%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO502^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 09:54:24 AM UTC 2026
% Result : Theorem 1.80s 1.50s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 34 ( 8 ~; 4 |; 2 &; 20 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
f: $i > $i ).
thf(func_def_3,type,
g: $i > $i ).
thf(f10,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f8,f9]) ).
thf(f9,plain,
( ( g @ b )
!= ( f @ b ) ),
inference(definition_unfolding,[status(thm)],[f5,f7]) ).
thf(f7,plain,
a = b,
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( a = b )
& ( ( f @ a )
= ( g @ b ) )
& ( ( f @ b )
!= ( g @ a ) ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( a != b )
| ( ( f @ b )
= ( g @ a ) )
| ( ( f @ a )
!= ( g @ b ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( a != b )
| ( ( f @ b )
= ( g @ a ) )
| ( ( f @ a )
!= ( g @ b ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BYQcrpb5CC/DTF2THF_20625.p',claim) ).
thf(f5,plain,
( ( f @ b )
!= ( g @ a ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f8,plain,
( ( g @ b )
= ( f @ b ) ),
inference(definition_unfolding,[status(thm)],[f6,f7]) ).
thf(f6,plain,
( ( f @ a )
= ( g @ b ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO502^1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n013.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 14:32:38 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.43 ---- Original DTF file ---
% 0.18/0.43 thf(spec,logic,$$dhol).
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 % File : SYO502^1 : TPTP v9.2.1. Released v4.1.0.
% 0.18/0.43 % Domain : Syntactic
% 0.18/0.43 % Problem : Rules sym and con handle positive equations at i
% 0.18/0.43 % Version : Especial.
% 0.18/0.43 % English :
% 0.18/0.43
% 0.18/0.43 % Refs : [BS09a] Brown & Smolka (2009), Terminating Tableaux for the Ba
% 0.18/0.43 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.18/0.43 % : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.18/0.43 % Source : [Bro09]
% 0.18/0.43 % Names : Example 3.2 [BS09a]
% 0.18/0.43 % : basic7 [Bro09]
% 0.18/0.43
% 0.18/0.43 % Status : Theorem
% 0.18/0.43 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0
% 0.18/0.43 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.18/0.43 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.18/0.43 % Maximal formula atoms : 3 ( 3 avg)
% 0.18/0.43 % Number of connectives : 8 ( 2 ~; 2 |; 0 &; 4 @)
% 0.18/0.43 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.43 % Maximal formula depth : 4 ( 4 avg)
% 0.18/0.43 % Number of types : 1 ( 0 usr)
% 0.18/0.43 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.18/0.43 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.18/0.43 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.18/0.43 % SPC : TH0_THM_EQU_NAR
% 0.18/0.43
% 0.18/0.43 % Comments : The fragment of simple type theory that restricts equations to
% 0.18/0.43 % base types and disallows lambda abstraction and quantification is
% 0.18/0.43 % decidable. This is an example.
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 thf(a,type,
% 0.18/0.43 a: $i ).
% 0.18/0.43
% 0.18/0.43 thf(b,type,
% 0.18/0.43 b: $i ).
% 0.18/0.43
% 0.18/0.43 thf(f,type,
% 0.18/0.43 f: $i > $i ).
% 0.18/0.43
% 0.18/0.43 thf(g,type,
% 0.18/0.43 g: $i > $i ).
% 0.18/0.43
% 0.18/0.43 thf(claim,conjecture,
% 0.18/0.43 ( ( a != b )
% 0.18/0.43 | ( ( f @ a )
% 0.18/0.43 != ( g @ b ) )
% 0.18/0.43 | ( ( f @ b )
% 0.18/0.43 = ( g @ a ) ) ) ).
% 0.18/0.43
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 ------------------------
% 1.65/1.46 ---- Embedded in THF ---
% 1.65/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.46 %%% Generated on Tue Feb 24 14:32:39 EST 2026
% 1.65/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.46 %%% Logic specification used:
% 1.65/1.46 %%% thf(spec, logic, $$dhol).
% 1.65/1.46
% 1.65/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BYQcrpb5CC/DTF2DTF20625.p
% See solution above
% 1.65/1.46 ------------------------
% 1.65/1.47 ---- Cleaned THF ---
% 1.65/1.47 thf(a,type,
% 1.65/1.47 a: $i ).
% 1.65/1.47
% 1.65/1.47 thf(b,type,
% 1.65/1.47 b: $i ).
% 1.65/1.47
% 1.65/1.47 thf(f,type,
% 1.65/1.47 f: $i > $i ).
% 1.65/1.47
% 1.65/1.47 thf(g,type,
% 1.65/1.47 g: $i > $i ).
% 1.65/1.47
% 1.65/1.47 thf(claim,conjecture,
% 1.65/1.47 ( ( a != b )
% 1.65/1.47 | ( ( f @ a )
% 1.65/1.47 != ( g @ b ) )
% 1.65/1.47 | ( ( f @ b )
% 1.65/1.47 = ( g @ a ) ) ) ).
% 1.65/1.47 ------------------------
% 1.65/1.49 % (20726)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_20625 for (2999ds/2Mi)
% 1.65/1.49 % (20722)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20625 for (2999ds/183Mi)
% 1.65/1.49 % (20728)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20625 for (2999ds/18Mi)
% 1.65/1.50 % (20725)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20625 for (2999ds/2Mi)
% 1.65/1.50 % (20722)First to succeed.
% 1.65/1.50 % (20724)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_20625 for (2999ds/27Mi)
% 1.65/1.50 % (20727)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_20625 for (2999ds/275Mi)
% 1.65/1.50 % (20725)Also succeeded, but the first one will report.
% 1.80/1.50 % (20723)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_20625 for (2999ds/4Mi)
% 1.80/1.50 % (20726)Instruction limit reached!
% 1.80/1.50 % (20726)------------------------------
% 1.80/1.50 % (20726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.50 % (20726)Termination reason: Unknown
% 1.80/1.50 % (20726)Termination phase: Saturation
% 1.80/1.50
% 1.80/1.50 % (20726)Memory used [KB]: 5500
% 1.80/1.50 % (20726)Time elapsed: 0.004 s
% 1.80/1.50 % (20726)Instructions burned: 3 (million)
% 1.80/1.50 % (20726)------------------------------
% 1.80/1.50 % (20726)------------------------------
% 1.80/1.50 % (20728)Also succeeded, but the first one will report.
% 1.80/1.50 % (20722)Refutation found. Thanks to Tanya!
% 1.80/1.50 % SZS status Theorem for DTF2THF_20625
% 1.80/1.50 % SZS output start Proof for DTF2THF_20625
% 1.80/1.50 thf(func_def_2, type, f: $i > $i).
% 1.80/1.50 thf(func_def_3, type, g: $i > $i).
% 1.80/1.50 thf(f10,plain,(
% 1.80/1.50 $false),
% 1.80/1.50 inference(subsumption_resolution,[status(thm)],[f8,f9])).
% 1.80/1.50 thf(f9,plain,(
% 1.80/1.50 ((g @ b) != (f @ b))),
% 1.80/1.50 inference(definition_unfolding,[status(thm)],[f5,f7])).
% 1.80/1.50 thf(f7,plain,(
% 1.80/1.50 (a = b)),
% 1.80/1.50 inference(cnf_transformation,[status(thm)],[f4])).
% 1.80/1.50 thf(f4,plain,(
% 1.80/1.50 (a = b) & ((f @ a) = (g @ b)) & ((f @ b) != (g @ a))),
% 1.80/1.50 inference(ennf_transformation,[status(thm)],[f2])).
% 1.80/1.50 thf(f2,negated_conjecture,(
% 1.80/1.50 ~((a != b) | ((f @ b) = (g @ a)) | ((f @ a) != (g @ b)))),
% 1.80/1.50 inference(negated_conjecture,[status(cth)],[f1])).
% 1.80/1.50 thf(f1,conjecture,(
% 1.80/1.50 (a != b) | ((f @ b) = (g @ a)) | ((f @ a) != (g @ b))),
% 1.80/1.50 file('/export/starexec/sandbox/tmp/tmp.BYQcrpb5CC/DTF2THF_20625.p',claim)).
% 1.80/1.50 thf(f5,plain,(
% 1.80/1.50 ((f @ b) != (g @ a))),
% 1.80/1.50 inference(cnf_transformation,[status(thm)],[f4])).
% 1.80/1.50 thf(f8,plain,(
% 1.80/1.50 ((g @ b) = (f @ b))),
% 1.80/1.50 inference(definition_unfolding,[status(thm)],[f6,f7])).
% 1.80/1.50 thf(f6,plain,(
% 1.80/1.50 ((f @ a) = (g @ b))),
% 1.80/1.50 inference(cnf_transformation,[status(thm)],[f4])).
% 1.80/1.50 % SZS output end Proof for DTF2THF_20625
% 1.80/1.50 % (20722)------------------------------
% 1.80/1.50 % (20722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.50 % (20722)Termination reason: Refutation
% 1.80/1.50
% 1.80/1.50 % (20722)Memory used [KB]: 5373
% 1.80/1.50 % (20722)Time elapsed: 0.003 s
% 1.80/1.50 % (20722)Instructions burned: 1 (million)
% 1.80/1.50 % (20722)------------------------------
% 1.80/1.50 % (20722)------------------------------
% 1.80/1.50 % (20721)Success in time 0.02 s
%------------------------------------------------------------------------------