%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO354^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 09:54:01 AM UTC 2026
% Result : Theorem 1.55s 1.35s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 32 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 125 ( 19 ~; 5 |; 8 &; 80 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 20 ^; 21 !; 3 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
n: $i > $i ).
thf(func_def_1,type,
m: $i > $i ).
thf(func_def_7,type,
sK0: ( $i > $i ) > $o ).
thf(func_def_10,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f32,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( n @ sK3 )
!= ( n @ sK3 ) ),
inference(superposition,[status(thm)],[f17,f19]) ).
thf(f19,plain,
! [X0: $i] :
( ( m @ X0 )
= ( n @ X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ ( n @ X1 ) )
= $true )
| ( ( X2 @ ( m @ X1 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( $true
!= ( sK0
@ ^ [Y0: $i] : ( n @ Y0 ) ) )
& ( ( sK0
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true )
& ! [X1: $i,X2: $i > $o] :
( ( ( X2 @ ( n @ X1 ) )
= $true )
| ( ( X2 @ ( m @ X1 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: ( $i > $i ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : ( n @ Y0 ) )
!= $true )
& ( ( X0
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true ) )
=> ( ( $true
!= ( sK0
@ ^ [Y0: $i] : ( n @ Y0 ) ) )
& ( ( sK0
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ? [X0: ( $i > $i ) > $o] :
( ( ( X0
@ ^ [Y0: $i] : ( n @ Y0 ) )
!= $true )
& ( ( X0
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true ) )
& ! [X1: $i,X2: $i > $o] :
( ( ( X2 @ ( n @ X1 ) )
= $true )
| ( ( X2 @ ( m @ X1 ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : ( n @ Y0 ) )
!= $true )
& ( ( X2
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true ) )
& ! [X0: $i,X1: $i > $o] :
( ( ( X1 @ ( n @ X0 ) )
= $true )
| ( ( X1 @ ( m @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i,X1: $i > $o] :
( ( ( X1 @ ( m @ X0 ) )
= $true )
=> ( ( X1 @ ( n @ X0 ) )
= $true ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( ( X2
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true )
=> ( ( X2
@ ^ [Y0: $i] : ( n @ Y0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( m @ X0 ) )
=> ( X1 @ ( n @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2
@ ^ [X3: $i] : ( m @ X3 ) )
=> ( X2
@ ^ [X4: $i] : ( n @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( m @ X0 ) )
=> ( X1 @ ( n @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2
@ ^ [X0: $i] : ( m @ X0 ) )
=> ( X2
@ ^ [X0: $i] : ( n @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( m @ X0 ) )
=> ( X1 @ ( n @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2
@ ^ [X0: $i] : ( m @ X0 ) )
=> ( X2
@ ^ [X0: $i] : ( n @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UBeu6ncpc8/DTF2THF_4049.p',cE4EXT) ).
thf(f17,plain,
( ( m @ sK3 )
!= ( n @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f16]) ).
thf(f16,plain,
m != n,
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true != $true )
| ( m != n ) ),
inference(constrained_superposition,[status(thm)],[f13,f14]) ).
thf(f14,plain,
( ( sK0 @ m )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( sK0
@ ^ [Y0: $i] : ( m @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f13,plain,
( ( sK0 @ n )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
!= ( sK0
@ ^ [Y0: $i] : ( n @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO354^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n008.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 14:28:39 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYO354^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : TPS problem E4EXT
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.16/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0125 [Bro09]
% 0.16/0.39 % : E4ext [Ben99]
% 0.16/0.39 % : E4EXT [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.16/0.39 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.39 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 8 @)
% 0.16/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 7 ( 7 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.16/0.39 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(n,type,
% 0.16/0.39 n: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(m,type,
% 0.16/0.39 m: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(cE4EXT,conjecture,
% 0.16/0.39 ( ! [X: $i,P: $i > $o] :
% 0.16/0.39 ( ( P @ ( m @ X ) )
% 0.16/0.39 => ( P @ ( n @ X ) ) )
% 0.16/0.39 => ! [Q: ( $i > $i ) > $o] :
% 0.16/0.39 ( ( Q
% 0.16/0.39 @ ^ [X: $i] : ( m @ X ) )
% 0.16/0.39 => ( Q
% 0.16/0.39 @ ^ [X: $i] : ( n @ X ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.55/1.31 ---- Embedded in THF ---
% 1.55/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.32 %%% Generated on Tue Feb 24 14:28:40 EST 2026
% 1.55/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.32 %%% Logic specification used:
% 1.55/1.32 %%% thf(spec, logic, $$dhol).
% 1.55/1.32
% 1.55/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.UBeu6ncpc8/DTF2DTF4049.p
% See solution above
% 1.55/1.32 ------------------------
% 1.55/1.32 ---- Cleaned THF ---
% 1.55/1.32 thf(n,type,
% 1.55/1.32 n: $i > $i ).
% 1.55/1.32
% 1.55/1.32 thf(m,type,
% 1.55/1.32 m: $i > $i ).
% 1.55/1.32
% 1.55/1.32 thf(cE4EXT,conjecture,
% 1.55/1.32 ( ! [X: $i,P: $i > $o] :
% 1.55/1.32 ( ( P @ ( m @ X ) )
% 1.55/1.32 => ( P @ ( n @ X ) ) )
% 1.55/1.32 => ! [Q: ( $i > $i ) > $o] :
% 1.55/1.32 ( ( Q
% 1.55/1.32 @ ^ [X: $i] : ( m @ X ) )
% 1.55/1.32 => ( Q
% 1.55/1.32 @ ^ [X: $i] : ( n @ X ) ) ) ) ).
% 1.55/1.33 ------------------------
% 1.55/1.35 % (4146)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4049 for (3000ds/183Mi)
% 1.55/1.35 % (4147)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_4049 for (3000ds/4Mi)
% 1.55/1.35 % (4150)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_4049 for (3000ds/2Mi)
% 1.55/1.35 % (4152)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4049 for (3000ds/18Mi)
% 1.55/1.35 % (4148)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_4049 for (3000ds/27Mi)
% 1.55/1.35 % (4151)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_4049 for (3000ds/275Mi)
% 1.55/1.35 % (4149)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4049 for (3000ds/2Mi)
% 1.55/1.35 % (4150)Instruction limit reached!
% 1.55/1.35 % (4150)------------------------------
% 1.55/1.35 % (4150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.35 % (4150)Termination reason: Unknown
% 1.55/1.35 % (4150)Termination phase: Saturation
% 1.55/1.35
% 1.55/1.35 % (4150)Memory used [KB]: 5373
% 1.55/1.35 % (4150)Time elapsed: 0.003 s
% 1.55/1.35 % (4150)Instructions burned: 2 (million)
% 1.55/1.35 % (4150)------------------------------
% 1.55/1.35 % (4150)------------------------------
% 1.55/1.35 % (4148)Refutation not found, incomplete strategy
% 1.55/1.35 % (4148)------------------------------
% 1.55/1.35 % (4148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.35 % (4148)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.35
% 1.55/1.35
% 1.55/1.35 % (4148)Memory used [KB]: 5500
% 1.55/1.35 % (4148)Time elapsed: 0.003 s
% 1.55/1.35 % (4148)Instructions burned: 1 (million)
% 1.55/1.35 % (4148)------------------------------
% 1.55/1.35 % (4148)------------------------------
% 1.55/1.35 % (4149)Instruction limit reached!
% 1.55/1.35 % (4149)------------------------------
% 1.55/1.35 % (4149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.35 % (4149)Termination reason: Unknown
% 1.55/1.35 % (4149)Termination phase: Saturation
% 1.55/1.35
% 1.55/1.35 % (4149)Memory used [KB]: 5500
% 1.55/1.35 % (4149)Time elapsed: 0.003 s
% 1.55/1.35 % (4149)Instructions burned: 3 (million)
% 1.55/1.35 % (4149)------------------------------
% 1.55/1.35 % (4149)------------------------------
% 1.55/1.35 % (4151)Refutation not found, incomplete strategy
% 1.55/1.35 % (4151)------------------------------
% 1.55/1.35 % (4151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.35 % (4151)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.35
% 1.55/1.35
% 1.55/1.35 % (4151)Memory used [KB]: 5500
% 1.55/1.35 % (4146)First to succeed.
% 1.55/1.35 % (4151)Time elapsed: 0.004 s
% 1.55/1.35 % (4151)Instructions burned: 3 (million)
% 1.55/1.35 % (4151)------------------------------
% 1.55/1.35 % (4151)------------------------------
% 1.55/1.35 % (4147)Instruction limit reached!
% 1.55/1.35 % (4147)------------------------------
% 1.55/1.35 % (4147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.35 % (4147)Termination reason: Unknown
% 1.55/1.35 % (4147)Termination phase: Saturation
% 1.55/1.35
% 1.55/1.35 % (4147)Memory used [KB]: 5500
% 1.55/1.35 % (4147)Time elapsed: 0.005 s
% 1.55/1.35 % (4147)Instructions burned: 4 (million)
% 1.55/1.35 % (4147)------------------------------
% 1.55/1.35 % (4147)------------------------------
% 1.55/1.35 % (4152)Also succeeded, but the first one will report.
% 1.55/1.35 % (4146)Refutation found. Thanks to Tanya!
% 1.55/1.35 % SZS status Theorem for DTF2THF_4049
% 1.55/1.35 % SZS output start Proof for DTF2THF_4049
% 1.55/1.35 thf(func_def_0, type, n: $i > $i).
% 1.55/1.35 thf(func_def_1, type, m: $i > $i).
% 1.55/1.35 thf(func_def_7, type, sK0: ($i > $i) > $o).
% 1.55/1.35 thf(func_def_10, type, ph2: !>[X0: $tType]:(X0)).
% 1.55/1.35 thf(f32,plain,(
% 1.55/1.35 $false),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.55/1.35 thf(f31,plain,(
% 1.55/1.35 ((n @ sK3) != (n @ sK3))),
% 1.55/1.35 inference(superposition,[status(thm)],[f17,f19])).
% 1.55/1.35 thf(f19,plain,(
% 1.55/1.35 ( ! [X0 : $i] : (((m @ X0) = (n @ X0))) )),
% 1.55/1.35 inference(leibniz_equality_elimination,[status(thm)],[f10])).
% 1.55/1.35 thf(f10,plain,(
% 1.55/1.35 ( ! [X2 : $i > $o,X1 : $i] : (((X2 @ (n @ X1)) = $true) | ((X2 @ (m @ X1)) != $true)) )),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f9])).
% 1.55/1.35 thf(f9,plain,(
% 1.55/1.35 (($true != (sK0 @ (^[Y0 : $i]: (n @ Y0)))) & ((sK0 @ (^[Y0 : $i]: (m @ Y0))) = $true)) & ! [X1 : $i,X2 : $i > $o] : (((X2 @ (n @ X1)) = $true) | ((X2 @ (m @ X1)) != $true))),
% 1.55/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.55/1.35 thf(f8,plain,(
% 1.55/1.35 ? [X0 : ($i > $i) > $o] : (((X0 @ (^[Y0 : $i]: (n @ Y0))) != $true) & ((X0 @ (^[Y0 : $i]: (m @ Y0))) = $true)) => (($true != (sK0 @ (^[Y0 : $i]: (n @ Y0)))) & ((sK0 @ (^[Y0 : $i]: (m @ Y0))) = $true))),
% 1.55/1.35 introduced(definition,[],[choice_axiom])).
% 1.55/1.35 thf(f7,plain,(
% 1.55/1.35 ? [X0 : ($i > $i) > $o] : (((X0 @ (^[Y0 : $i]: (n @ Y0))) != $true) & ((X0 @ (^[Y0 : $i]: (m @ Y0))) = $true)) & ! [X1 : $i,X2 : $i > $o] : (((X2 @ (n @ X1)) = $true) | ((X2 @ (m @ X1)) != $true))),
% 1.55/1.35 inference(rectify,[status(thm)],[f6])).
% 1.55/1.35 thf(f6,plain,(
% 1.55/1.35 ? [X2 : ($i > $i) > $o] : (((X2 @ (^[Y0 : $i]: (n @ Y0))) != $true) & ((X2 @ (^[Y0 : $i]: (m @ Y0))) = $true)) & ! [X0 : $i,X1 : $i > $o] : (((X1 @ (n @ X0)) = $true) | ((X1 @ (m @ X0)) != $true))),
% 1.55/1.35 inference(ennf_transformation,[status(thm)],[f5])).
% 1.55/1.35 thf(f5,plain,(
% 1.55/1.35 ~(! [X0 : $i,X1 : $i > $o] : (((X1 @ (m @ X0)) = $true) => ((X1 @ (n @ X0)) = $true)) => ! [X2 : ($i > $i) > $o] : (((X2 @ (^[Y0 : $i]: (m @ Y0))) = $true) => ((X2 @ (^[Y0 : $i]: (n @ Y0))) = $true)))),
% 1.55/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.35 thf(f4,plain,(
% 1.55/1.35 ~(! [X0 : $i,X1 : $i > $o] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ (^[X3 : $i] : (m @ X3))) => (X2 @ (^[X4 : $i] : (n @ X4)))))),
% 1.55/1.35 inference(rectify,[status(thm)],[f2])).
% 1.55/1.35 thf(f2,negated_conjecture,(
% 1.55/1.35 ~(! [X0 : $i,X1 : $i > $o] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ (^[X0 : $i] : (m @ X0))) => (X2 @ (^[X0 : $i] : (n @ X0)))))),
% 1.55/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.35 thf(f1,conjecture,(
% 1.55/1.35 ! [X0 : $i,X1 : $i > $o] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ (^[X0 : $i] : (m @ X0))) => (X2 @ (^[X0 : $i] : (n @ X0))))),
% 1.55/1.35 file('/export/starexec/sandbox2/tmp/tmp.UBeu6ncpc8/DTF2THF_4049.p',cE4EXT)).
% 1.55/1.35 thf(f17,plain,(
% 1.55/1.35 ((m @ sK3) != (n @ sK3))),
% 1.55/1.35 inference(negative_extensionality,[status(thm)],[f16])).
% 1.55/1.35 thf(f16,plain,(
% 1.55/1.35 (m != n)),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.55/1.35 thf(f15,plain,(
% 1.55/1.35 ($true != $true) | (m != n)),
% 1.55/1.35 inference(constrained_superposition,[status(thm)],[f13,f14])).
% 1.55/1.35 thf(f14,plain,(
% 1.55/1.35 ((sK0 @ m) = $true)),
% 1.55/1.35 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.55/1.35 thf(f11,plain,(
% 1.55/1.35 ((sK0 @ (^[Y0 : $i]: (m @ Y0))) = $true)),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f9])).
% 1.55/1.35 thf(f13,plain,(
% 1.55/1.35 ((sK0 @ n) != $true)),
% 1.55/1.35 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.55/1.35 thf(f12,plain,(
% 1.55/1.35 ($true != (sK0 @ (^[Y0 : $i]: (n @ Y0))))),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f9])).
% 1.55/1.35 % SZS output end Proof for DTF2THF_4049
% 1.55/1.35 % (4146)------------------------------
% 1.55/1.35 % (4146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.35 % (4146)Termination reason: Refutation
% 1.55/1.35
% 1.55/1.35 % (4146)Memory used [KB]: 5500
% 1.55/1.35 % (4146)Time elapsed: 0.005 s
% 1.55/1.35 % (4146)Instructions burned: 2 (million)
% 1.55/1.35 % (4146)------------------------------
% 1.55/1.35 % (4146)------------------------------
% 1.55/1.35 % (4145)Success in time 0.018 s
%------------------------------------------------------------------------------