%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO885^1.033.003 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n027.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 09:55:01 AM UTC 2026
% Result : Theorem 2.08s 1.71s
% Output : Refutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 221 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 20 avg)
% Number of connectives : 255 ( 25 ~; 16 |; 4 &; 210 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 34 ( 24 ^; 8 !; 2 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
f: $i > $i > $i > $i ).
thf(func_def_8,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( f @ a0 @ a1 @ a2 )
!= ( f @ a0 @ a1 @ a2 ) )
| ( a1 != a1 ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( a1
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : a1
@ a2
@ a1
@ a0 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( f @ a0
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] : a1
@ a0
@ a1
@ a2 )
@ a2 ) ) ),
inference(equality_resolution,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i > $i > $i > $i] :
( ( ( f @ a0 @ a1 @ a2 )
!= ( f @ a0 @ ( X1 @ a0 @ a2 @ a1 ) @ a2 ) )
| ( a1
!= ( X1 @ a2 @ a1 @ a0 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( f @ a0 @ ( X1 @ a0 @ a1 @ a2 ) @ a2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: $i > $i > $i > $i] :
( ( a1
!= ( X1 @ a2 @ a1 @ a0 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( f @ a0 @ ( X1 @ a0 @ a1 @ a2 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] : a2
@ a0
@ a1
@ a2 ) ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( f @ a0 @ ( X1 @ a0 @ a2 @ a1 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] : a2
@ a0
@ a2
@ a1 ) ) ) ),
inference(equality_resolution,[status(thm)],[f9]) ).
thf(f9,plain,
! [X2: $i > $i > $i > $i,X3: $i > $i > $i > $i] :
( ( a2
!= ( X2 @ a2 @ a1 @ a0 ) )
| ( a1
!= ( X3 @ a2 @ a1 @ a0 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( f @ a0 @ ( X3 @ a0 @ a2 @ a1 ) @ ( X2 @ a0 @ a2 @ a1 ) ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( f @ a0 @ ( X3 @ a0 @ a1 @ a2 ) @ ( X2 @ a0 @ a1 @ a2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
! [X2: $i > $i > $i > $i,X3: $i > $i > $i > $i] :
( ( a2
!= ( X2 @ a2 @ a1 @ a0 ) )
| ( a1
!= ( X3 @ a2 @ a1 @ a0 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( f
@ ( ^ [Y3: $i,Y4: $i,Y5: $i] : a0
@ Y0
@ Y1
@ Y2 )
@ ( X3 @ Y0 @ Y1 @ Y2 )
@ ( X2 @ Y0 @ Y1 @ Y2 ) )
@ a0
@ a2
@ a1 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( f
@ ( ^ [Y3: $i,Y4: $i,Y5: $i] : a0
@ Y0
@ Y1
@ Y2 )
@ ( X3 @ Y0 @ Y1 @ Y2 )
@ ( X2 @ Y0 @ Y1 @ Y2 ) )
@ a0
@ a1
@ a2 ) ) ),
inference(equality_resolution,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i > $i > $i > $i] :
( ( ( f @ a0 @ a1 @ a2 )
!= ( X0 @ a2 @ a1 @ a0 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( X0 @ a0 @ a2 @ a1 ) )
| ( ( X0 @ a0 @ a1 @ a2 )
!= ( f @ a0 @ a1 @ a2 ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
! [X0: $i > $i > $i > $i] :
( ( ( f @ a0 @ a1 @ a2 )
!= ( X0 @ a0 @ a2 @ a1 ) )
| ( ( f @ a0 @ a1 @ a2 )
!= ( X0 @ a2 @ a1 @ a0 ) )
| ( ( X0 @ a0 @ a1 @ a2 )
!= ( f @ a0 @ a1 @ a2 ) ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $i > $i > $i] :
( ( ( f @ a0 @ a1 @ a2 )
= ( X0 @ a0 @ a2 @ a1 ) )
& ( ( X0 @ a0 @ a1 @ a2 )
= ( f @ a0 @ a1 @ a2 ) )
& ( ( f @ a0 @ a1 @ a2 )
= ( X0 @ a2 @ a1 @ a0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $i > $i > $i] :
( ( ( f @ a0 @ a1 @ a2 )
= ( X0 @ a0 @ a2 @ a1 ) )
& ( ( X0 @ a0 @ a1 @ a2 )
= ( f @ a0 @ a1 @ a2 ) )
& ( ( f @ a0 @ a1 @ a2 )
= ( X0 @ a2 @ a1 @ a0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SwXrwsIJio/DTF2THF_3294.p',goal) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO885^1.033.003 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n027.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 14:50:52 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.49 ---- Original DTF file ---
% 0.32/0.49 thf(spec,logic,$$dhol).
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 % File : SYO885^1.033.003 : TPTP v9.2.1. Released v7.5.0.
% 0.32/0.49 % Domain : Syntactic
% 0.32/0.49 % Problem : Test higher-order unification procedure, 3,3,3
% 0.32/0.49 % Version : Biased.
% 0.32/0.49 % English :
% 0.32/0.49
% 0.32/0.49 % Refs : [VBN20] Vukmirovic et al. (2020), Efficient Full Higher-order
% 0.32/0.49 % : [Ben21] Bentkamp (2021) Email to Geoff Sutcliffe
% 0.32/0.49 % Source : [Ben21]
% 0.32/0.49 % Names : solid.3.3.3.p [Ben21]
% 0.32/0.49
% 0.32/0.49 % Status : Theorem
% 0.32/0.49 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0
% 0.32/0.49 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.32/0.49 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.32/0.49 % Maximal formula atoms : 3 ( 3 avg)
% 0.32/0.49 % Number of connectives : 20 ( 0 ~; 0 |; 2 &; 18 @)
% 0.32/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 4 ( 4 avg)
% 0.32/0.49 % Number of types : 1 ( 0 usr)
% 0.32/0.49 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 5 ( 4 usr; 3 con; 0-3 aty)
% 0.32/0.49 % Number of variables : 1 ( 0 ^; 0 !; 1 ?; 1 :)
% 0.32/0.49 % SPC : TH0_THM_EQU_NAR
% 0.32/0.49
% 0.32/0.49 % Comments : Possible solution: F -> ^[X0: $i,X1: $i,X2: $i]: f @ a0 @ a1 @ a2
% 0.32/0.49 % : Solved by almost all HO provers (requires no unification -- just
% 0.32/0.49 % deleting all the arguments)
% 0.32/0.49 % : Biased because it was desiged for testing features in
% 0.32/0.49 % Zipperposition.
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(a0_type,type,
% 0.32/0.49 a0: $i ).
% 0.32/0.49
% 0.32/0.49 thf(a1_type,type,
% 0.32/0.49 a1: $i ).
% 0.32/0.49
% 0.32/0.49 thf(a2_type,type,
% 0.32/0.49 a2: $i ).
% 0.32/0.49
% 0.32/0.49 thf(f_type,type,
% 0.32/0.49 f: $i > $i > $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(goal,conjecture,
% 0.32/0.49 ? [F: $i > $i > $i > $i] :
% 0.32/0.49 ( ( ( F @ a0 @ a1 @ a2 )
% 0.32/0.49 = ( f @ a0 @ a1 @ a2 ) )
% 0.32/0.49 & ( ( F @ a0 @ a2 @ a1 )
% 0.32/0.49 = ( f @ a0 @ a1 @ a2 ) )
% 0.32/0.49 & ( ( F @ a2 @ a1 @ a0 )
% 0.32/0.49 = ( f @ a0 @ a1 @ a2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 1.93/1.67 ---- Embedded in THF ---
% 1.93/1.67 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.93/1.67 %%% Generated on Tue Feb 24 14:50:53 EST 2026
% 1.93/1.67 %%% using '$$dhol' embedding, version 1.3.0.
% 1.93/1.67 %%% Logic specification used:
% 1.93/1.67 %%% thf(spec, logic, $$dhol).
% 1.93/1.67
% 1.93/1.67 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SwXrwsIJio/DTF2DTF3294.p
% See solution above
% 1.93/1.67 ------------------------
% 1.93/1.68 ---- Cleaned THF ---
% 1.93/1.68 thf(a0_type,type,
% 1.93/1.68 a0: $i ).
% 1.93/1.68
% 1.93/1.68 thf(a1_type,type,
% 1.93/1.68 a1: $i ).
% 1.93/1.68
% 1.93/1.68 thf(a2_type,type,
% 1.93/1.68 a2: $i ).
% 1.93/1.68
% 1.93/1.68 thf(f_type,type,
% 1.93/1.68 f: $i > $i > $i > $i ).
% 1.93/1.68
% 1.93/1.68 thf(goal,conjecture,
% 1.93/1.68 ? [F: $i > $i > $i > $i] :
% 1.93/1.68 ( ( ( F @ a0 @ a1 @ a2 )
% 1.93/1.68 = ( f @ a0 @ a1 @ a2 ) )
% 1.93/1.68 & ( ( F @ a0 @ a2 @ a1 )
% 1.93/1.68 = ( f @ a0 @ a1 @ a2 ) )
% 1.93/1.68 & ( ( F @ a2 @ a1 @ a0 )
% 1.93/1.68 = ( f @ a0 @ a1 @ a2 ) ) ) ).
% 1.93/1.68 ------------------------
% 2.08/1.70 % (3394)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_3294 for (2999ds/27Mi)
% 2.08/1.70 % (3393)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_3294 for (2999ds/4Mi)
% 2.08/1.70 % (3397)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_3294 for (2999ds/275Mi)
% 2.08/1.70 % (3398)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3294 for (2999ds/18Mi)
% 2.08/1.70 % (3396)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_3294 for (2999ds/2Mi)
% 2.08/1.70 % (3392)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3294 for (2999ds/183Mi)
% 2.08/1.70 % (3395)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3294 for (2999ds/2Mi)
% 2.08/1.70 % (3397)Refutation not found, incomplete strategy
% 2.08/1.70 % (3397)------------------------------
% 2.08/1.70 % (3397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.70 % (3397)Termination reason: Refutation not found, incomplete strategy
% 2.08/1.70
% 2.08/1.70 % (3396)Instruction limit reached!
% 2.08/1.70 % (3396)------------------------------
% 2.08/1.70 % (3396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.70 % (3396)Termination reason: Unknown
% 2.08/1.70 % (3396)Termination phase: Saturation
% 2.08/1.70
% 2.08/1.70 % (3396)Memory used [KB]: 5373
% 2.08/1.70 % (3396)Time elapsed: 0.003 s
% 2.08/1.70 % (3396)Instructions burned: 2 (million)
% 2.08/1.70 % (3396)------------------------------
% 2.08/1.70 % (3396)------------------------------
% 2.08/1.70
% 2.08/1.70 % (3397)Memory used [KB]: 5373
% 2.08/1.70 % (3397)Time elapsed: 0.003 s
% 2.08/1.70 % (3397)Instructions burned: 1 (million)
% 2.08/1.70 % (3397)------------------------------
% 2.08/1.70 % (3397)------------------------------
% 2.08/1.70 % (3394)Refutation not found, incomplete strategy
% 2.08/1.70 % (3394)------------------------------
% 2.08/1.70 % (3394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.70 % (3394)Termination reason: Refutation not found, incomplete strategy
% 2.08/1.70
% 2.08/1.70
% 2.08/1.70 % (3394)Memory used [KB]: 5500
% 2.08/1.70 % (3394)Time elapsed: 0.003 s
% 2.08/1.70 % (3394)Instructions burned: 1 (million)
% 2.08/1.70 % (3394)------------------------------
% 2.08/1.70 % (3394)------------------------------
% 2.08/1.70 % (3395)Refutation not found, incomplete strategy
% 2.08/1.70 % (3395)------------------------------
% 2.08/1.70 % (3395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.70 % (3395)Termination reason: Refutation not found, incomplete strategy
% 2.08/1.70
% 2.08/1.70
% 2.08/1.70 % (3395)Memory used [KB]: 5373
% 2.08/1.70 % (3395)Time elapsed: 0.002 s
% 2.08/1.70 % (3395)Instructions burned: 1 (million)
% 2.08/1.70 % (3395)------------------------------
% 2.08/1.70 % (3395)------------------------------
% 2.08/1.70 % (3392)Refutation not found, incomplete strategy
% 2.08/1.70 % (3392)------------------------------
% 2.08/1.70 % (3392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.70 % (3392)Termination reason: Refutation not found, incomplete strategy
% 2.08/1.70
% 2.08/1.70
% 2.08/1.70 % (3392)Memory used [KB]: 5500
% 2.08/1.70 % (3392)Time elapsed: 0.003 s
% 2.08/1.70 % (3392)Instructions burned: 3 (million)
% 2.08/1.70 % (3392)------------------------------
% 2.08/1.70 % (3392)------------------------------
% 2.08/1.70 % (3393)Instruction limit reached!
% 2.08/1.70 % (3393)------------------------------
% 2.08/1.70 % (3393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.70 % (3393)Termination reason: Unknown
% 2.08/1.70 % (3393)Termination phase: Saturation
% 2.08/1.70
% 2.08/1.70 % (3393)Memory used [KB]: 5500
% 2.08/1.70 % (3393)Time elapsed: 0.005 s
% 2.08/1.70 % (3393)Instructions burned: 5 (million)
% 2.08/1.70 % (3393)------------------------------
% 2.08/1.70 % (3393)------------------------------
% 2.08/1.70 % (3398)First to succeed.
% 2.08/1.71 % (3398)Refutation found. Thanks to Tanya!
% 2.08/1.71 % SZS status Theorem for DTF2THF_3294
% 2.08/1.71 % SZS output start Proof for DTF2THF_3294
% 2.08/1.71 thf(func_def_3, type, f: $i > $i > $i > $i).
% 2.08/1.71 thf(func_def_8, type, ph1: !>[X0: $tType]:(X0)).
% 2.08/1.71 thf(f22,plain,(
% 2.08/1.71 $false),
% 2.08/1.71 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 2.08/1.71 thf(f21,plain,(
% 2.08/1.71 ((f @ a0 @ a1 @ a2) != (f @ a0 @ a1 @ a2)) | (a1 != a1)),
% 2.08/1.71 inference(beta_eta_normalization,[status(thm)],[f19])).
% 2.08/1.71 thf(f19,plain,(
% 2.08/1.71 (a1 != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (a1)))))) @ a2 @ a1 @ a0)) | ((f @ a0 @ a1 @ a2) != (f @ a0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (a1)))))) @ a0 @ a1 @ a2) @ a2))),
% 2.08/1.71 inference(equality_resolution,[status(thm)],[f16])).
% 2.08/1.71 thf(f16,plain,(
% 2.08/1.71 ( ! [X1 : $i > $i > $i > $i] : (((f @ a0 @ a1 @ a2) != (f @ a0 @ (X1 @ a0 @ a2 @ a1) @ a2)) | (a1 != (X1 @ a2 @ a1 @ a0)) | ((f @ a0 @ a1 @ a2) != (f @ a0 @ (X1 @ a0 @ a1 @ a2) @ a2))) )),
% 2.08/1.71 inference(beta_eta_normalization,[status(thm)],[f15])).
% 2.08/1.71 thf(f15,plain,(
% 2.08/1.71 ( ! [X1 : $i > $i > $i > $i] : ((a1 != (X1 @ a2 @ a1 @ a0)) | ((f @ a0 @ a1 @ a2) != (f @ a0 @ (X1 @ a0 @ a1 @ a2) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (a2)))))) @ a0 @ a1 @ a2))) | ((f @ a0 @ a1 @ a2) != (f @ a0 @ (X1 @ a0 @ a2 @ a1) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (a2)))))) @ a0 @ a2 @ a1)))) )),
% 2.08/1.71 inference(equality_resolution,[status(thm)],[f9])).
% 2.08/1.71 thf(f9,plain,(
% 2.08/1.71 ( ! [X2 : $i > $i > $i > $i,X3 : $i > $i > $i > $i] : ((a2 != (X2 @ a2 @ a1 @ a0)) | (a1 != (X3 @ a2 @ a1 @ a0)) | ((f @ a0 @ a1 @ a2) != (f @ a0 @ (X3 @ a0 @ a2 @ a1) @ (X2 @ a0 @ a2 @ a1))) | ((f @ a0 @ a1 @ a2) != (f @ a0 @ (X3 @ a0 @ a1 @ a2) @ (X2 @ a0 @ a1 @ a2)))) )),
% 2.08/1.71 inference(beta_eta_normalization,[status(thm)],[f7])).
% 2.08/1.71 thf(f7,plain,(
% 2.08/1.71 ( ! [X2 : $i > $i > $i > $i,X3 : $i > $i > $i > $i] : ((a2 != (X2 @ a2 @ a1 @ a0)) | (a1 != (X3 @ a2 @ a1 @ a0)) | ((f @ a0 @ a1 @ a2) != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (f @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (a0)))))) @ Y0 @ Y1 @ Y2) @ (X3 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2))))))) @ a0 @ a2 @ a1)) | ((f @ a0 @ a1 @ a2) != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (f @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (a0)))))) @ Y0 @ Y1 @ Y2) @ (X3 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2))))))) @ a0 @ a1 @ a2))) )),
% 2.08/1.71 inference(equality_resolution,[status(thm)],[f5])).
% 2.08/1.71 thf(f5,plain,(
% 2.08/1.71 ( ! [X0 : $i > $i > $i > $i] : (((f @ a0 @ a1 @ a2) != (X0 @ a2 @ a1 @ a0)) | ((f @ a0 @ a1 @ a2) != (X0 @ a0 @ a2 @ a1)) | ((X0 @ a0 @ a1 @ a2) != (f @ a0 @ a1 @ a2))) )),
% 2.08/1.71 inference(cnf_transformation,[status(thm)],[f4])).
% 2.08/1.71 thf(f4,plain,(
% 2.08/1.71 ! [X0 : $i > $i > $i > $i] : (((f @ a0 @ a1 @ a2) != (X0 @ a0 @ a2 @ a1)) | ((f @ a0 @ a1 @ a2) != (X0 @ a2 @ a1 @ a0)) | ((X0 @ a0 @ a1 @ a2) != (f @ a0 @ a1 @ a2)))),
% 2.08/1.71 inference(ennf_transformation,[status(thm)],[f2])).
% 2.08/1.71 thf(f2,negated_conjecture,(
% 2.08/1.71 ~? [X0 : $i > $i > $i > $i] : (((f @ a0 @ a1 @ a2) = (X0 @ a0 @ a2 @ a1)) & ((X0 @ a0 @ a1 @ a2) = (f @ a0 @ a1 @ a2)) & ((f @ a0 @ a1 @ a2) = (X0 @ a2 @ a1 @ a0)))),
% 2.08/1.71 inference(negated_conjecture,[status(cth)],[f1])).
% 2.08/1.71 thf(f1,conjecture,(
% 2.08/1.71 ? [X0 : $i > $i > $i > $i] : (((f @ a0 @ a1 @ a2) = (X0 @ a0 @ a2 @ a1)) & ((X0 @ a0 @ a1 @ a2) = (f @ a0 @ a1 @ a2)) & ((f @ a0 @ a1 @ a2) = (X0 @ a2 @ a1 @ a0)))),
% 2.08/1.71 file('/export/starexec/sandbox/tmp/tmp.SwXrwsIJio/DTF2THF_3294.p',goal)).
% 2.08/1.71 % SZS output end Proof for DTF2THF_3294
% 2.08/1.71 % (3398)------------------------------
% 2.08/1.71 % (3398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.08/1.71 % (3398)Termination reason: Refutation
% 2.08/1.71
% 2.08/1.71 % (3398)Memory used [KB]: 5500
% 2.08/1.71 % (3398)Time elapsed: 0.007 s
% 2.08/1.71 % (3398)Instructions burned: 7 (million)
% 2.08/1.71 % (3398)------------------------------
% 2.08/1.71 % (3398)------------------------------
% 2.08/1.71 % (3391)Success in time 0.022 s
%------------------------------------------------------------------------------