65/1.45 ( ! [X1 : g] : (((sK1 @ X1 @ sK0) = X1)) )),
% 1.65/1.45 inference(equality_proxy_clausification,[status(thm)],[f26])).
% 1.65/1.45 thf(f26,plain,(
% 1.65/1.45 ( ! [X1 : g] : (($true = ((sK1 @ X1 @ sK0) = X1))) )),
% 1.65/1.45 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.65/1.45 thf(f25,plain,(
% 1.65/1.45 ( ! [X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ Y0 @ sK0) = Y0)) @ X1))) )),
% 1.65/1.45 inference(pi_clausification,[status(thm)],[f24])).
% 1.65/1.45 thf(f24,plain,(
% 1.65/1.45 ($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK0) = Y0))))),
% 1.65/1.45 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.65/1.45 thf(f23,plain,(
% 1.65/1.45 ($true = ((^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))) @ sK1 @ sK0))),
% 1.65/1.45 inference(definition_unfolding,[status(thm)],[f18,f21])).
% 1.65/1.45 thf(f21,plain,(
% 1.65/1.45 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f9])).
% 1.65/1.45 thf(f9,plain,(
% 1.65/1.45 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
% 1.65/1.45 inference(fool_elimination,[status(thm)],[f2])).
% 1.65/1.45 thf(f2,axiom,(
% 1.65/1.45 (cGRP_RIGHT_UNIT = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ((X0 @ X2 @ X1) = X2))))),
% 1.65/1.45 file('/export/starexec/sandbox2/tmp/tmp.Fe6bS95qwX/DTF2THF_21744.p',cGRP_RIGHT_UNIT_def)).
% 1.65/1.45 thf(f18,plain,(
% 1.65/1.45 ($true = (cGRP_RIGHT_UNIT @ sK1 @ sK0))),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.45 thf(f19,plain,(
% 1.65/1.45 (sK2 != (sK1 @ sK0 @ sK2))),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.45 % SZS output end Proof for DTF2THF_21744
% 1.65/1.45 % (21842)------------------------------
% 1.65/1.45 % (21842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (21842)Termination reason: Refutation
% 1.65/1.45
% 1.65/1.45 % (21842)Memory used [KB]: 6012
% 1.65/1.45 % (21842)Time elapsed: 0.037 s
% 1.65/1.45 % (21842)Instructions burned: 68 (million)
% 1.65/1.45 % (21842)------------------------------
% 1.65/1.45 % (21842)------------------------------
% 1.65/1.45 % (21841)Success in time 0.048 s
%------------------------------------------------------------------------------