%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO018^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 09:53:09 AM UTC 2026
% Result : Theorem 1.68s 1.43s
% Output : Refutation 1.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO018^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n002.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:21:33 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SYO018^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.48 % Domain : Syntactic
% 0.20/0.48 % Problem : Formula requiring b and Eta
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.20/0.48 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Ben09]
% 0.20/0.48 % Names : Example 19 [BB05]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % : Without Boolean extensionality : CounterSatisfiable
% 0.20/0.48 % : Without eta extensionality : CounterSatisfiable
% 0.20/0.48 % Rating : 0.17 v9.1.0, 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.5.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.0.0, 0.50 v4.1.0, 0.67 v4.0.0, 0.33 v3.7.0
% 0.20/0.48 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.20/0.48 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 8 ( 8 avg)
% 0.20/0.48 % Number of connectives : 13 ( 0 ~; 0 |; 2 &; 10 @)
% 0.20/0.48 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 11 ( 11 avg)
% 0.20/0.48 % Number of types : 2 ( 0 usr)
% 0.20/0.48 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.20/0.48 % Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 0.20/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.48
% 0.20/0.48 % Comments :
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(f,type,
% 0.20/0.48 f: $o > $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(p,type,
% 0.20/0.48 p: ( $i > $i ) > $o ).
% 0.20/0.48
% 0.20/0.48 thf(a,type,
% 0.20/0.48 a: ( $i > $i ) > $o ).
% 0.20/0.48
% 0.20/0.48 thf(b,type,
% 0.20/0.48 b: $o ).
% 0.20/0.48
% 0.20/0.48 thf(conj,conjecture,
% 0.20/0.48 ( ( p
% 0.20/0.48 @ ^ [X: $i] :
% 0.20/0.48 ( f
% 0.20/0.48 @ ( ( a
% 0.20/0.48 @ ^ [X: $i] : ( f @ b @ X ) )
% 0.20/0.48 & b )
% 0.20/0.48 @ X ) )
% 0.20/0.48 => ( p
% 0.20/0.48 @ ( f
% 0.20/0.48 @ ( b
% 0.20/0.48 & ( a @ ( f @ b ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.49/1.39 ---- Embedded in THF ---
% 1.49/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.39 %%% Generated on Tue Feb 24 14:21:34 EST 2026
% 1.49/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.39 %%% Logic specification used:
% 1.49/1.39 %%% thf(spec, logic, $$dhol).
% 1.49/1.39
% 1.49/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LiSl7e39qB/DTF2DTF29984.p
% 1.49/1.39 thf(f, type, f: ($o > ($i > $i))).
% 1.49/1.39 thf(p, type, p: (($i > $i) > $o)).
% 1.49/1.39 thf(a, type, a: (($i > $i) > $o)).
% 1.49/1.39 thf(b, type, b: $o).
% 1.49/1.39 thf(conj, conjecture, ((p @ (^ [X:$i]: (((f @ ((a @ (^ [X:$i]: (((f @ b) @ X)))) & b)) @ X)))) => (p @ (f @ (b & (a @ (f @ b))))))).
% 1.49/1.39 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.LiSl7e39qB/DTF2DTF29984.p
% 1.49/1.39 ------------------------
% 1.68/1.40 ---- Cleaned THF ---
% 1.68/1.40 thf(f,type,
% 1.68/1.40 f: $o > $i > $i ).
% 1.68/1.40
% 1.68/1.40 thf(p,type,
% 1.68/1.40 p: ( $i > $i ) > $o ).
% 1.68/1.40
% 1.68/1.40 thf(a,type,
% 1.68/1.40 a: ( $i > $i ) > $o ).
% 1.68/1.40
% 1.68/1.40 thf(b,type,
% 1.68/1.40 b: $o ).
% 1.68/1.40
% 1.68/1.40 thf(conj,conjecture,
% 1.68/1.40 ( ( p
% 1.68/1.40 @ ^ [X: $i] :
% 1.68/1.40 ( f
% 1.68/1.40 @ ( ( a
% 1.68/1.40 @ ^ [X: $i] : ( f @ b @ X ) )
% 1.68/1.40 & b )
% 1.68/1.40 @ X ) )
% 1.68/1.40 => ( p
% 1.68/1.40 @ ( f
% 1.68/1.40 @ ( b
% 1.68/1.40 & ( a @ ( f @ b ) ) ) ) ) ) ).
% 1.68/1.40 ------------------------
% 1.68/1.42 % (30082)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29984 for (3000ds/183Mi)
% 1.68/1.42 % (30083)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_29984 for (3000ds/4Mi)
% 1.68/1.42 % (30084)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_29984 for (3000ds/27Mi)
% 1.68/1.42 % (30085)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29984 for (3000ds/2Mi)
% 1.68/1.42 % (30086)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_29984 for (3000ds/2Mi)
% 1.68/1.42 % (30087)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_29984 for (3000ds/275Mi)
% 1.68/1.42 % (30088)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29984 for (3000ds/18Mi)
% 1.68/1.42 % (30086)First to succeed.
% 1.68/1.42 % (30087)Also succeeded, but the first one will report.
% 1.68/1.42 % (30085)Also succeeded, but the first one will report.
% 1.68/1.43 % (30086)Refutation found. Thanks to Tanya!
% 1.68/1.43 % SZS status Theorem for DTF2THF_29984
% 1.68/1.43 % SZS output start Proof for DTF2THF_29984
% 1.68/1.43 thf(func_def_0, type, f: $o > $i > $i).
% 1.68/1.43 thf(func_def_1, type, p: ($i > $i) > $o).
% 1.68/1.43 thf(func_def_2, type, a: ($i > $i) > $o).
% 1.68/1.43 thf(f10,plain,(
% 1.68/1.43 $false),
% 1.68/1.43 inference(trivial_inequality_removal,[status(thm)],[f9])).
% 1.68/1.43 thf(f9,plain,(
% 1.68/1.43 ($false = $true)),
% 1.68/1.43 inference(boolean_simplification,[status(thm)],[f8])).
% 1.68/1.43 thf(f8,plain,(
% 1.68/1.43 ((~ $true) = $true)),
% 1.68/1.43 inference(boolean_simplification,[status(thm)],[f7])).
% 1.68/1.43 thf(f7,plain,(
% 1.68/1.43 ($true = (~ ((p @ (f @ ((a @ (f @ b)) & b))) => (p @ (f @ ((a @ (f @ b)) & b))))))),
% 1.68/1.43 inference(beta_eta_normalization,[status(thm)],[f6])).
% 1.68/1.43 thf(f6,plain,(
% 1.68/1.43 ($true = (~ ((p @ (^[Y0 : $i]: (f @ ((a @ (^[Y1 : $i]: (f @ b @ Y1))) & b) @ Y0))) => (p @ (f @ ((a @ (f @ b)) & b))))))),
% 1.68/1.43 inference(cnf_transformation,[status(thm)],[f5])).
% 1.68/1.43 thf(f5,plain,(
% 1.68/1.43 ($true = (~ ((p @ (^[Y0 : $i]: (f @ ((a @ (^[Y1 : $i]: (f @ b @ Y1))) & b) @ Y0))) => (p @ (f @ ((a @ (f @ b)) & b))))))),
% 1.68/1.43 inference(fool_elimination,[status(thm)],[f4])).
% 1.68/1.43 thf(f4,plain,(
% 1.68/1.43 ~((p @ (^[X0 : $i] : (f @ b & (a @ (^[X1 : $i] : (f @ b @ X1))) @ X0))) => (p @ (f @ b & (a @ (f @ b)))))),
% 1.68/1.43 inference(rectify,[status(thm)],[f2])).
% 1.68/1.43 thf(f2,negated_conjecture,(
% 1.68/1.43 ~((p @ (^[X0 : $i] : (f @ b & (a @ (^[X0 : $i] : (f @ b @ X0))) @ X0))) => (p @ (f @ b & (a @ (f @ b)))))),
% 1.68/1.43 inference(negated_conjecture,[status(cth)],[f1])).
% 1.68/1.43 thf(f1,conjecture,(
% 1.68/1.43 (p @ (^[X0 : $i] : (f @ b & (a @ (^[X0 : $i] : (f @ b @ X0))) @ X0))) => (p @ (f @ b & (a @ (f @ b))))),
% 1.68/1.43 file('/export/starexec/sandbox/tmp/tmp.LiSl7e39qB/DTF2THF_29984.p',conj)).
% 1.68/1.43 % SZS output end Proof for DTF2THF_29984
% 1.68/1.43 % (30086)------------------------------
% 1.68/1.43 % (30086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.43 % (30086)Termination reason: Refutation
% 1.68/1.43
% 1.68/1.43 % (30086)Memory used [KB]: 5373
% 1.68/1.43 % (30086)Time elapsed: 0.003 s
% 1.68/1.43 % (30086)Instructions burned: 1 (million)
% 1.68/1.43 % (30086)------------------------------
% 1.68/1.43 % (30086)------------------------------
% 1.68/1.43 % (30081)Success in time 0.018 s
%------------------------------------------------------------------------------