%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG270^5 : 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 : 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 08:37:47 AM UTC 2026
% Result : Theorem 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 218 ( 11 ~; 0 |; 3 &; 200 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 33 !; 12 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
c_star: a > a > a ).
thf(func_def_5,type,
sK0: a ).
thf(func_def_6,type,
sK1: a ).
thf(func_def_7,type,
sK2: a ).
thf(func_def_8,type,
sK3: a ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( c_star @ sK2 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK3 ) ) )
!= ( c_star @ sK2 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK3 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f15,f10]) ).
thf(f10,plain,
! [X2: a,X0: a,X1: a] :
( ( c_star @ X2 @ ( c_star @ X0 @ X1 ) )
= ( c_star @ ( c_star @ X2 @ X0 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: a,X1: a,X2: a] :
( ( c_star @ X2 @ ( c_star @ X0 @ X1 ) )
= ( c_star @ ( c_star @ X2 @ X0 ) @ X1 ) )
& ( ( c_star @ sK2 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK3 ) ) )
!= ( c_star @ ( c_star @ ( c_star @ sK2 @ sK0 ) @ sK1 ) @ sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f7]) ).
thf(f7,plain,
( ? [X3: a,X4: a,X5: a,X6: a] :
( ( c_star @ ( c_star @ ( c_star @ X5 @ X3 ) @ X4 ) @ X6 )
!= ( c_star @ X5 @ ( c_star @ X3 @ ( c_star @ X4 @ X6 ) ) ) )
=> ( ( c_star @ sK2 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK3 ) ) )
!= ( c_star @ ( c_star @ ( c_star @ sK2 @ sK0 ) @ sK1 ) @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: a,X1: a,X2: a] :
( ( c_star @ X2 @ ( c_star @ X0 @ X1 ) )
= ( c_star @ ( c_star @ X2 @ X0 ) @ X1 ) )
& ? [X3: a,X4: a,X5: a,X6: a] :
( ( c_star @ ( c_star @ ( c_star @ X5 @ X3 ) @ X4 ) @ X6 )
!= ( c_star @ X5 @ ( c_star @ X3 @ ( c_star @ X4 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
( ! [X0: a,X1: a,X2: a] :
( ( c_star @ X2 @ ( c_star @ X0 @ X1 ) )
= ( c_star @ ( c_star @ X2 @ X0 ) @ X1 ) )
& ? [X6: a,X5: a,X3: a,X4: a] :
( ( c_star @ ( c_star @ ( c_star @ X3 @ X6 ) @ X5 ) @ X4 )
!= ( c_star @ X3 @ ( c_star @ X6 @ ( c_star @ X5 @ X4 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a,X1: a,X2: a] :
( ( c_star @ X2 @ ( c_star @ X0 @ X1 ) )
= ( c_star @ ( c_star @ X2 @ X0 ) @ X1 ) )
=> ! [X3: a,X5: a,X6: a,X4: a] :
( ( c_star @ ( c_star @ ( c_star @ X3 @ X6 ) @ X5 ) @ X4 )
= ( c_star @ X3 @ ( c_star @ X6 @ ( c_star @ X5 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a,X2: a,X0: a] :
( ( c_star @ ( c_star @ X0 @ X1 ) @ X2 )
= ( c_star @ X0 @ ( c_star @ X1 @ X2 ) ) )
=> ! [X3: a,X6: a,X5: a,X4: a] :
( ( c_star @ ( c_star @ ( c_star @ X3 @ X4 ) @ X5 ) @ X6 )
= ( c_star @ X3 @ ( c_star @ X4 @ ( c_star @ X5 @ X6 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: a,X2: a,X0: a] :
( ( c_star @ ( c_star @ X0 @ X1 ) @ X2 )
= ( c_star @ X0 @ ( c_star @ X1 @ X2 ) ) )
=> ! [X3: a,X6: a,X5: a,X4: a] :
( ( c_star @ ( c_star @ ( c_star @ X3 @ X4 ) @ X5 ) @ X6 )
= ( c_star @ X3 @ ( c_star @ X4 @ ( c_star @ X5 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RB1c0cQZZZ/DTF2THF_23786.p',cTHM23_pme) ).
thf(f15,plain,
( ( c_star @ sK2 @ ( c_star @ ( c_star @ sK0 @ sK1 ) @ sK3 ) )
!= ( c_star @ sK2 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK3 ) ) ) ),
inference(superposition,[status(thm)],[f11,f10]) ).
thf(f11,plain,
( ( c_star @ sK2 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK3 ) ) )
!= ( c_star @ ( c_star @ sK2 @ ( c_star @ sK0 @ sK1 ) ) @ sK3 ) ),
inference(forward_demodulation,[status(thm)],[f9,f10]) ).
thf(f9,plain,
( ( c_star @ sK2 @ ( c_star @ sK0 @ ( c_star @ sK1 @ sK3 ) ) )
!= ( c_star @ ( c_star @ ( c_star @ sK2 @ sK0 ) @ sK1 ) @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG270^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n028.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 03:43:12 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : ALG270^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : General Algebra
% 0.19/0.45 % Problem : TPS problem THM23
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0266 [Bro09]
% 0.19/0.45 % : THM23 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.19/0.45 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.45 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 20 @)
% 0.19/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 6 ( 6 avg)
% 0.19/0.45 % Number of types : 1 ( 1 usr)
% 0.19/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.19/0.45 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 % : Polymorphic definitions expanded.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(c_star,type,
% 0.19/0.45 c_star: a > a > a ).
% 0.19/0.45
% 0.19/0.45 thf(cTHM23_pme,conjecture,
% 0.19/0.45 ( ! [Xx: a,Xy: a,Xz: a] :
% 0.19/0.45 ( ( c_star @ ( c_star @ Xx @ Xy ) @ Xz )
% 0.19/0.45 = ( c_star @ Xx @ ( c_star @ Xy @ Xz ) ) )
% 0.19/0.45 => ! [W: a,X: a,Y: a,Z: a] :
% 0.19/0.45 ( ( c_star @ ( c_star @ ( c_star @ W @ X ) @ Y ) @ Z )
% 0.19/0.45 = ( c_star @ W @ ( c_star @ X @ ( c_star @ Y @ Z ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 03:43:12 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RB1c0cQZZZ/DTF2DTF23786.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(a_type,type,
% 1.49/1.26 a: $tType ).
% 1.49/1.26
% 1.49/1.26 thf(c_star,type,
% 1.49/1.26 c_star: a > a > a ).
% 1.49/1.26
% 1.49/1.26 thf(cTHM23_pme,conjecture,
% 1.49/1.26 ( ! [Xx: a,Xy: a,Xz: a] :
% 1.49/1.26 ( ( c_star @ ( c_star @ Xx @ Xy ) @ Xz )
% 1.49/1.26 = ( c_star @ Xx @ ( c_star @ Xy @ Xz ) ) )
% 1.49/1.26 => ! [W: a,X: a,Y: a,Z: a] :
% 1.49/1.26 ( ( c_star @ ( c_star @ ( c_star @ W @ X ) @ Y ) @ Z )
% 1.49/1.26 = ( c_star @ W @ ( c_star @ X @ ( c_star @ Y @ Z ) ) ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.27 % (24119)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_23786 for (2999ds/275Mi)
% 1.49/1.28 % (24120)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23786 for (2999ds/18Mi)
% 1.49/1.28 % (24119)First to succeed.
% 1.49/1.28 % (24120)Also succeeded, but the first one will report.
% 1.49/1.28 % (24119)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Theorem for DTF2THF_23786
% 1.49/1.28 % SZS output start Proof for DTF2THF_23786
% 1.49/1.28 thf(type_def_5, type, a: $tType).
% 1.49/1.28 thf(func_def_0, type, a: $tType).
% 1.49/1.28 thf(func_def_1, type, c_star: a > a > a).
% 1.49/1.28 thf(func_def_5, type, sK0: a).
% 1.49/1.28 thf(func_def_6, type, sK1: a).
% 1.49/1.28 thf(func_def_7, type, sK2: a).
% 1.49/1.28 thf(func_def_8, type, sK3: a).
% 1.49/1.28 thf(f17,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.49/1.28 thf(f16,plain,(
% 1.49/1.28 ((c_star @ sK2 @ (c_star @ sK0 @ (c_star @ sK1 @ sK3))) != (c_star @ sK2 @ (c_star @ sK0 @ (c_star @ sK1 @ sK3))))),
% 1.49/1.28 inference(forward_demodulation,[status(thm)],[f15,f10])).
% 1.49/1.28 thf(f10,plain,(
% 1.49/1.28 ( ! [X2 : a,X0 : a,X1 : a] : (((c_star @ X2 @ (c_star @ X0 @ X1)) = (c_star @ (c_star @ X2 @ X0) @ X1))) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f8])).
% 1.49/1.28 thf(f8,plain,(
% 1.49/1.28 ! [X0 : a,X1 : a,X2 : a] : ((c_star @ X2 @ (c_star @ X0 @ X1)) = (c_star @ (c_star @ X2 @ X0) @ X1)) & ((c_star @ sK2 @ (c_star @ sK0 @ (c_star @ sK1 @ sK3))) != (c_star @ (c_star @ (c_star @ sK2 @ sK0) @ sK1) @ sK3))),
% 1.49/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f7])).
% 1.49/1.28 thf(f7,plain,(
% 1.49/1.28 ? [X3 : a,X4 : a,X5 : a,X6 : a] : ((c_star @ (c_star @ (c_star @ X5 @ X3) @ X4) @ X6) != (c_star @ X5 @ (c_star @ X3 @ (c_star @ X4 @ X6)))) => ((c_star @ sK2 @ (c_star @ sK0 @ (c_star @ sK1 @ sK3))) != (c_star @ (c_star @ (c_star @ sK2 @ sK0) @ sK1) @ sK3))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f6,plain,(
% 1.49/1.28 ! [X0 : a,X1 : a,X2 : a] : ((c_star @ X2 @ (c_star @ X0 @ X1)) = (c_star @ (c_star @ X2 @ X0) @ X1)) & ? [X3 : a,X4 : a,X5 : a,X6 : a] : ((c_star @ (c_star @ (c_star @ X5 @ X3) @ X4) @ X6) != (c_star @ X5 @ (c_star @ X3 @ (c_star @ X4 @ X6))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f5])).
% 1.49/1.28 thf(f5,plain,(
% 1.49/1.28 ! [X0 : a,X1 : a,X2 : a] : ((c_star @ X2 @ (c_star @ X0 @ X1)) = (c_star @ (c_star @ X2 @ X0) @ X1)) & ? [X6 : a,X5 : a,X3 : a,X4 : a] : ((c_star @ (c_star @ (c_star @ X3 @ X6) @ X5) @ X4) != (c_star @ X3 @ (c_star @ X6 @ (c_star @ X5 @ X4))))),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f4])).
% 1.49/1.28 thf(f4,plain,(
% 1.49/1.28 ~(! [X0 : a,X1 : a,X2 : a] : ((c_star @ X2 @ (c_star @ X0 @ X1)) = (c_star @ (c_star @ X2 @ X0) @ X1)) => ! [X3 : a,X5 : a,X6 : a,X4 : a] : ((c_star @ (c_star @ (c_star @ X3 @ X6) @ X5) @ X4) = (c_star @ X3 @ (c_star @ X6 @ (c_star @ X5 @ X4)))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f2])).
% 1.49/1.28 thf(f2,negated_conjecture,(
% 1.49/1.28 ~(! [X1 : a,X2 : a,X0 : a] : ((c_star @ (c_star @ X0 @ X1) @ X2) = (c_star @ X0 @ (c_star @ X1 @ X2))) => ! [X3 : a,X6 : a,X5 : a,X4 : a] : ((c_star @ (c_star @ (c_star @ X3 @ X4) @ X5) @ X6) = (c_star @ X3 @ (c_star @ X4 @ (c_star @ X5 @ X6)))))),
% 1.49/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.28 thf(f1,conjecture,(
% 1.49/1.28 ! [X1 : a,X2 : a,X0 : a] : ((c_star @ (c_star @ X0 @ X1) @ X2) = (c_star @ X0 @ (c_star @ X1 @ X2))) => ! [X3 : a,X6 : a,X5 : a,X4 : a] : ((c_star @ (c_star @ (c_star @ X3 @ X4) @ X5) @ X6) = (c_star @ X3 @ (c_star @ X4 @ (c_star @ X5 @ X6))))),
% 1.49/1.28 file('/export/starexec/sandbox/tmp/tmp.RB1c0cQZZZ/DTF2THF_23786.p',cTHM23_pme)).
% 1.49/1.28 thf(f15,plain,(
% 1.49/1.28 ((c_star @ sK2 @ (c_star @ (c_star @ sK0 @ sK1) @ sK3)) != (c_star @ sK2 @ (c_star @ sK0 @ (c_star @ sK1 @ sK3))))),
% 1.49/1.28 inference(superposition,[status(thm)],[f11,f10])).
% 1.49/1.28 thf(f11,plain,(
% 1.49/1.28 ((c_star @ sK2 @ (c_star @ sK0 @ (c_star @ sK1 @ sK3))) != (c_star @ (c_star @ sK2 @ (c_star @ sK0 @ sK1)) @ sK3))),
% 1.49/1.28 inference(forward_demodulation,[status(thm)],[f9,f10])).
% 1.49/1.28 thf(f9,plain,(
% 1.49/1.28 ((c_star @ sK2 @ (c_star @ sK0 @ (c_star @ sK1 @ sK3))) != (c_star @ (c_star @ (c_star @ sK2 @ sK0) @ sK1) @ sK3))),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f8])).
% 1.49/1.28 % SZS output end Proof for DTF2THF_23786
% 1.49/1.28 % (24119)------------------------------
% 1.49/1.28 % (24119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (24119)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (24119)Memory used [KB]: 5500
% 1.49/1.28 % (24119)Time elapsed: 0.003 s
% 1.49/1.28 % (24119)Instructions burned: 1 (million)
% 1.49/1.28 % (24119)------------------------------
% 1.49/1.28 % (24119)------------------------------
% 1.49/1.28 % (24113)Success in time 0.013 s
%------------------------------------------------------------------------------