%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO501^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 1.64s 1.41s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 5 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 64 ( 22 ~; 6 |; 0 &; 36 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
f: $i > $o > $i ).
thf(func_def_3,type,
p: $i > $o ).
thf(f10,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f9]) ).
thf(f9,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ~ $true ) = $true ),
inference(boolean_simplification,[status(thm)],[f7]) ).
thf(f7,plain,
( $true
= ( ~ ( ~ ( p @ ( f @ x @ y ) )
| ( p @ ( f @ x @ y ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( ~ ( p
@ ( f @ x
@ ~ ~ y ) )
| ( p @ ( f @ x @ y ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ~ ( p
@ ( f @ x
@ ~ ~ y ) )
| ( p @ ( f @ x @ y ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( p @ ( f @ x @ y ) )
| ~ ( p
@ ( f @ x
@ ~ ~ y ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( p @ ( f @ x @ y ) )
| ~ ( p
@ ( f @ x
@ ~ ~ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( p @ ( f @ x @ y ) )
| ~ ( p
@ ( f @ x
@ ~ ~ y ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7SmSTSU5jh/DTF2THF_15510.p',claim) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO501^1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.36 % Computer : n026.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Tue Feb 24 14:33:10 EST 2026
% 0.18/0.36 % CPUTime :
% 0.18/0.36 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO501^1 : TPTP v9.2.1. Released v4.1.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : An unsatisfiable normal set with embedded formulas
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BS09a] Brown & Smolka (2009), Terminating Tableaux for the Ba
% 0.30/0.46 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.30/0.46 % : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : Example 3.1 [BS09a]
% 0.30/0.46 % : basic6 [Bro09]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v4.1.0
% 0.30/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.30/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.30/0.46 % Number of connectives : 10 ( 3 ~; 1 |; 0 &; 6 @)
% 0.30/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : The fragment of simple type theory that restricts equations to
% 0.30/0.46 % base types and disallows lambda abstraction and quantification is
% 0.30/0.46 % decidable. This is an example.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(x,type,
% 0.30/0.46 x: $i ).
% 0.30/0.46
% 0.30/0.46 thf(y,type,
% 0.30/0.46 y: $o ).
% 0.30/0.46
% 0.30/0.46 thf(f,type,
% 0.30/0.46 f: $i > $o > $i ).
% 0.30/0.46
% 0.30/0.46 thf(p,type,
% 0.30/0.46 p: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(claim,conjecture,
% 0.30/0.46 ( ~ ( p
% 0.30/0.46 @ ( f @ x
% 0.30/0.46 @ ~ ~ y ) )
% 0.30/0.46 | ( p @ ( f @ x @ y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.48/1.37 ---- Embedded in THF ---
% 1.48/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.38 %%% Generated on Tue Feb 24 14:33:11 EST 2026
% 1.48/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.38 %%% Logic specification used:
% 1.48/1.38 %%% thf(spec, logic, $$dhol).
% 1.48/1.38
% 1.48/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7SmSTSU5jh/DTF2DTF15510.p
% See solution above
% 1.48/1.38 ------------------------
% 1.48/1.38 ---- Cleaned THF ---
% 1.48/1.38 thf(x,type,
% 1.48/1.38 x: $i ).
% 1.48/1.38
% 1.48/1.38 thf(y,type,
% 1.48/1.38 y: $o ).
% 1.48/1.38
% 1.48/1.38 thf(f,type,
% 1.48/1.38 f: $i > $o > $i ).
% 1.48/1.38
% 1.48/1.38 thf(p,type,
% 1.48/1.38 p: $i > $o ).
% 1.48/1.38
% 1.48/1.38 thf(claim,conjecture,
% 1.48/1.38 ( ~ ( p
% 1.48/1.38 @ ( f @ x
% 1.48/1.38 @ ~ ~ y ) )
% 1.48/1.38 | ( p @ ( f @ x @ y ) ) ) ).
% 1.48/1.38 ------------------------
% 1.64/1.40 % (15609)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_15510 for (3000ds/27Mi)
% 1.64/1.40 % (15610)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15510 for (3000ds/2Mi)
% 1.64/1.40 % (15607)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15510 for (3000ds/183Mi)
% 1.64/1.40 % (15608)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_15510 for (3000ds/4Mi)
% 1.64/1.40 % (15612)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_15510 for (3000ds/275Mi)
% 1.64/1.40 % (15611)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_15510 for (3000ds/2Mi)
% 1.64/1.40 % (15613)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15510 for (3000ds/18Mi)
% 1.64/1.40 % (15611)First to succeed.
% 1.64/1.41 % (15607)Also succeeded, but the first one will report.
% 1.64/1.41 % (15612)Also succeeded, but the first one will report.
% 1.64/1.41 % (15611)Refutation found. Thanks to Tanya!
% 1.64/1.41 % SZS status Theorem for DTF2THF_15510
% 1.64/1.41 % SZS output start Proof for DTF2THF_15510
% 1.64/1.41 thf(func_def_2, type, f: $i > $o > $i).
% 1.64/1.41 thf(func_def_3, type, p: $i > $o).
% 1.64/1.41 thf(f10,plain,(
% 1.64/1.41 $false),
% 1.64/1.41 inference(trivial_inequality_removal,[status(thm)],[f9])).
% 1.64/1.41 thf(f9,plain,(
% 1.64/1.41 ($true = $false)),
% 1.64/1.41 inference(boolean_simplification,[status(thm)],[f8])).
% 1.64/1.41 thf(f8,plain,(
% 1.64/1.41 ((~ $true) = $true)),
% 1.64/1.41 inference(boolean_simplification,[status(thm)],[f7])).
% 1.64/1.41 thf(f7,plain,(
% 1.64/1.41 ($true = (~ ((~ (p @ (f @ x @ y))) | (p @ (f @ x @ y)))))),
% 1.64/1.41 inference(boolean_simplification,[status(thm)],[f6])).
% 1.64/1.41 thf(f6,plain,(
% 1.64/1.41 ($true = (~ ((~ (p @ (f @ x @ (~ (~ y))))) | (p @ (f @ x @ y)))))),
% 1.64/1.41 inference(cnf_transformation,[status(thm)],[f5])).
% 1.64/1.41 thf(f5,plain,(
% 1.64/1.41 ($true = (~ ((~ (p @ (f @ x @ (~ (~ y))))) | (p @ (f @ x @ y)))))),
% 1.64/1.41 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.41 thf(f4,plain,(
% 1.64/1.41 ~((p @ (f @ x @ y)) | ~(p @ (f @ x @ ~~y)))),
% 1.64/1.41 inference(rectify,[status(thm)],[f2])).
% 1.64/1.41 thf(f2,negated_conjecture,(
% 1.64/1.41 ~((p @ (f @ x @ y)) | ~(p @ (f @ x @ ~~y)))),
% 1.64/1.41 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.41 thf(f1,conjecture,(
% 1.64/1.41 (p @ (f @ x @ y)) | ~(p @ (f @ x @ ~~y))),
% 1.64/1.41 file('/export/starexec/sandbox2/tmp/tmp.7SmSTSU5jh/DTF2THF_15510.p',claim)).
% 1.64/1.41 % SZS output end Proof for DTF2THF_15510
% 1.64/1.41 % (15611)------------------------------
% 1.64/1.41 % (15611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.41 % (15611)Termination reason: Refutation
% 1.64/1.41
% 1.64/1.41 % (15611)Memory used [KB]: 5373
% 1.64/1.41 % (15611)Time elapsed: 0.003 s
% 1.64/1.41 % (15611)Instructions burned: 1 (million)
% 1.64/1.41 % (15611)------------------------------
% 1.64/1.41 % (15611)------------------------------
% 1.64/1.41 % (15606)Success in time 0.012 s
%------------------------------------------------------------------------------