%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG298^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 08:37:52 AM UTC 2026
% Result : Theorem 1.56s 1.39s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 62 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 375 ( 12 ~; 0 |; 33 &; 324 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 0 ^; 89 !; 33 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
c: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(func_def_0,type,
c: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_3,type,
c_starc: c > c > c ).
thf(func_def_4,type,
c_starb: b > b > b ).
thf(func_def_5,type,
c_stara: a > a > a ).
thf(func_def_9,type,
sK0: a > b ).
thf(func_def_10,type,
sK1: b > c ).
thf(func_def_11,type,
sK2: a > c ).
thf(func_def_12,type,
sK3: b > a ).
thf(func_def_13,type,
sK4: b ).
thf(func_def_14,type,
sK5: b ).
thf(f82,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( sK1 @ ( c_starb @ sK4 @ sK5 ) )
!= ( sK1 @ ( c_starb @ sK4 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f14,f74]) ).
thf(f74,plain,
! [X0: b,X1: b] :
( ( sK1 @ ( c_starb @ X0 @ X1 ) )
= ( c_starc @ ( sK1 @ X0 ) @ ( sK1 @ X1 ) ) ),
inference(superposition,[status(thm)],[f57,f17]) ).
thf(f17,plain,
! [X0: b] :
( ( sK2 @ ( sK3 @ X0 ) )
= ( sK1 @ X0 ) ),
inference(superposition,[status(thm)],[f13,f15]) ).
thf(f15,plain,
! [X5: b] :
( ( sK0 @ ( sK3 @ X5 ) )
= X5 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X3: a,X4: a] :
( ( c_starb @ ( sK0 @ X4 ) @ ( sK0 @ X3 ) )
= ( sK0 @ ( c_stara @ X4 @ X3 ) ) )
& ! [X5: b] :
( ( sK0 @ ( sK3 @ X5 ) )
= X5 )
& ( ( c_starc @ ( sK1 @ sK4 ) @ ( sK1 @ sK5 ) )
!= ( sK1 @ ( c_starb @ sK4 @ sK5 ) ) )
& ! [X9: a] :
( ( sK2 @ X9 )
= ( sK1 @ ( sK0 @ X9 ) ) )
& ! [X10: a,X11: a] :
( ( c_starc @ ( sK2 @ X10 ) @ ( sK2 @ X11 ) )
= ( sK2 @ ( c_stara @ X10 @ X11 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f7,f10,f9,f8]) ).
thf(f8,plain,
( ? [X0: a > b,X1: b > c,X2: a > c] :
( ! [X3: a,X4: a] :
( ( c_starb @ ( X0 @ X4 ) @ ( X0 @ X3 ) )
= ( X0 @ ( c_stara @ X4 @ X3 ) ) )
& ! [X5: b] :
? [X6: a] :
( ( X0 @ X6 )
= X5 )
& ? [X7: b,X8: b] :
( ( X1 @ ( c_starb @ X7 @ X8 ) )
!= ( c_starc @ ( X1 @ X7 ) @ ( X1 @ X8 ) ) )
& ! [X9: a] :
( ( X1 @ ( X0 @ X9 ) )
= ( X2 @ X9 ) )
& ! [X10: a,X11: a] :
( ( X2 @ ( c_stara @ X10 @ X11 ) )
= ( c_starc @ ( X2 @ X10 ) @ ( X2 @ X11 ) ) ) )
=> ( ! [X4: a,X3: a] :
( ( c_starb @ ( sK0 @ X4 ) @ ( sK0 @ X3 ) )
= ( sK0 @ ( c_stara @ X4 @ X3 ) ) )
& ! [X5: b] :
? [X6: a] :
( ( sK0 @ X6 )
= X5 )
& ? [X8: b,X7: b] :
( ( sK1 @ ( c_starb @ X7 @ X8 ) )
!= ( c_starc @ ( sK1 @ X7 ) @ ( sK1 @ X8 ) ) )
& ! [X9: a] :
( ( sK2 @ X9 )
= ( sK1 @ ( sK0 @ X9 ) ) )
& ! [X11: a,X10: a] :
( ( c_starc @ ( sK2 @ X10 ) @ ( sK2 @ X11 ) )
= ( sK2 @ ( c_stara @ X10 @ X11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X5: b] :
( ? [X6: a] :
( ( sK0 @ X6 )
= X5 )
=> ( ( sK0 @ ( sK3 @ X5 ) )
= X5 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X8: b,X7: b] :
( ( sK1 @ ( c_starb @ X7 @ X8 ) )
!= ( c_starc @ ( sK1 @ X7 ) @ ( sK1 @ X8 ) ) )
=> ( ( c_starc @ ( sK1 @ sK4 ) @ ( sK1 @ sK5 ) )
!= ( sK1 @ ( c_starb @ sK4 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a > b,X1: b > c,X2: a > c] :
( ! [X3: a,X4: a] :
( ( c_starb @ ( X0 @ X4 ) @ ( X0 @ X3 ) )
= ( X0 @ ( c_stara @ X4 @ X3 ) ) )
& ! [X5: b] :
? [X6: a] :
( ( X0 @ X6 )
= X5 )
& ? [X7: b,X8: b] :
( ( X1 @ ( c_starb @ X7 @ X8 ) )
!= ( c_starc @ ( X1 @ X7 ) @ ( X1 @ X8 ) ) )
& ! [X9: a] :
( ( X1 @ ( X0 @ X9 ) )
= ( X2 @ X9 ) )
& ! [X10: a,X11: a] :
( ( X2 @ ( c_stara @ X10 @ X11 ) )
= ( c_starc @ ( X2 @ X10 ) @ ( X2 @ X11 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a > b,X2: b > c,X0: a > c] :
( ! [X4: a,X3: a] :
( ( X1 @ ( c_stara @ X3 @ X4 ) )
= ( c_starb @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) )
& ! [X6: b] :
? [X7: a] :
( ( X1 @ X7 )
= X6 )
& ? [X10: b,X11: b] :
( ( c_starc @ ( X2 @ X10 ) @ ( X2 @ X11 ) )
!= ( X2 @ ( c_starb @ X10 @ X11 ) ) )
& ! [X5: a] :
( ( X2 @ ( X1 @ X5 ) )
= ( X0 @ X5 ) )
& ! [X8: a,X9: a] :
( ( X0 @ ( c_stara @ X8 @ X9 ) )
= ( c_starc @ ( X0 @ X8 ) @ ( X0 @ X9 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
? [X1: a > b,X2: b > c,X0: a > c] :
( ? [X10: b,X11: b] :
( ( c_starc @ ( X2 @ X10 ) @ ( X2 @ X11 ) )
!= ( X2 @ ( c_starb @ X10 @ X11 ) ) )
& ! [X5: a] :
( ( X2 @ ( X1 @ X5 ) )
= ( X0 @ X5 ) )
& ! [X4: a,X3: a] :
( ( X1 @ ( c_stara @ X3 @ X4 ) )
= ( c_starb @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) )
& ! [X8: a,X9: a] :
( ( X0 @ ( c_stara @ X8 @ X9 ) )
= ( c_starc @ ( X0 @ X8 ) @ ( X0 @ X9 ) ) )
& ! [X6: b] :
? [X7: a] :
( ( X1 @ X7 )
= X6 ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X1: a > b,X2: b > c,X0: a > c] :
( ( ! [X5: a] :
( ( X2 @ ( X1 @ X5 ) )
= ( X0 @ X5 ) )
& ! [X4: a,X3: a] :
( ( X1 @ ( c_stara @ X3 @ X4 ) )
= ( c_starb @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) )
& ! [X8: a,X9: a] :
( ( X0 @ ( c_stara @ X8 @ X9 ) )
= ( c_starc @ ( X0 @ X8 ) @ ( X0 @ X9 ) ) )
& ! [X6: b] :
? [X7: a] :
( ( X1 @ X7 )
= X6 ) )
=> ! [X11: b,X10: b] :
( ( c_starc @ ( X2 @ X10 ) @ ( X2 @ X11 ) )
= ( X2 @ ( c_starb @ X10 @ X11 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > c,X0: a > b,X2: b > c] :
( ( ! [X3: a,X4: a] :
( ( X0 @ ( c_stara @ X3 @ X4 ) )
= ( c_starb @ ( X0 @ X3 ) @ ( X0 @ X4 ) ) )
& ! [X3: a] :
( ( X2 @ ( X0 @ X3 ) )
= ( X1 @ X3 ) )
& ! [X4: b] :
? [X3: a] :
( ( X0 @ X3 )
= X4 )
& ! [X3: a,X4: a] :
( ( X1 @ ( c_stara @ X3 @ X4 ) )
= ( c_starc @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) ) )
=> ! [X3: b,X4: b] :
( ( X2 @ ( c_starb @ X3 @ X4 ) )
= ( c_starc @ ( X2 @ X3 ) @ ( X2 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > c,X0: a > b,X2: b > c] :
( ( ! [X3: a,X4: a] :
( ( X0 @ ( c_stara @ X3 @ X4 ) )
= ( c_starb @ ( X0 @ X3 ) @ ( X0 @ X4 ) ) )
& ! [X3: a] :
( ( X2 @ ( X0 @ X3 ) )
= ( X1 @ X3 ) )
& ! [X4: b] :
? [X3: a] :
( ( X0 @ X3 )
= X4 )
& ! [X3: a,X4: a] :
( ( X1 @ ( c_stara @ X3 @ X4 ) )
= ( c_starc @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) ) )
=> ! [X3: b,X4: b] :
( ( X2 @ ( c_starb @ X3 @ X4 ) )
= ( c_starc @ ( X2 @ X3 ) @ ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.acyxL8fZlC/DTF2THF_7970.p',cTHM270_pme) ).
thf(f13,plain,
! [X9: a] :
( ( sK2 @ X9 )
= ( sK1 @ ( sK0 @ X9 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f57,plain,
! [X0: b,X1: b] :
( ( sK1 @ ( c_starb @ X0 @ X1 ) )
= ( c_starc @ ( sK2 @ ( sK3 @ X0 ) ) @ ( sK1 @ X1 ) ) ),
inference(superposition,[status(thm)],[f38,f15]) ).
thf(f38,plain,
! [X0: a,X1: b] :
( ( sK1 @ ( c_starb @ ( sK0 @ X0 ) @ X1 ) )
= ( c_starc @ ( sK2 @ X0 ) @ ( sK1 @ X1 ) ) ),
inference(superposition,[status(thm)],[f18,f24]) ).
thf(f24,plain,
! [X0: a,X1: b] :
( ( sK2 @ ( c_stara @ X0 @ ( sK3 @ X1 ) ) )
= ( sK1 @ ( c_starb @ ( sK0 @ X0 ) @ X1 ) ) ),
inference(superposition,[status(thm)],[f13,f20]) ).
thf(f20,plain,
! [X0: b,X1: a] :
( ( c_starb @ ( sK0 @ X1 ) @ X0 )
= ( sK0 @ ( c_stara @ X1 @ ( sK3 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f16,f15]) ).
thf(f16,plain,
! [X3: a,X4: a] :
( ( c_starb @ ( sK0 @ X4 ) @ ( sK0 @ X3 ) )
= ( sK0 @ ( c_stara @ X4 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f18,plain,
! [X0: b,X1: a] :
( ( sK2 @ ( c_stara @ X1 @ ( sK3 @ X0 ) ) )
= ( c_starc @ ( sK2 @ X1 ) @ ( sK1 @ X0 ) ) ),
inference(superposition,[status(thm)],[f12,f17]) ).
thf(f12,plain,
! [X10: a,X11: a] :
( ( c_starc @ ( sK2 @ X10 ) @ ( sK2 @ X11 ) )
= ( sK2 @ ( c_stara @ X10 @ X11 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f14,plain,
( ( c_starc @ ( sK1 @ sK4 ) @ ( sK1 @ sK5 ) )
!= ( sK1 @ ( c_starb @ sK4 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG298^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.30 % Computer : n017.cluster.edu
% 0.14/0.30 % Model : x86_64 x86_64
% 0.14/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.30 % Memory : 8042.1875MB
% 0.14/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.30 % CPULimit : 300
% 0.14/0.30 % WCLimit : 300
% 0.14/0.30 % DateTime : Tue Feb 24 03:42:26 EST 2026
% 0.14/0.30 % CPUTime :
% 0.14/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : ALG298^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.40 % Domain : General Algebra
% 0.17/0.40 % Problem : TPS problem THM270
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English :
% 0.17/0.40
% 0.17/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Bro09]
% 0.17/0.40 % Names : tps_0400 [Bro09]
% 0.17/0.40 % : THM270 [TPS]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v4.0.0
% 0.17/0.40 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.17/0.40 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 5 ( 5 avg)
% 0.17/0.40 % Number of connectives : 29 ( 0 ~; 0 |; 3 &; 25 @)
% 0.17/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 10 ( 10 avg)
% 0.17/0.40 % Number of types : 3 ( 3 usr)
% 0.17/0.40 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 4 ( 3 usr; 0 con; 2-2 aty)
% 0.17/0.40 % Number of variables : 12 ( 0 ^; 11 !; 1 ?; 12 :)
% 0.17/0.40 % SPC : TH0_THM_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.40 % : Polymorphic definitions expanded.
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(c_type,type,
% 0.17/0.40 c: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(b_type,type,
% 0.17/0.40 b: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(a_type,type,
% 0.17/0.40 a: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(c_starc,type,
% 0.17/0.40 c_starc: c > c > c ).
% 0.17/0.40
% 0.17/0.40 thf(c_starb,type,
% 0.17/0.40 c_starb: b > b > b ).
% 0.17/0.40
% 0.17/0.40 thf(c_stara,type,
% 0.17/0.40 c_stara: a > a > a ).
% 0.17/0.40
% 0.17/0.40 thf(cTHM270_pme,conjecture,
% 0.17/0.40 ! [Xf: a > b,Xg: a > c,Xh: b > c] :
% 0.17/0.40 ( ( ! [Xx: a] :
% 0.17/0.40 ( ( Xh @ ( Xf @ Xx ) )
% 0.17/0.40 = ( Xg @ Xx ) )
% 0.17/0.40 & ! [Xy: b] :
% 0.17/0.40 ? [Xx: a] :
% 0.17/0.40 ( ( Xf @ Xx )
% 0.17/0.40 = Xy )
% 0.17/0.40 & ! [Xx: a,Xy: a] :
% 0.17/0.40 ( ( Xf @ ( c_stara @ Xx @ Xy ) )
% 0.17/0.40 = ( c_starb @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
% 0.17/0.40 & ! [Xx: a,Xy: a] :
% 0.17/0.40 ( ( Xg @ ( c_stara @ Xx @ Xy ) )
% 0.17/0.40 = ( c_starc @ ( Xg @ Xx ) @ ( Xg @ Xy ) ) ) )
% 0.17/0.40 => ! [Xx: b,Xy: b] :
% 0.17/0.40 ( ( Xh @ ( c_starb @ Xx @ Xy ) )
% 0.17/0.40 = ( c_starc @ ( Xh @ Xx ) @ ( Xh @ Xy ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.56/1.36 ---- Embedded in THF ---
% 1.56/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.36 %%% Generated on Tue Feb 24 03:42:27 EST 2026
% 1.56/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.36 %%% Logic specification used:
% 1.56/1.36 %%% thf(spec, logic, $$dhol).
% 1.56/1.36
% 1.56/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.acyxL8fZlC/DTF2DTF7970.p
% See solution above
% 1.56/1.36 ------------------------
% 1.56/1.36 ---- Cleaned THF ---
% 1.56/1.36 thf(c_type,type,
% 1.56/1.36 c: $tType ).
% 1.56/1.36
% 1.56/1.36 thf(b_type,type,
% 1.56/1.36 b: $tType ).
% 1.56/1.36
% 1.56/1.36 thf(a_type,type,
% 1.56/1.36 a: $tType ).
% 1.56/1.36
% 1.56/1.36 thf(c_starc,type,
% 1.56/1.36 c_starc: c > c > c ).
% 1.56/1.36
% 1.56/1.36 thf(c_starb,type,
% 1.56/1.36 c_starb: b > b > b ).
% 1.56/1.36
% 1.56/1.36 thf(c_stara,type,
% 1.56/1.36 c_stara: a > a > a ).
% 1.56/1.36
% 1.56/1.36 thf(cTHM270_pme,conjecture,
% 1.56/1.36 ! [Xf: a > b,Xg: a > c,Xh: b > c] :
% 1.56/1.36 ( ( ! [Xx: a] :
% 1.56/1.36 ( ( Xh @ ( Xf @ Xx ) )
% 1.56/1.36 = ( Xg @ Xx ) )
% 1.56/1.36 & ! [Xy: b] :
% 1.56/1.36 ? [Xx: a] :
% 1.56/1.36 ( ( Xf @ Xx )
% 1.56/1.36 = Xy )
% 1.56/1.36 & ! [Xx: a,Xy: a] :
% 1.56/1.36 ( ( Xf @ ( c_stara @ Xx @ Xy ) )
% 1.56/1.36 = ( c_starb @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
% 1.56/1.36 & ! [Xx: a,Xy: a] :
% 1.56/1.36 ( ( Xg @ ( c_stara @ Xx @ Xy ) )
% 1.56/1.36 = ( c_starc @ ( Xg @ Xx ) @ ( Xg @ Xy ) ) ) )
% 1.56/1.36 => ! [Xx: b,Xy: b] :
% 1.56/1.36 ( ( Xh @ ( c_starb @ Xx @ Xy ) )
% 1.56/1.36 = ( c_starc @ ( Xh @ Xx ) @ ( Xh @ Xy ) ) ) ) ).
% 1.56/1.36 ------------------------
% 1.56/1.38 % (8068)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7970 for (3000ds/183Mi)
% 1.56/1.38 % (8069)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_7970 for (3000ds/4Mi)
% 1.56/1.38 % (8074)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7970 for (3000ds/18Mi)
% 1.56/1.38 % (8070)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_7970 for (3000ds/27Mi)
% 1.56/1.38 % (8072)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_7970 for (3000ds/2Mi)
% 1.56/1.38 % (8071)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7970 for (3000ds/2Mi)
% 1.56/1.38 % (8072)Instruction limit reached!
% 1.56/1.38 % (8072)------------------------------
% 1.56/1.38 % (8072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (8072)Termination reason: Unknown
% 1.56/1.38 % (8072)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (8072)Memory used [KB]: 5500
% 1.56/1.38 % (8072)Time elapsed: 0.003 s
% 1.56/1.38 % (8072)Instructions burned: 3 (million)
% 1.56/1.38 % (8072)------------------------------
% 1.56/1.38 % (8072)------------------------------
% 1.56/1.38 % (8068)First to succeed.
% 1.56/1.38 % (8069)Instruction limit reached!
% 1.56/1.38 % (8069)------------------------------
% 1.56/1.38 % (8069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (8069)Termination reason: Unknown
% 1.56/1.38 % (8069)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (8071)Instruction limit reached!
% 1.56/1.38 % (8071)------------------------------
% 1.56/1.38 % (8071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (8071)Termination reason: Unknown
% 1.56/1.38 % (8071)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (8071)Memory used [KB]: 5500
% 1.56/1.38 % (8071)Time elapsed: 0.003 s
% 1.56/1.38 % (8071)Instructions burned: 2 (million)
% 1.56/1.38 % (8071)------------------------------
% 1.56/1.38 % (8071)------------------------------
% 1.56/1.38 % (8069)Memory used [KB]: 5500
% 1.56/1.38 % (8069)Time elapsed: 0.004 s
% 1.56/1.38 % (8069)Instructions burned: 4 (million)
% 1.56/1.38 % (8069)------------------------------
% 1.56/1.38 % (8069)------------------------------
% 1.56/1.39 % (8073)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_7970 for (3000ds/275Mi)
% 1.56/1.39 % (8068)Refutation found. Thanks to Tanya!
% 1.56/1.39 % SZS status Theorem for DTF2THF_7970
% 1.56/1.39 % SZS output start Proof for DTF2THF_7970
% 1.56/1.39 thf(type_def_5, type, c: $tType).
% 1.56/1.39 thf(type_def_7, type, b: $tType).
% 1.56/1.39 thf(type_def_8, type, a: $tType).
% 1.56/1.39 thf(func_def_0, type, c: $tType).
% 1.56/1.39 thf(func_def_1, type, b: $tType).
% 1.56/1.39 thf(func_def_2, type, a: $tType).
% 1.56/1.39 thf(func_def_3, type, c_starc: c > c > c).
% 1.56/1.39 thf(func_def_4, type, c_starb: b > b > b).
% 1.56/1.39 thf(func_def_5, type, c_stara: a > a > a).
% 1.56/1.39 thf(func_def_9, type, sK0: a > b).
% 1.56/1.39 thf(func_def_10, type, sK1: b > c).
% 1.56/1.39 thf(func_def_11, type, sK2: a > c).
% 1.56/1.39 thf(func_def_12, type, sK3: b > a).
% 1.56/1.39 thf(func_def_13, type, sK4: b).
% 1.56/1.39 thf(func_def_14, type, sK5: b).
% 1.56/1.39 thf(f82,plain,(
% 1.56/1.39 $false),
% 1.56/1.39 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.56/1.39 thf(f81,plain,(
% 1.56/1.39 ((sK1 @ (c_starb @ sK4 @ sK5)) != (sK1 @ (c_starb @ sK4 @ sK5)))),
% 1.56/1.39 inference(superposition,[status(thm)],[f14,f74])).
% 1.56/1.39 thf(f74,plain,(
% 1.56/1.39 ( ! [X0 : b,X1 : b] : (((sK1 @ (c_starb @ X0 @ X1)) = (c_starc @ (sK1 @ X0) @ (sK1 @ X1)))) )),
% 1.56/1.39 inference(superposition,[status(thm)],[f57,f17])).
% 1.56/1.39 thf(f17,plain,(
% 1.56/1.39 ( ! [X0 : b] : (((sK2 @ (sK3 @ X0)) = (sK1 @ X0))) )),
% 1.56/1.39 inference(superposition,[status(thm)],[f13,f15])).
% 1.56/1.39 thf(f15,plain,(
% 1.56/1.39 ( ! [X5 : b] : (((sK0 @ (sK3 @ X5)) = X5)) )),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.56/1.39 thf(f11,plain,(
% 1.56/1.39 ! [X3 : a,X4 : a] : ((c_starb @ (sK0 @ X4) @ (sK0 @ X3)) = (sK0 @ (c_stara @ X4 @ X3))) & ! [X5 : b] : ((sK0 @ (sK3 @ X5)) = X5) & ((c_starc @ (sK1 @ sK4) @ (sK1 @ sK5)) != (sK1 @ (c_starb @ sK4 @ sK5))) & ! [X9 : a] : ((sK2 @ X9) = (sK1 @ (sK0 @ X9))) & ! [X10 : a,X11 : a] : ((c_starc @ (sK2 @ X10) @ (sK2 @ X11)) = (sK2 @ (c_stara @ X10 @ X11)))),
% 1.56/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f7,f10,f9,f8])).
% 1.56/1.39 thf(f8,plain,(
% 1.56/1.39 ? [X0 : a > b,X1 : b > c,X2 : a > c] : (! [X3 : a,X4 : a] : ((c_starb @ (X0 @ X4) @ (X0 @ X3)) = (X0 @ (c_stara @ X4 @ X3))) & ! [X5 : b] : ? [X6 : a] : ((X0 @ X6) = X5) & ? [X7 : b,X8 : b] : ((X1 @ (c_starb @ X7 @ X8)) != (c_starc @ (X1 @ X7) @ (X1 @ X8))) & ! [X9 : a] : ((X1 @ (X0 @ X9)) = (X2 @ X9)) & ! [X10 : a,X11 : a] : ((X2 @ (c_stara @ X10 @ X11)) = (c_starc @ (X2 @ X10) @ (X2 @ X11)))) => (! [X4 : a,X3 : a] : ((c_starb @ (sK0 @ X4) @ (sK0 @ X3)) = (sK0 @ (c_stara @ X4 @ X3))) & ! [X5 : b] : ? [X6 : a] : ((sK0 @ X6) = X5) & ? [X8 : b,X7 : b] : ((sK1 @ (c_starb @ X7 @ X8)) != (c_starc @ (sK1 @ X7) @ (sK1 @ X8))) & ! [X9 : a] : ((sK2 @ X9) = (sK1 @ (sK0 @ X9))) & ! [X11 : a,X10 : a] : ((c_starc @ (sK2 @ X10) @ (sK2 @ X11)) = (sK2 @ (c_stara @ X10 @ X11))))),
% 1.56/1.39 introduced(definition,[],[choice_axiom])).
% 1.56/1.39 thf(f9,plain,(
% 1.56/1.39 ! [X5 : b] : (? [X6 : a] : ((sK0 @ X6) = X5) => ((sK0 @ (sK3 @ X5)) = X5))),
% 1.56/1.39 introduced(definition,[],[choice_axiom])).
% 1.56/1.39 thf(f10,plain,(
% 1.56/1.39 ? [X8 : b,X7 : b] : ((sK1 @ (c_starb @ X7 @ X8)) != (c_starc @ (sK1 @ X7) @ (sK1 @ X8))) => ((c_starc @ (sK1 @ sK4) @ (sK1 @ sK5)) != (sK1 @ (c_starb @ sK4 @ sK5)))),
% 1.56/1.39 introduced(definition,[],[choice_axiom])).
% 1.56/1.39 thf(f7,plain,(
% 1.56/1.39 ? [X0 : a > b,X1 : b > c,X2 : a > c] : (! [X3 : a,X4 : a] : ((c_starb @ (X0 @ X4) @ (X0 @ X3)) = (X0 @ (c_stara @ X4 @ X3))) & ! [X5 : b] : ? [X6 : a] : ((X0 @ X6) = X5) & ? [X7 : b,X8 : b] : ((X1 @ (c_starb @ X7 @ X8)) != (c_starc @ (X1 @ X7) @ (X1 @ X8))) & ! [X9 : a] : ((X1 @ (X0 @ X9)) = (X2 @ X9)) & ! [X10 : a,X11 : a] : ((X2 @ (c_stara @ X10 @ X11)) = (c_starc @ (X2 @ X10) @ (X2 @ X11))))),
% 1.56/1.39 inference(rectify,[status(thm)],[f6])).
% 1.56/1.39 thf(f6,plain,(
% 1.56/1.39 ? [X1 : a > b,X2 : b > c,X0 : a > c] : (! [X4 : a,X3 : a] : ((X1 @ (c_stara @ X3 @ X4)) = (c_starb @ (X1 @ X3) @ (X1 @ X4))) & ! [X6 : b] : ? [X7 : a] : ((X1 @ X7) = X6) & ? [X10 : b,X11 : b] : ((c_starc @ (X2 @ X10) @ (X2 @ X11)) != (X2 @ (c_starb @ X10 @ X11))) & ! [X5 : a] : ((X2 @ (X1 @ X5)) = (X0 @ X5)) & ! [X8 : a,X9 : a] : ((X0 @ (c_stara @ X8 @ X9)) = (c_starc @ (X0 @ X8) @ (X0 @ X9))))),
% 1.56/1.39 inference(flattening,[status(thm)],[f5])).
% 1.56/1.39 thf(f5,plain,(
% 1.56/1.39 ? [X1 : a > b,X2 : b > c,X0 : a > c] : (? [X10 : b,X11 : b] : ((c_starc @ (X2 @ X10) @ (X2 @ X11)) != (X2 @ (c_starb @ X10 @ X11))) & (! [X5 : a] : ((X2 @ (X1 @ X5)) = (X0 @ X5)) & ! [X4 : a,X3 : a] : ((X1 @ (c_stara @ X3 @ X4)) = (c_starb @ (X1 @ X3) @ (X1 @ X4))) & ! [X8 : a,X9 : a] : ((X0 @ (c_stara @ X8 @ X9)) = (c_starc @ (X0 @ X8) @ (X0 @ X9))) & ! [X6 : b] : ? [X7 : a] : ((X1 @ X7) = X6)))),
% 1.56/1.39 inference(ennf_transformation,[status(thm)],[f4])).
% 1.56/1.39 thf(f4,plain,(
% 1.56/1.39 ~! [X1 : a > b,X2 : b > c,X0 : a > c] : ((! [X5 : a] : ((X2 @ (X1 @ X5)) = (X0 @ X5)) & ! [X4 : a,X3 : a] : ((X1 @ (c_stara @ X3 @ X4)) = (c_starb @ (X1 @ X3) @ (X1 @ X4))) & ! [X8 : a,X9 : a] : ((X0 @ (c_stara @ X8 @ X9)) = (c_starc @ (X0 @ X8) @ (X0 @ X9))) & ! [X6 : b] : ? [X7 : a] : ((X1 @ X7) = X6)) => ! [X11 : b,X10 : b] : ((c_starc @ (X2 @ X10) @ (X2 @ X11)) = (X2 @ (c_starb @ X10 @ X11))))),
% 1.56/1.39 inference(rectify,[status(thm)],[f2])).
% 1.56/1.39 thf(f2,negated_conjecture,(
% 1.56/1.39 ~! [X1 : a > c,X0 : a > b,X2 : b > c] : ((! [X3 : a,X4 : a] : ((X0 @ (c_stara @ X3 @ X4)) = (c_starb @ (X0 @ X3) @ (X0 @ X4))) & ! [X3 : a] : ((X2 @ (X0 @ X3)) = (X1 @ X3)) & ! [X4 : b] : ? [X3 : a] : ((X0 @ X3) = X4) & ! [X3 : a,X4 : a] : ((X1 @ (c_stara @ X3 @ X4)) = (c_starc @ (X1 @ X3) @ (X1 @ X4)))) => ! [X3 : b,X4 : b] : ((X2 @ (c_starb @ X3 @ X4)) = (c_starc @ (X2 @ X3) @ (X2 @ X4))))),
% 1.56/1.39 inference(negated_conjecture,[status(cth)],[f1])).
% 1.56/1.39 thf(f1,conjecture,(
% 1.56/1.39 ! [X1 : a > c,X0 : a > b,X2 : b > c] : ((! [X3 : a,X4 : a] : ((X0 @ (c_stara @ X3 @ X4)) = (c_starb @ (X0 @ X3) @ (X0 @ X4))) & ! [X3 : a] : ((X2 @ (X0 @ X3)) = (X1 @ X3)) & ! [X4 : b] : ? [X3 : a] : ((X0 @ X3) = X4) & ! [X3 : a,X4 : a] : ((X1 @ (c_stara @ X3 @ X4)) = (c_starc @ (X1 @ X3) @ (X1 @ X4)))) => ! [X3 : b,X4 : b] : ((X2 @ (c_starb @ X3 @ X4)) = (c_starc @ (X2 @ X3) @ (X2 @ X4))))),
% 1.56/1.39 file('/export/starexec/sandbox/tmp/tmp.acyxL8fZlC/DTF2THF_7970.p',cTHM270_pme)).
% 1.56/1.39 thf(f13,plain,(
% 1.56/1.39 ( ! [X9 : a] : (((sK2 @ X9) = (sK1 @ (sK0 @ X9)))) )),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.56/1.39 thf(f57,plain,(
% 1.56/1.39 ( ! [X0 : b,X1 : b] : (((sK1 @ (c_starb @ X0 @ X1)) = (c_starc @ (sK2 @ (sK3 @ X0)) @ (sK1 @ X1)))) )),
% 1.56/1.39 inference(superposition,[status(thm)],[f38,f15])).
% 1.56/1.39 thf(f38,plain,(
% 1.56/1.39 ( ! [X0 : a,X1 : b] : (((sK1 @ (c_starb @ (sK0 @ X0) @ X1)) = (c_starc @ (sK2 @ X0) @ (sK1 @ X1)))) )),
% 1.56/1.39 inference(superposition,[status(thm)],[f18,f24])).
% 1.56/1.39 thf(f24,plain,(
% 1.56/1.39 ( ! [X0 : a,X1 : b] : (((sK2 @ (c_stara @ X0 @ (sK3 @ X1))) = (sK1 @ (c_starb @ (sK0 @ X0) @ X1)))) )),
% 1.56/1.39 inference(superposition,[status(thm)],[f13,f20])).
% 1.56/1.39 thf(f20,plain,(
% 1.56/1.39 ( ! [X0 : b,X1 : a] : (((c_starb @ (sK0 @ X1) @ X0) = (sK0 @ (c_stara @ X1 @ (sK3 @ X0))))) )),
% 1.56/1.39 inference(superposition,[status(thm)],[f16,f15])).
% 1.56/1.39 thf(f16,plain,(
% 1.56/1.39 ( ! [X3 : a,X4 : a] : (((c_starb @ (sK0 @ X4) @ (sK0 @ X3)) = (sK0 @ (c_stara @ X4 @ X3)))) )),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.56/1.39 thf(f18,plain,(
% 1.56/1.39 ( ! [X0 : b,X1 : a] : (((sK2 @ (c_stara @ X1 @ (sK3 @ X0))) = (c_starc @ (sK2 @ X1) @ (sK1 @ X0)))) )),
% 1.56/1.39 inference(superposition,[status(thm)],[f12,f17])).
% 1.56/1.39 thf(f12,plain,(
% 1.56/1.39 ( ! [X10 : a,X11 : a] : (((c_starc @ (sK2 @ X10) @ (sK2 @ X11)) = (sK2 @ (c_stara @ X10 @ X11)))) )),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.56/1.39 thf(f14,plain,(
% 1.56/1.39 ((c_starc @ (sK1 @ sK4) @ (sK1 @ sK5)) != (sK1 @ (c_starb @ sK4 @ sK5)))),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.56/1.39 % SZS output end Proof for DTF2THF_7970
% 1.56/1.39 % (8068)------------------------------
% 1.56/1.39 % (8068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (8068)Termination reason: Refutation
% 1.56/1.39
% 1.56/1.39 % (8068)Memory used [KB]: 5628
% 1.56/1.39 % (8068)Time elapsed: 0.010 s
% 1.56/1.39 % (8068)Instructions burned: 22 (million)
% 1.56/1.39 % (8068)------------------------------
% 1.56/1.39 % (8068)------------------------------
% 1.56/1.39 % (8067)Success in time 0.017 s
%------------------------------------------------------------------------------