%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO350^5 : 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 : n003.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 09:54:00 AM UTC 2026
% Result : Theorem 1.35s 1.26s
% Output : Refutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 53 ( 10 ~; 1 |; 4 &; 30 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
g: $i > $i ).
thf(func_def_1,type,
p: ( $i > $i ) > $o ).
thf(func_def_2,type,
f: $i > $i ).
thf(func_def_7,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f14,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f13,f8]) ).
thf(f8,plain,
! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( p @ g )
!= $true )
& ( ( p @ f )
= $true )
& ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( p @ g )
!= $true )
& ( ( p @ f )
= $true )
& ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( ( p @ f )
= $true )
=> ( ( p @ g )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( p @ f )
=> ( p @ g ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( p @ f )
=> ( p @ g ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( p @ f )
=> ( p @ g ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GROJvTsL7B/DTF2THF_10251.p',cE1FUNC) ).
thf(f13,plain,
( ( f @ sK2 )
!= ( g @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f12]) ).
thf(f12,plain,
f != g,
inference(trivial_inequality_removal,[status(thm)],[f11]) ).
thf(f11,plain,
( ( f != g )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f10,f9]) ).
thf(f9,plain,
( ( p @ f )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f10,plain,
( ( p @ g )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO350^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 14:28:10 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SYO350^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.41 % Domain : Syntactic
% 0.16/0.41 % Problem : TPS problem E1FUNC
% 0.16/0.41 % Version : Especial.
% 0.16/0.41 % English : Example from [Ben99] p.115.
% 0.16/0.41
% 0.16/0.41 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.16/0.41 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.41 % Source : [Bro09]
% 0.16/0.41 % Names : tps_0067 [Bro09]
% 0.16/0.41 % : E1FUNC [TPS]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.16/0.41 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.41 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 3 ( 3 avg)
% 0.16/0.41 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.16/0.41 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 4 ( 4 avg)
% 0.16/0.41 % Number of types : 2 ( 0 usr)
% 0.16/0.41 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.16/0.41 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.16/0.41 % SPC : TH0_THM_EQU_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(g,type,
% 0.16/0.41 g: $i > $i ).
% 0.16/0.41
% 0.16/0.41 thf(p,type,
% 0.16/0.41 p: ( $i > $i ) > $o ).
% 0.16/0.41
% 0.16/0.41 thf(f,type,
% 0.16/0.41 f: $i > $i ).
% 0.16/0.41
% 0.16/0.41 thf(cE1FUNC,conjecture,
% 0.16/0.41 ( ! [X: $i] :
% 0.16/0.41 ( ( f @ X )
% 0.16/0.41 = ( g @ X ) )
% 0.16/0.41 => ( ( p @ f )
% 0.16/0.41 => ( p @ g ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.35/1.23 ---- Embedded in THF ---
% 1.35/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.35/1.23 %%% Generated on Tue Feb 24 14:28:11 EST 2026
% 1.35/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.35/1.23 %%% Logic specification used:
% 1.35/1.23 %%% thf(spec, logic, $$dhol).
% 1.35/1.23
% 1.35/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.GROJvTsL7B/DTF2DTF10251.p
% See solution above
% 1.35/1.23 ------------------------
% 1.35/1.24 ---- Cleaned THF ---
% 1.35/1.24 thf(g,type,
% 1.35/1.24 g: $i > $i ).
% 1.35/1.24
% 1.35/1.24 thf(p,type,
% 1.35/1.24 p: ( $i > $i ) > $o ).
% 1.35/1.24
% 1.35/1.24 thf(f,type,
% 1.35/1.24 f: $i > $i ).
% 1.35/1.24
% 1.35/1.24 thf(cE1FUNC,conjecture,
% 1.35/1.24 ( ! [X: $i] :
% 1.35/1.24 ( ( f @ X )
% 1.35/1.24 = ( g @ X ) )
% 1.35/1.24 => ( ( p @ f )
% 1.35/1.24 => ( p @ g ) ) ) ).
% 1.35/1.24 ------------------------
% 1.35/1.26 % (10360)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10251 for (2999ds/18Mi)
% 1.35/1.26 % (10355)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_10251 for (2999ds/4Mi)
% 1.35/1.26 % (10358)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_10251 for (2999ds/2Mi)
% 1.35/1.26 % (10357)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10251 for (2999ds/2Mi)
% 1.35/1.26 % (10359)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_10251 for (2999ds/275Mi)
% 1.35/1.26 % (10354)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10251 for (2999ds/183Mi)
% 1.35/1.26 % (10356)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_10251 for (2999ds/27Mi)
% 1.35/1.26 % (10358)Instruction limit reached!
% 1.35/1.26 % (10358)------------------------------
% 1.35/1.26 % (10358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.26 % (10358)Termination reason: Unknown
% 1.35/1.26 % (10358)Termination phase: Saturation
% 1.35/1.26
% 1.35/1.26 % (10358)Memory used [KB]: 5500
% 1.35/1.26 % (10358)Time elapsed: 0.003 s
% 1.35/1.26 % (10358)Instructions burned: 2 (million)
% 1.35/1.26 % (10358)------------------------------
% 1.35/1.26 % (10358)------------------------------
% 1.35/1.26 % (10359)Refutation not found, incomplete strategy
% 1.35/1.26 % (10359)------------------------------
% 1.35/1.26 % (10359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.26 % (10359)Termination reason: Refutation not found, incomplete strategy
% 1.35/1.26
% 1.35/1.26
% 1.35/1.26 % (10359)Memory used [KB]: 5500
% 1.35/1.26 % (10359)Time elapsed: 0.003 s
% 1.35/1.26 % (10359)Instructions burned: 1 (million)
% 1.35/1.26 % (10359)------------------------------
% 1.35/1.26 % (10359)------------------------------
% 1.35/1.26 % (10354)First to succeed.
% 1.35/1.26 % (10357)Refutation not found, incomplete strategy
% 1.35/1.26 % (10357)------------------------------
% 1.35/1.26 % (10357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.26 % (10357)Termination reason: Refutation not found, incomplete strategy
% 1.35/1.26
% 1.35/1.26
% 1.35/1.26 % (10357)Memory used [KB]: 5500
% 1.35/1.26 % (10357)Time elapsed: 0.003 s
% 1.35/1.26 % (10357)Instructions burned: 1 (million)
% 1.35/1.26 % (10357)------------------------------
% 1.35/1.26 % (10357)------------------------------
% 1.35/1.26 % (10356)Refutation not found, incomplete strategy
% 1.35/1.26 % (10356)------------------------------
% 1.35/1.26 % (10356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.26 % (10356)Termination reason: Refutation not found, incomplete strategy
% 1.35/1.26
% 1.35/1.26
% 1.35/1.26 % (10356)Memory used [KB]: 5500
% 1.35/1.26 % (10356)Time elapsed: 0.002 s
% 1.35/1.26 % (10356)Instructions burned: 1 (million)
% 1.35/1.26 % (10356)------------------------------
% 1.35/1.26 % (10356)------------------------------
% 1.35/1.26 % (10355)Refutation not found, incomplete strategy
% 1.35/1.26 % (10355)------------------------------
% 1.35/1.26 % (10355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.26 % (10355)Termination reason: Refutation not found, incomplete strategy
% 1.35/1.26
% 1.35/1.26
% 1.35/1.26 % (10355)Memory used [KB]: 5500
% 1.35/1.26 % (10355)Time elapsed: 0.003 s
% 1.35/1.26 % (10355)Instructions burned: 1 (million)
% 1.35/1.26 % (10355)------------------------------
% 1.35/1.26 % (10355)------------------------------
% 1.35/1.26 % (10360)Also succeeded, but the first one will report.
% 1.35/1.26 % (10354)Refutation found. Thanks to Tanya!
% 1.35/1.26 % SZS status Theorem for DTF2THF_10251
% 1.35/1.26 % SZS output start Proof for DTF2THF_10251
% 1.35/1.26 thf(func_def_0, type, g: $i > $i).
% 1.35/1.26 thf(func_def_1, type, p: ($i > $i) > $o).
% 1.35/1.26 thf(func_def_2, type, f: $i > $i).
% 1.35/1.26 thf(func_def_7, type, ph1: !>[X0: $tType]:(X0)).
% 1.35/1.26 thf(f14,plain,(
% 1.35/1.26 $false),
% 1.35/1.26 inference(subsumption_resolution,[status(thm)],[f13,f8])).
% 1.35/1.26 thf(f8,plain,(
% 1.35/1.26 ( ! [X0 : $i] : (((f @ X0) = (g @ X0))) )),
% 1.35/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.35/1.26 thf(f7,plain,(
% 1.35/1.26 ((p @ g) != $true) & ((p @ f) = $true) & ! [X0 : $i] : ((f @ X0) = (g @ X0))),
% 1.35/1.26 inference(flattening,[status(thm)],[f6])).
% 1.35/1.26 thf(f6,plain,(
% 1.35/1.26 (((p @ g) != $true) & ((p @ f) = $true)) & ! [X0 : $i] : ((f @ X0) = (g @ X0))),
% 1.35/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.35/1.26 thf(f5,plain,(
% 1.35/1.26 ~(! [X0 : $i] : ((f @ X0) = (g @ X0)) => (((p @ f) = $true) => ((p @ g) = $true)))),
% 1.35/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.35/1.26 thf(f4,plain,(
% 1.35/1.26 ~(! [X0 : $i] : ((f @ X0) = (g @ X0)) => ((p @ f) => (p @ g)))),
% 1.35/1.26 inference(rectify,[status(thm)],[f2])).
% 1.35/1.26 thf(f2,negated_conjecture,(
% 1.35/1.26 ~(! [X0 : $i] : ((f @ X0) = (g @ X0)) => ((p @ f) => (p @ g)))),
% 1.35/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.35/1.26 thf(f1,conjecture,(
% 1.35/1.26 ! [X0 : $i] : ((f @ X0) = (g @ X0)) => ((p @ f) => (p @ g))),
% 1.35/1.26 file('/export/starexec/sandbox/tmp/tmp.GROJvTsL7B/DTF2THF_10251.p',cE1FUNC)).
% 1.35/1.26 thf(f13,plain,(
% 1.35/1.26 ((f @ sK2) != (g @ sK2))),
% 1.35/1.26 inference(negative_extensionality,[status(thm)],[f12])).
% 1.35/1.26 thf(f12,plain,(
% 1.35/1.26 (f != g)),
% 1.35/1.26 inference(trivial_inequality_removal,[status(thm)],[f11])).
% 1.35/1.26 thf(f11,plain,(
% 1.35/1.26 (f != g) | ($true != $true)),
% 1.35/1.26 inference(constrained_superposition,[status(thm)],[f10,f9])).
% 1.35/1.26 thf(f9,plain,(
% 1.35/1.26 ((p @ f) = $true)),
% 1.35/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.35/1.26 thf(f10,plain,(
% 1.35/1.26 ((p @ g) != $true)),
% 1.35/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.35/1.26 % SZS output end Proof for DTF2THF_10251
% 1.35/1.26 % (10354)------------------------------
% 1.35/1.26 % (10354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.26 % (10354)Termination reason: Refutation
% 1.35/1.26
% 1.35/1.26 % (10354)Memory used [KB]: 5500
% 1.35/1.26 % (10354)Time elapsed: 0.003 s
% 1.35/1.26 % (10354)Instructions burned: 1 (million)
% 1.35/1.26 % (10354)------------------------------
% 1.35/1.26 % (10354)------------------------------
% 1.35/1.26 % (10353)Success in time 0.018 s
%------------------------------------------------------------------------------