%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG001^5 : 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 : n005.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 08:37:24 AM UTC 2026
% Result : Theorem 1.46s 1.29s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 310 ( 13 ~; 0 |; 15 &; 277 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 0 ^; 61 !; 32 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_6,type,
sK0: b > a ).
thf(func_def_7,type,
sK1: a > a > a ).
thf(func_def_8,type,
sK2: g > b ).
thf(func_def_9,type,
sK3: g > g > g ).
thf(func_def_10,type,
sK4: b > b > b ).
thf(func_def_11,type,
sK5: g ).
thf(func_def_12,type,
sK6: g ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK0 @ ( sK2 @ ( sK3 @ sK5 @ sK6 ) ) )
!= ( sK0 @ ( sK2 @ ( sK3 @ sK5 @ sK6 ) ) ) ),
inference(superposition,[status(thm)],[f14,f11]) ).
thf(f11,plain,
! [X10: g,X9: g] :
( ( sK2 @ ( sK3 @ X9 @ X10 ) )
= ( sK4 @ ( sK2 @ X9 ) @ ( sK2 @ X10 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( sK0 @ ( sK2 @ ( sK3 @ sK5 @ sK6 ) ) )
!= ( sK1 @ ( sK0 @ ( sK2 @ sK5 ) ) @ ( sK0 @ ( sK2 @ sK6 ) ) ) )
& ! [X7: b,X8: b] :
( ( sK1 @ ( sK0 @ X8 ) @ ( sK0 @ X7 ) )
= ( sK0 @ ( sK4 @ X8 @ X7 ) ) )
& ! [X9: g,X10: g] :
( ( sK2 @ ( sK3 @ X9 @ X10 ) )
= ( sK4 @ ( sK2 @ X9 ) @ ( sK2 @ X10 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: b > a,X1: a > a > a,X2: g > b,X3: g > g > g,X4: b > b > b] :
( ? [X5: g,X6: g] :
( ( X0 @ ( X2 @ ( X3 @ X5 @ X6 ) ) )
!= ( X1 @ ( X0 @ ( X2 @ X5 ) ) @ ( X0 @ ( X2 @ X6 ) ) ) )
& ! [X7: b,X8: b] :
( ( X1 @ ( X0 @ X8 ) @ ( X0 @ X7 ) )
= ( X0 @ ( X4 @ X8 @ X7 ) ) )
& ! [X9: g,X10: g] :
( ( X2 @ ( X3 @ X9 @ X10 ) )
= ( X4 @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) )
=> ( ? [X6: g,X5: g] :
( ( sK0 @ ( sK2 @ ( sK3 @ X5 @ X6 ) ) )
!= ( sK1 @ ( sK0 @ ( sK2 @ X5 ) ) @ ( sK0 @ ( sK2 @ X6 ) ) ) )
& ! [X8: b,X7: b] :
( ( sK1 @ ( sK0 @ X8 ) @ ( sK0 @ X7 ) )
= ( sK0 @ ( sK4 @ X8 @ X7 ) ) )
& ! [X10: g,X9: g] :
( ( sK2 @ ( sK3 @ X9 @ X10 ) )
= ( sK4 @ ( sK2 @ X9 ) @ ( sK2 @ X10 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X6: g,X5: g] :
( ( sK0 @ ( sK2 @ ( sK3 @ X5 @ X6 ) ) )
!= ( sK1 @ ( sK0 @ ( sK2 @ X5 ) ) @ ( sK0 @ ( sK2 @ X6 ) ) ) )
=> ( ( sK0 @ ( sK2 @ ( sK3 @ sK5 @ sK6 ) ) )
!= ( sK1 @ ( sK0 @ ( sK2 @ sK5 ) ) @ ( sK0 @ ( sK2 @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: b > a,X1: a > a > a,X2: g > b,X3: g > g > g,X4: b > b > b] :
( ? [X5: g,X6: g] :
( ( X0 @ ( X2 @ ( X3 @ X5 @ X6 ) ) )
!= ( X1 @ ( X0 @ ( X2 @ X5 ) ) @ ( X0 @ ( X2 @ X6 ) ) ) )
& ! [X7: b,X8: b] :
( ( X1 @ ( X0 @ X8 ) @ ( X0 @ X7 ) )
= ( X0 @ ( X4 @ X8 @ X7 ) ) )
& ! [X9: g,X10: g] :
( ( X2 @ ( X3 @ X9 @ X10 ) )
= ( X4 @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X3: b > a,X4: a > a > a,X2: g > b,X0: g > g > g,X1: b > b > b] :
( ? [X10: g,X9: g] :
( ( X3 @ ( X2 @ ( X0 @ X10 @ X9 ) ) )
!= ( X4 @ ( X3 @ ( X2 @ X10 ) ) @ ( X3 @ ( X2 @ X9 ) ) ) )
& ! [X8: b,X7: b] :
( ( X4 @ ( X3 @ X7 ) @ ( X3 @ X8 ) )
= ( X3 @ ( X1 @ X7 @ X8 ) ) )
& ! [X5: g,X6: g] :
( ( X2 @ ( X0 @ X5 @ X6 ) )
= ( X1 @ ( X2 @ X5 ) @ ( X2 @ X6 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
? [X3: b > a,X4: a > a > a,X2: g > b,X0: g > g > g,X1: b > b > b] :
( ? [X10: g,X9: g] :
( ( X3 @ ( X2 @ ( X0 @ X10 @ X9 ) ) )
!= ( X4 @ ( X3 @ ( X2 @ X10 ) ) @ ( X3 @ ( X2 @ X9 ) ) ) )
& ! [X8: b,X7: b] :
( ( X4 @ ( X3 @ X7 ) @ ( X3 @ X8 ) )
= ( X3 @ ( X1 @ X7 @ X8 ) ) )
& ! [X5: g,X6: g] :
( ( X2 @ ( X0 @ X5 @ X6 ) )
= ( X1 @ ( X2 @ X5 ) @ ( X2 @ X6 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X3: b > a,X4: a > a > a,X2: g > b,X0: g > g > g,X1: b > b > b] :
( ( ! [X8: b,X7: b] :
( ( X4 @ ( X3 @ X7 ) @ ( X3 @ X8 ) )
= ( X3 @ ( X1 @ X7 @ X8 ) ) )
& ! [X5: g,X6: g] :
( ( X2 @ ( X0 @ X5 @ X6 ) )
= ( X1 @ ( X2 @ X5 ) @ ( X2 @ X6 ) ) ) )
=> ! [X10: g,X9: g] :
( ( X3 @ ( X2 @ ( X0 @ X10 @ X9 ) ) )
= ( X4 @ ( X3 @ ( X2 @ X10 ) ) @ ( X3 @ ( X2 @ X9 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: g > g > g,X3: b > b > b,X0: g > b,X1: b > a,X4: a > a > a] :
( ( ! [X5: g,X6: g] :
( ( X0 @ ( X2 @ X5 @ X6 ) )
= ( X3 @ ( X0 @ X5 ) @ ( X0 @ X6 ) ) )
& ! [X5: b,X6: b] :
( ( X1 @ ( X3 @ X5 @ X6 ) )
= ( X4 @ ( X1 @ X5 ) @ ( X1 @ X6 ) ) ) )
=> ! [X6: g,X5: g] :
( ( X1 @ ( X0 @ ( X2 @ X5 @ X6 ) ) )
= ( X4 @ ( X1 @ ( X0 @ X5 ) ) @ ( X1 @ ( X0 @ X6 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: g > g > g,X3: b > b > b,X0: g > b,X1: b > a,X4: a > a > a] :
( ( ! [X5: g,X6: g] :
( ( X0 @ ( X2 @ X5 @ X6 ) )
= ( X3 @ ( X0 @ X5 ) @ ( X0 @ X6 ) ) )
& ! [X5: b,X6: b] :
( ( X1 @ ( X3 @ X5 @ X6 ) )
= ( X4 @ ( X1 @ X5 ) @ ( X1 @ X6 ) ) ) )
=> ! [X6: g,X5: g] :
( ( X1 @ ( X0 @ ( X2 @ X5 @ X6 ) ) )
= ( X4 @ ( X1 @ ( X0 @ X5 ) ) @ ( X1 @ ( X0 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zRiXtsyW3L/DTF2THF_18311.p',cTHM133_pme) ).
thf(f14,plain,
( ( sK0 @ ( sK2 @ ( sK3 @ sK5 @ sK6 ) ) )
!= ( sK0 @ ( sK4 @ ( sK2 @ sK5 ) @ ( sK2 @ sK6 ) ) ) ),
inference(superposition,[status(thm)],[f13,f12]) ).
thf(f12,plain,
! [X8: b,X7: b] :
( ( sK1 @ ( sK0 @ X8 ) @ ( sK0 @ X7 ) )
= ( sK0 @ ( sK4 @ X8 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f13,plain,
( ( sK0 @ ( sK2 @ ( sK3 @ sK5 @ sK6 ) ) )
!= ( sK1 @ ( sK0 @ ( sK2 @ sK5 ) ) @ ( sK0 @ ( sK2 @ sK6 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG001^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 03:30:14 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : ALG001^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : General Algebra
% 0.18/0.45 % Problem : TPS problem THM133
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : The composition of homomorphisms of binary operators is a
% 0.18/0.45 % homomorphisms. Boyer et al JAR 2 page 284.
% 0.18/0.45
% 0.18/0.45 % Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.18/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0365 [Bro09]
% 0.18/0.45 % : THM133 [TPS]
% 0.18/0.45 % : Problem 221-223 [BL+86]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 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, 0.00 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.18/0.45 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.18/0.45 % Number of connectives : 26 ( 0 ~; 0 |; 1 &; 24 @)
% 0.18/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 10 ( 10 avg)
% 0.18/0.45 % Number of types : 3 ( 3 usr)
% 0.18/0.45 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.45 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 % : Polymorphic definitions expanded.
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(g_type,type,
% 0.18/0.45 g: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(b_type,type,
% 0.18/0.45 b: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(a_type,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(cTHM133_pme,conjecture,
% 0.18/0.45 ! [Xh1: g > b,Xh2: b > a,Xf1: g > g > g,Xf2: b > b > b,Xf3: a > a > a] :
% 0.18/0.45 ( ( ! [Xx: g,Xy: g] :
% 0.18/0.45 ( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
% 0.18/0.45 = ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) )
% 0.18/0.45 & ! [Xx: b,Xy: b] :
% 0.18/0.45 ( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
% 0.18/0.45 = ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) )
% 0.18/0.45 => ! [Xx: g,Xy: g] :
% 0.18/0.45 ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.18/0.45 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 03:30:15 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zRiXtsyW3L/DTF2DTF18311.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(g_type,type,
% 1.46/1.27 g: $tType ).
% 1.46/1.27
% 1.46/1.27 thf(b_type,type,
% 1.46/1.27 b: $tType ).
% 1.46/1.27
% 1.46/1.27 thf(a_type,type,
% 1.46/1.27 a: $tType ).
% 1.46/1.27
% 1.46/1.27 thf(cTHM133_pme,conjecture,
% 1.46/1.27 ! [Xh1: g > b,Xh2: b > a,Xf1: g > g > g,Xf2: b > b > b,Xf3: a > a > a] :
% 1.46/1.27 ( ( ! [Xx: g,Xy: g] :
% 1.46/1.27 ( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
% 1.46/1.27 = ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) )
% 1.46/1.27 & ! [Xx: b,Xy: b] :
% 1.46/1.27 ( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
% 1.46/1.27 = ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) )
% 1.46/1.27 => ! [Xx: g,Xy: g] :
% 1.46/1.27 ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.46/1.27 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.28 % (18641)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_18311 for (2999ds/4Mi)
% 1.46/1.29 % (18640)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18311 for (2999ds/183Mi)
% 1.46/1.29 % (18641)First to succeed.
% 1.46/1.29 % (18640)Also succeeded, but the first one will report.
% 1.46/1.29 % (18641)Refutation found. Thanks to Tanya!
% 1.46/1.29 % SZS status Theorem for DTF2THF_18311
% 1.46/1.29 % SZS output start Proof for DTF2THF_18311
% 1.46/1.29 thf(type_def_5, type, g: $tType).
% 1.46/1.29 thf(type_def_6, type, b: $tType).
% 1.46/1.29 thf(type_def_8, type, a: $tType).
% 1.46/1.29 thf(func_def_0, type, g: $tType).
% 1.46/1.29 thf(func_def_1, type, b: $tType).
% 1.46/1.29 thf(func_def_2, type, a: $tType).
% 1.46/1.29 thf(func_def_6, type, sK0: b > a).
% 1.46/1.29 thf(func_def_7, type, sK1: a > a > a).
% 1.46/1.29 thf(func_def_8, type, sK2: g > b).
% 1.46/1.29 thf(func_def_9, type, sK3: g > g > g).
% 1.46/1.29 thf(func_def_10, type, sK4: b > b > b).
% 1.46/1.29 thf(func_def_11, type, sK5: g).
% 1.46/1.29 thf(func_def_12, type, sK6: g).
% 1.46/1.29 thf(f16,plain,(
% 1.46/1.29 $false),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.46/1.29 thf(f15,plain,(
% 1.46/1.29 ((sK0 @ (sK2 @ (sK3 @ sK5 @ sK6))) != (sK0 @ (sK2 @ (sK3 @ sK5 @ sK6))))),
% 1.46/1.29 inference(superposition,[status(thm)],[f14,f11])).
% 1.46/1.29 thf(f11,plain,(
% 1.46/1.29 ( ! [X10 : g,X9 : g] : (((sK2 @ (sK3 @ X9 @ X10)) = (sK4 @ (sK2 @ X9) @ (sK2 @ X10)))) )),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.29 thf(f10,plain,(
% 1.46/1.29 ((sK0 @ (sK2 @ (sK3 @ sK5 @ sK6))) != (sK1 @ (sK0 @ (sK2 @ sK5)) @ (sK0 @ (sK2 @ sK6)))) & ! [X7 : b,X8 : b] : ((sK1 @ (sK0 @ X8) @ (sK0 @ X7)) = (sK0 @ (sK4 @ X8 @ X7))) & ! [X9 : g,X10 : g] : ((sK2 @ (sK3 @ X9 @ X10)) = (sK4 @ (sK2 @ X9) @ (sK2 @ X10)))),
% 1.46/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f7,f9,f8])).
% 1.46/1.29 thf(f8,plain,(
% 1.46/1.29 ? [X0 : b > a,X1 : a > a > a,X2 : g > b,X3 : g > g > g,X4 : b > b > b] : (? [X5 : g,X6 : g] : ((X0 @ (X2 @ (X3 @ X5 @ X6))) != (X1 @ (X0 @ (X2 @ X5)) @ (X0 @ (X2 @ X6)))) & ! [X7 : b,X8 : b] : ((X1 @ (X0 @ X8) @ (X0 @ X7)) = (X0 @ (X4 @ X8 @ X7))) & ! [X9 : g,X10 : g] : ((X2 @ (X3 @ X9 @ X10)) = (X4 @ (X2 @ X9) @ (X2 @ X10)))) => (? [X6 : g,X5 : g] : ((sK0 @ (sK2 @ (sK3 @ X5 @ X6))) != (sK1 @ (sK0 @ (sK2 @ X5)) @ (sK0 @ (sK2 @ X6)))) & ! [X8 : b,X7 : b] : ((sK1 @ (sK0 @ X8) @ (sK0 @ X7)) = (sK0 @ (sK4 @ X8 @ X7))) & ! [X10 : g,X9 : g] : ((sK2 @ (sK3 @ X9 @ X10)) = (sK4 @ (sK2 @ X9) @ (sK2 @ X10))))),
% 1.46/1.29 introduced(definition,[],[choice_axiom])).
% 1.46/1.29 thf(f9,plain,(
% 1.46/1.29 ? [X6 : g,X5 : g] : ((sK0 @ (sK2 @ (sK3 @ X5 @ X6))) != (sK1 @ (sK0 @ (sK2 @ X5)) @ (sK0 @ (sK2 @ X6)))) => ((sK0 @ (sK2 @ (sK3 @ sK5 @ sK6))) != (sK1 @ (sK0 @ (sK2 @ sK5)) @ (sK0 @ (sK2 @ sK6))))),
% 1.46/1.29 introduced(definition,[],[choice_axiom])).
% 1.46/1.29 thf(f7,plain,(
% 1.46/1.29 ? [X0 : b > a,X1 : a > a > a,X2 : g > b,X3 : g > g > g,X4 : b > b > b] : (? [X5 : g,X6 : g] : ((X0 @ (X2 @ (X3 @ X5 @ X6))) != (X1 @ (X0 @ (X2 @ X5)) @ (X0 @ (X2 @ X6)))) & ! [X7 : b,X8 : b] : ((X1 @ (X0 @ X8) @ (X0 @ X7)) = (X0 @ (X4 @ X8 @ X7))) & ! [X9 : g,X10 : g] : ((X2 @ (X3 @ X9 @ X10)) = (X4 @ (X2 @ X9) @ (X2 @ X10))))),
% 1.46/1.29 inference(rectify,[status(thm)],[f6])).
% 1.46/1.29 thf(f6,plain,(
% 1.46/1.29 ? [X3 : b > a,X4 : a > a > a,X2 : g > b,X0 : g > g > g,X1 : b > b > b] : (? [X10 : g,X9 : g] : ((X3 @ (X2 @ (X0 @ X10 @ X9))) != (X4 @ (X3 @ (X2 @ X10)) @ (X3 @ (X2 @ X9)))) & ! [X8 : b,X7 : b] : ((X4 @ (X3 @ X7) @ (X3 @ X8)) = (X3 @ (X1 @ X7 @ X8))) & ! [X5 : g,X6 : g] : ((X2 @ (X0 @ X5 @ X6)) = (X1 @ (X2 @ X5) @ (X2 @ X6))))),
% 1.46/1.29 inference(flattening,[status(thm)],[f5])).
% 1.46/1.29 thf(f5,plain,(
% 1.46/1.29 ? [X3 : b > a,X4 : a > a > a,X2 : g > b,X0 : g > g > g,X1 : b > b > b] : (? [X10 : g,X9 : g] : ((X3 @ (X2 @ (X0 @ X10 @ X9))) != (X4 @ (X3 @ (X2 @ X10)) @ (X3 @ (X2 @ X9)))) & (! [X8 : b,X7 : b] : ((X4 @ (X3 @ X7) @ (X3 @ X8)) = (X3 @ (X1 @ X7 @ X8))) & ! [X5 : g,X6 : g] : ((X2 @ (X0 @ X5 @ X6)) = (X1 @ (X2 @ X5) @ (X2 @ X6)))))),
% 1.46/1.29 inference(ennf_transformation,[status(thm)],[f4])).
% 1.46/1.29 thf(f4,plain,(
% 1.46/1.29 ~! [X3 : b > a,X4 : a > a > a,X2 : g > b,X0 : g > g > g,X1 : b > b > b] : ((! [X8 : b,X7 : b] : ((X4 @ (X3 @ X7) @ (X3 @ X8)) = (X3 @ (X1 @ X7 @ X8))) & ! [X5 : g,X6 : g] : ((X2 @ (X0 @ X5 @ X6)) = (X1 @ (X2 @ X5) @ (X2 @ X6)))) => ! [X10 : g,X9 : g] : ((X3 @ (X2 @ (X0 @ X10 @ X9))) = (X4 @ (X3 @ (X2 @ X10)) @ (X3 @ (X2 @ X9)))))),
% 1.46/1.29 inference(rectify,[status(thm)],[f2])).
% 1.46/1.29 thf(f2,negated_conjecture,(
% 1.46/1.29 ~! [X2 : g > g > g,X3 : b > b > b,X0 : g > b,X1 : b > a,X4 : a > a > a] : ((! [X5 : g,X6 : g] : ((X0 @ (X2 @ X5 @ X6)) = (X3 @ (X0 @ X5) @ (X0 @ X6))) & ! [X5 : b,X6 : b] : ((X1 @ (X3 @ X5 @ X6)) = (X4 @ (X1 @ X5) @ (X1 @ X6)))) => ! [X6 : g,X5 : g] : ((X1 @ (X0 @ (X2 @ X5 @ X6))) = (X4 @ (X1 @ (X0 @ X5)) @ (X1 @ (X0 @ X6)))))),
% 1.46/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.29 thf(f1,conjecture,(
% 1.46/1.29 ! [X2 : g > g > g,X3 : b > b > b,X0 : g > b,X1 : b > a,X4 : a > a > a] : ((! [X5 : g,X6 : g] : ((X0 @ (X2 @ X5 @ X6)) = (X3 @ (X0 @ X5) @ (X0 @ X6))) & ! [X5 : b,X6 : b] : ((X1 @ (X3 @ X5 @ X6)) = (X4 @ (X1 @ X5) @ (X1 @ X6)))) => ! [X6 : g,X5 : g] : ((X1 @ (X0 @ (X2 @ X5 @ X6))) = (X4 @ (X1 @ (X0 @ X5)) @ (X1 @ (X0 @ X6)))))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.zRiXtsyW3L/DTF2THF_18311.p',cTHM133_pme)).
% 1.46/1.29 thf(f14,plain,(
% 1.46/1.29 ((sK0 @ (sK2 @ (sK3 @ sK5 @ sK6))) != (sK0 @ (sK4 @ (sK2 @ sK5) @ (sK2 @ sK6))))),
% 1.46/1.29 inference(superposition,[status(thm)],[f13,f12])).
% 1.46/1.29 thf(f12,plain,(
% 1.46/1.29 ( ! [X8 : b,X7 : b] : (((sK1 @ (sK0 @ X8) @ (sK0 @ X7)) = (sK0 @ (sK4 @ X8 @ X7)))) )),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.29 thf(f13,plain,(
% 1.46/1.29 ((sK0 @ (sK2 @ (sK3 @ sK5 @ sK6))) != (sK1 @ (sK0 @ (sK2 @ sK5)) @ (sK0 @ (sK2 @ sK6))))),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.29 % SZS output end Proof for DTF2THF_18311
% 1.46/1.29 % (18641)------------------------------
% 1.46/1.29 % (18641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (18641)Termination reason: Refutation
% 1.46/1.29
% 1.46/1.29 % (18641)Memory used [KB]: 5500
% 1.46/1.29 % (18641)Time elapsed: 0.004 s
% 1.46/1.29 % (18641)Instructions burned: 2 (million)
% 1.46/1.29 % (18641)------------------------------
% 1.46/1.29 % (18641)------------------------------
% 1.46/1.29 % (18639)Success in time 0.013 s
%------------------------------------------------------------------------------