%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO352^5 : 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 : n025.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 0.32s 1.43s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 102 ( 18 ~; 5 |; 8 &; 58 @)
% ( 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 : 24 ( 0 ^; 21 !; 3 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
n: $i > $i ).
thf(func_def_1,type,
m: $i > $i ).
thf(func_def_5,type,
sK0: ( $i > $i ) > $o ).
thf(func_def_8,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f38,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( n @ sK3 )
!= ( n @ sK3 ) ),
inference(superposition,[status(thm)],[f15,f17]) ).
thf(f17,plain,
! [X0: $i] :
( ( m @ X0 )
= ( n @ X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( m @ X1 ) )
!= $true )
| ( $true
= ( X0 @ ( n @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( m @ X1 ) )
!= $true )
| ( $true
= ( X0 @ ( n @ X1 ) ) ) )
& ( ( sK0 @ n )
!= $true )
& ( ( sK0 @ m )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X2: ( $i > $i ) > $o] :
( ( ( X2 @ n )
!= $true )
& ( ( X2 @ m )
= $true ) )
=> ( ( ( sK0 @ n )
!= $true )
& ( ( sK0 @ m )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( m @ X1 ) )
!= $true )
| ( $true
= ( X0 @ ( n @ X1 ) ) ) )
& ? [X2: ( $i > $i ) > $o] :
( ( ( X2 @ n )
!= $true )
& ( ( X2 @ m )
= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X1: $i > $o,X0: $i] :
( ( ( X1 @ ( m @ X0 ) )
!= $true )
| ( ( X1 @ ( n @ X0 ) )
= $true ) )
& ? [X2: ( $i > $i ) > $o] :
( ( ( X2 @ n )
!= $true )
& ( ( X2 @ m )
= $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 @ m )
= $true )
=> ( ( X2 @ n )
= $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 @ m )
=> ( X2 @ n ) ) ),
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 @ m )
=> ( X2 @ n ) ) ),
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 @ m )
=> ( X2 @ n ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kZI6l4Ot5q/DTF2THF_19356.p',cE5EXT) ).
thf(f15,plain,
( ( n @ sK3 )
!= ( m @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f14]) ).
thf(f14,plain,
m != n,
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
( ( m != n )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
( ( sK0 @ m )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
( ( sK0 @ n )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO352^5 : 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
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:28:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SYO352^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Syntactic
% 0.20/0.47 % Problem : TPS problem E5EXT
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : Nontrivial direction of functional extensionality using Leibniz
% 0.20/0.47 % equality.
% 0.20/0.47
% 0.20/0.47 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.20/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_0100 [Bro09]
% 0.20/0.47 % : E5ext [Ben99]
% 0.20/0.47 % : E5EXT [TPS]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % 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
% 0.20/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.47 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 6 @)
% 0.20/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 7 ( 7 avg)
% 0.20/0.47 % Number of types : 2 ( 0 usr)
% 0.20/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.20/0.47 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.20/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(n,type,
% 0.20/0.47 n: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(m,type,
% 0.20/0.47 m: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(cE5EXT,conjecture,
% 0.20/0.47 ( ! [X: $i,P: $i > $o] :
% 0.20/0.47 ( ( P @ ( m @ X ) )
% 0.20/0.47 => ( P @ ( n @ X ) ) )
% 0.20/0.47 => ! [Q: ( $i > $i ) > $o] :
% 0.20/0.47 ( ( Q @ m )
% 0.20/0.47 => ( Q @ n ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 0.32/1.40 ---- Embedded in THF ---
% 0.32/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.40 %%% Generated on Tue Feb 24 14:28:43 EST 2026
% 0.32/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.40 %%% Logic specification used:
% 0.32/1.40 %%% thf(spec, logic, $$dhol).
% 0.32/1.40
% 0.32/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.kZI6l4Ot5q/DTF2DTF19356.p
% See solution above
% 0.32/1.40 ------------------------
% 0.32/1.41 ---- Cleaned THF ---
% 0.32/1.41 thf(n,type,
% 0.32/1.41 n: $i > $i ).
% 0.32/1.41
% 0.32/1.41 thf(m,type,
% 0.32/1.41 m: $i > $i ).
% 0.32/1.41
% 0.32/1.41 thf(cE5EXT,conjecture,
% 0.32/1.41 ( ! [X: $i,P: $i > $o] :
% 0.32/1.41 ( ( P @ ( m @ X ) )
% 0.32/1.41 => ( P @ ( n @ X ) ) )
% 0.32/1.41 => ! [Q: ( $i > $i ) > $o] :
% 0.32/1.41 ( ( Q @ m )
% 0.32/1.41 => ( Q @ n ) ) ) ).
% 0.32/1.41 ------------------------
% 0.32/1.43 % (19455)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_19356 for (3000ds/4Mi)
% 0.32/1.43 % (19454)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19356 for (3000ds/183Mi)
% 0.32/1.43 % (19456)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_19356 for (3000ds/27Mi)
% 0.32/1.43 % (19457)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19356 for (3000ds/2Mi)
% 0.32/1.43 % (19458)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_19356 for (3000ds/2Mi)
% 0.32/1.43 % (19460)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19356 for (3000ds/18Mi)
% 0.32/1.43 % (19459)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_19356 for (3000ds/275Mi)
% 0.32/1.43 % (19457)Instruction limit reached!
% 0.32/1.43 % (19457)------------------------------
% 0.32/1.43 % (19457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (19457)Termination reason: Unknown
% 0.32/1.43 % (19457)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (19457)Memory used [KB]: 5500
% 0.32/1.43 % (19457)Time elapsed: 0.003 s
% 0.32/1.43 % (19457)Instructions burned: 2 (million)
% 0.32/1.43 % (19457)------------------------------
% 0.32/1.43 % (19457)------------------------------
% 0.32/1.43 % (19456)Refutation not found, incomplete strategy
% 0.32/1.43 % (19456)------------------------------
% 0.32/1.43 % (19456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (19456)Termination reason: Refutation not found, incomplete strategy
% 0.32/1.43
% 0.32/1.43
% 0.32/1.43 % (19456)Memory used [KB]: 5500
% 0.32/1.43 % (19456)Time elapsed: 0.003 s
% 0.32/1.43 % (19456)Instructions burned: 2 (million)
% 0.32/1.43 % (19456)------------------------------
% 0.32/1.43 % (19456)------------------------------
% 0.32/1.43 % (19458)Instruction limit reached!
% 0.32/1.43 % (19458)------------------------------
% 0.32/1.43 % (19458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (19458)Termination reason: Unknown
% 0.32/1.43 % (19458)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (19458)Memory used [KB]: 5500
% 0.32/1.43 % (19458)Time elapsed: 0.003 s
% 0.32/1.43 % (19458)Instructions burned: 2 (million)
% 0.32/1.43 % (19458)------------------------------
% 0.32/1.43 % (19458)------------------------------
% 0.32/1.43 % (19459)Refutation not found, incomplete strategy
% 0.32/1.43 % (19459)------------------------------
% 0.32/1.43 % (19459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (19459)Termination reason: Refutation not found, incomplete strategy
% 0.32/1.43
% 0.32/1.43
% 0.32/1.43 % (19459)Memory used [KB]: 5500
% 0.32/1.43 % (19459)Time elapsed: 0.003 s
% 0.32/1.43 % (19459)Instructions burned: 2 (million)
% 0.32/1.43 % (19459)------------------------------
% 0.32/1.43 % (19459)------------------------------
% 0.32/1.43 % (19460)First to succeed.
% 0.32/1.43 % (19455)Instruction limit reached!
% 0.32/1.43 % (19455)------------------------------
% 0.32/1.43 % (19455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (19455)Termination reason: Unknown
% 0.32/1.43 % (19455)Termination phase: Saturation
% 0.32/1.43
% 0.32/1.43 % (19455)Memory used [KB]: 5500
% 0.32/1.43 % (19455)Time elapsed: 0.005 s
% 0.32/1.43 % (19455)Instructions burned: 5 (million)
% 0.32/1.43 % (19455)------------------------------
% 0.32/1.43 % (19455)------------------------------
% 0.32/1.43 % (19454)Also succeeded, but the first one will report.
% 0.32/1.43 % (19460)Refutation found. Thanks to Tanya!
% 0.32/1.43 % SZS status Theorem for DTF2THF_19356
% 0.32/1.43 % SZS output start Proof for DTF2THF_19356
% 0.32/1.43 thf(func_def_0, type, n: $i > $i).
% 0.32/1.43 thf(func_def_1, type, m: $i > $i).
% 0.32/1.43 thf(func_def_5, type, sK0: ($i > $i) > $o).
% 0.32/1.43 thf(func_def_8, type, ph2: !>[X0: $tType]:(X0)).
% 0.32/1.43 thf(f38,plain,(
% 0.32/1.43 $false),
% 0.32/1.43 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 0.32/1.43 thf(f37,plain,(
% 0.32/1.43 ((n @ sK3) != (n @ sK3))),
% 0.32/1.43 inference(superposition,[status(thm)],[f15,f17])).
% 0.32/1.43 thf(f17,plain,(
% 0.32/1.43 ( ! [X0 : $i] : (((m @ X0) = (n @ X0))) )),
% 0.32/1.43 inference(leibniz_equality_elimination,[status(thm)],[f12])).
% 0.32/1.43 thf(f12,plain,(
% 0.32/1.43 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (m @ X1)) != $true) | ($true = (X0 @ (n @ X1)))) )),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f9])).
% 0.32/1.43 thf(f9,plain,(
% 0.32/1.43 ! [X0 : $i > $o,X1 : $i] : (((X0 @ (m @ X1)) != $true) | ($true = (X0 @ (n @ X1)))) & (((sK0 @ n) != $true) & ((sK0 @ m) = $true))),
% 0.32/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 0.32/1.43 thf(f8,plain,(
% 0.32/1.43 ? [X2 : ($i > $i) > $o] : (((X2 @ n) != $true) & ((X2 @ m) = $true)) => (((sK0 @ n) != $true) & ((sK0 @ m) = $true))),
% 0.32/1.43 introduced(definition,[],[choice_axiom])).
% 0.32/1.43 thf(f7,plain,(
% 0.32/1.43 ! [X0 : $i > $o,X1 : $i] : (((X0 @ (m @ X1)) != $true) | ($true = (X0 @ (n @ X1)))) & ? [X2 : ($i > $i) > $o] : (((X2 @ n) != $true) & ((X2 @ m) = $true))),
% 0.32/1.43 inference(rectify,[status(thm)],[f6])).
% 0.32/1.43 thf(f6,plain,(
% 0.32/1.43 ! [X1 : $i > $o,X0 : $i] : (((X1 @ (m @ X0)) != $true) | ((X1 @ (n @ X0)) = $true)) & ? [X2 : ($i > $i) > $o] : (((X2 @ n) != $true) & ((X2 @ m) = $true))),
% 0.32/1.43 inference(ennf_transformation,[status(thm)],[f5])).
% 0.32/1.43 thf(f5,plain,(
% 0.32/1.43 ~(! [X0 : $i,X1 : $i > $o] : (((X1 @ (m @ X0)) = $true) => ((X1 @ (n @ X0)) = $true)) => ! [X2 : ($i > $i) > $o] : (((X2 @ m) = $true) => ((X2 @ n) = $true)))),
% 0.32/1.43 inference(fool_elimination,[status(thm)],[f4])).
% 0.32/1.43 thf(f4,plain,(
% 0.32/1.43 ~(! [X0 : $i,X1 : $i > $o] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ m) => (X2 @ n)))),
% 0.32/1.43 inference(rectify,[status(thm)],[f2])).
% 0.32/1.43 thf(f2,negated_conjecture,(
% 0.32/1.43 ~(! [X0 : $i,X1 : $i > $o] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ m) => (X2 @ n)))),
% 0.32/1.43 inference(negated_conjecture,[status(cth)],[f1])).
% 0.32/1.43 thf(f1,conjecture,(
% 0.32/1.43 ! [X0 : $i,X1 : $i > $o] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : ($i > $i) > $o] : ((X2 @ m) => (X2 @ n))),
% 0.32/1.43 file('/export/starexec/sandbox/tmp/tmp.kZI6l4Ot5q/DTF2THF_19356.p',cE5EXT)).
% 0.32/1.43 thf(f15,plain,(
% 0.32/1.43 ((n @ sK3) != (m @ sK3))),
% 0.32/1.43 inference(negative_extensionality,[status(thm)],[f14])).
% 0.32/1.43 thf(f14,plain,(
% 0.32/1.43 (m != n)),
% 0.32/1.43 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 0.32/1.43 thf(f13,plain,(
% 0.32/1.43 (m != n) | ($true != $true)),
% 0.32/1.43 inference(constrained_superposition,[status(thm)],[f11,f10])).
% 0.32/1.43 thf(f10,plain,(
% 0.32/1.43 ((sK0 @ m) = $true)),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f9])).
% 0.32/1.43 thf(f11,plain,(
% 0.32/1.43 ((sK0 @ n) != $true)),
% 0.32/1.43 inference(cnf_transformation,[status(thm)],[f9])).
% 0.32/1.43 % SZS output end Proof for DTF2THF_19356
% 0.32/1.43 % (19460)------------------------------
% 0.32/1.43 % (19460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.43 % (19460)Termination reason: Refutation
% 0.32/1.43
% 0.32/1.43 % (19460)Memory used [KB]: 5500
% 0.32/1.43 % (19460)Time elapsed: 0.004 s
% 0.32/1.43 % (19460)Instructions burned: 4 (million)
% 0.32/1.43 % (19460)------------------------------
% 0.32/1.43 % (19460)------------------------------
% 0.32/1.43 % (19453)Success in time 0.008 s
%------------------------------------------------------------------------------