%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO290^5 : 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 : n021.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 09:53:52 AM UTC 2026
% Result : Theorem 0.23s 1.33s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 4 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 45 ( 10 ~; 5 |; 0 &; 30 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 10 ^; 0 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
g2: a > a ).
thf(func_def_2,type,
g1: a > a ).
thf(func_def_3,type,
p: ( a > a ) > $o ).
thf(f9,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f8]) ).
thf(f8,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ~ $true ) = $true ),
inference(boolean_simplification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ( p
@ ^ [Y0: a] : ( g1 @ ( g2 @ Y0 ) ) )
| ~ ( p
@ ^ [Y0: a] : ( g1 @ ( g2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ( p
@ ^ [Y0: a] : ( g1 @ ( g2 @ Y0 ) ) )
| ~ ( p
@ ^ [Y0: a] : ( g1 @ ( g2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ~ ( p
@ ^ [X0: a] : ( g1 @ ( g2 @ X0 ) ) )
| ( p
@ ^ [X1: a] : ( g1 @ ( g2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ~ ( p
@ ^ [X0: a] : ( g1 @ ( g2 @ X0 ) ) )
| ( p
@ ^ [X1: a] : ( g1 @ ( g2 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ~ ( p
@ ^ [X0: a] : ( g1 @ ( g2 @ X0 ) ) )
| ( p
@ ^ [X1: a] : ( g1 @ ( g2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KQNfs734lC/DTF2THF_9181.p',cTRANS_BUG_EX2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO290^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n021.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
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 14:27:38 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : SYO290^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : TPS problem from BASIC-HO-THMS
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0696 [Bro09]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.16/0.39 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 2 ( 2 avg)
% 0.16/0.39 % Number of connectives : 8 ( 1 ~; 1 |; 0 &; 6 @)
% 0.16/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 7 ( 7 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.16/0.39 % Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 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(a_type,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(g2,type,
% 0.16/0.39 g2: a > a ).
% 0.16/0.39
% 0.16/0.39 thf(g1,type,
% 0.16/0.39 g1: a > a ).
% 0.16/0.39
% 0.16/0.39 thf(p,type,
% 0.16/0.39 p: ( a > a ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cTRANS_BUG_EX2,conjecture,
% 0.16/0.39 ( ~ ( p
% 0.16/0.39 @ ^ [Xw: a] : ( g1 @ ( g2 @ Xw ) ) )
% 0.16/0.39 | ( p
% 0.16/0.39 @ ^ [Xx: a] : ( g1 @ ( g2 @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 0.23/1.30 ---- Embedded in THF ---
% 0.23/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.23/1.30 %%% Generated on Tue Feb 24 14:27:39 EST 2026
% 0.23/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.23/1.30 %%% Logic specification used:
% 0.23/1.30 %%% thf(spec, logic, $$dhol).
% 0.23/1.30
% 0.23/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.KQNfs734lC/DTF2DTF9181.p
% See solution above
% 0.23/1.30 ------------------------
% 0.23/1.31 ---- Cleaned THF ---
% 0.23/1.31 thf(a_type,type,
% 0.23/1.31 a: $tType ).
% 0.23/1.31
% 0.23/1.31 thf(g2,type,
% 0.23/1.31 g2: a > a ).
% 0.23/1.31
% 0.23/1.31 thf(g1,type,
% 0.23/1.31 g1: a > a ).
% 0.23/1.31
% 0.23/1.31 thf(p,type,
% 0.23/1.31 p: ( a > a ) > $o ).
% 0.23/1.31
% 0.23/1.31 thf(cTRANS_BUG_EX2,conjecture,
% 0.23/1.31 ( ~ ( p
% 0.23/1.31 @ ^ [Xw: a] : ( g1 @ ( g2 @ Xw ) ) )
% 0.23/1.31 | ( p
% 0.23/1.31 @ ^ [Xx: a] : ( g1 @ ( g2 @ Xx ) ) ) ) ).
% 0.23/1.31 ------------------------
% 0.23/1.33 % (9281)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_9181 for (3000ds/27Mi)
% 0.23/1.33 % (9282)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9181 for (3000ds/2Mi)
% 0.23/1.33 % (9283)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_9181 for (3000ds/2Mi)
% 0.23/1.33 % (9279)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9181 for (3000ds/183Mi)
% 0.23/1.33 % (9284)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_9181 for (3000ds/275Mi)
% 0.23/1.33 % (9280)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_9181 for (3000ds/4Mi)
% 0.23/1.33 % (9285)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9181 for (3000ds/18Mi)
% 0.23/1.33 % (9283)First to succeed.
% 0.23/1.33 % (9279)Also succeeded, but the first one will report.
% 0.23/1.33 % (9280)Also succeeded, but the first one will report.
% 0.23/1.33 % (9283)Refutation found. Thanks to Tanya!
% 0.23/1.33 % SZS status Theorem for DTF2THF_9181
% 0.23/1.33 % SZS output start Proof for DTF2THF_9181
% 0.23/1.33 thf(type_def_5, type, a: $tType).
% 0.23/1.33 thf(func_def_0, type, a: $tType).
% 0.23/1.33 thf(func_def_1, type, g2: a > a).
% 0.23/1.33 thf(func_def_2, type, g1: a > a).
% 0.23/1.33 thf(func_def_3, type, p: (a > a) > $o).
% 0.23/1.33 thf(f9,plain,(
% 0.23/1.33 $false),
% 0.23/1.33 inference(trivial_inequality_removal,[status(thm)],[f8])).
% 0.23/1.33 thf(f8,plain,(
% 0.23/1.33 ($false = $true)),
% 0.23/1.33 inference(boolean_simplification,[status(thm)],[f7])).
% 0.23/1.33 thf(f7,plain,(
% 0.23/1.33 ((~ $true) = $true)),
% 0.23/1.33 inference(boolean_simplification,[status(thm)],[f6])).
% 0.23/1.33 thf(f6,plain,(
% 0.23/1.33 ($true = (~ ((p @ (^[Y0 : a]: (g1 @ (g2 @ Y0)))) | (~ (p @ (^[Y0 : a]: (g1 @ (g2 @ Y0))))))))),
% 0.23/1.33 inference(cnf_transformation,[status(thm)],[f5])).
% 0.23/1.33 thf(f5,plain,(
% 0.23/1.33 ($true = (~ ((p @ (^[Y0 : a]: (g1 @ (g2 @ Y0)))) | (~ (p @ (^[Y0 : a]: (g1 @ (g2 @ Y0))))))))),
% 0.23/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 0.23/1.33 thf(f4,plain,(
% 0.23/1.33 ~(~(p @ (^[X0 : a] : (g1 @ (g2 @ X0)))) | (p @ (^[X1 : a] : (g1 @ (g2 @ X1)))))),
% 0.23/1.33 inference(rectify,[status(thm)],[f2])).
% 0.23/1.33 thf(f2,negated_conjecture,(
% 0.23/1.33 ~(~(p @ (^[X0 : a] : (g1 @ (g2 @ X0)))) | (p @ (^[X1 : a] : (g1 @ (g2 @ X1)))))),
% 0.23/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/1.33 thf(f1,conjecture,(
% 0.23/1.33 ~(p @ (^[X0 : a] : (g1 @ (g2 @ X0)))) | (p @ (^[X1 : a] : (g1 @ (g2 @ X1))))),
% 0.23/1.33 file('/export/starexec/sandbox/tmp/tmp.KQNfs734lC/DTF2THF_9181.p',cTRANS_BUG_EX2)).
% 0.23/1.33 % SZS output end Proof for DTF2THF_9181
% 0.23/1.33 % (9283)------------------------------
% 0.23/1.33 % (9283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.33 % (9283)Termination reason: Refutation
% 0.23/1.33
% 0.23/1.33 % (9283)Memory used [KB]: 5373
% 0.23/1.33 % (9283)Time elapsed: 0.003 s
% 0.23/1.33 % (9283)Instructions burned: 1 (million)
% 0.23/1.33 % (9283)------------------------------
% 0.23/1.33 % (9283)------------------------------
% 0.23/1.33 % (9278)Success in time 0.018 s
%------------------------------------------------------------------------------