%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO012^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 09:53:08 AM UTC 2026
% Result : Theorem 1.53s 1.32s
% Output : Refutation 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO012^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n017.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 14:19:56 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 : SYO012^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : Formula valid with Boolean extentionality 1
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.16/0.39 % : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.16/0.39 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Ben09]
% 0.16/0.39 % Names : Example 15a [BB05]
% 0.16/0.39 % : E2ext [Ben99]
% 0.16/0.39 % : E2EXT [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % : Without Boolean extensionality : CounterSatisfiable
% 0.16/0.39 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 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 v5.0.0, 0.50 v4.1.0, 0.67 v4.0.0, 0.33 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.39 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 6 ( 6 avg)
% 0.16/0.39 % Number of connectives : 5 ( 0 ~; 0 |; 2 &; 2 @)
% 0.16/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 4 ( 4 avg)
% 0.16/0.39 % Number of types : 1 ( 0 usr)
% 0.16/0.39 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 3 ( 3 usr; 2 con; 0-1 aty)
% 0.16/0.39 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments :
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(a,type,
% 0.16/0.39 a: $o ).
% 0.16/0.39
% 0.16/0.39 thf(b,type,
% 0.16/0.39 b: $o ).
% 0.16/0.39
% 0.16/0.39 thf(p,type,
% 0.16/0.39 p: $o > $o ).
% 0.16/0.39
% 0.16/0.39 thf(conj,conjecture,
% 0.16/0.39 ( ( p
% 0.16/0.39 @ ( a
% 0.16/0.39 & b ) )
% 0.16/0.39 => ( p
% 0.16/0.39 @ ( b
% 0.16/0.39 & a ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.34/1.29 ---- Embedded in THF ---
% 1.34/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.34/1.29 %%% Generated on Tue Feb 24 14:19:56 EST 2026
% 1.34/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.34/1.29 %%% Logic specification used:
% 1.34/1.29 %%% thf(spec, logic, $$dhol).
% 1.34/1.29
% 1.34/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.kEVCTjdGh3/DTF2DTF3916.p
% 1.34/1.29 thf(a, type, a: $o).
% 1.34/1.29 thf(b, type, b: $o).
% 1.34/1.29 thf(p, type, p: ($o > $o)).
% 1.34/1.29 thf(conj, conjecture, ((p @ (a & b)) => (p @ (b & a)))).
% 1.34/1.29 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.kEVCTjdGh3/DTF2DTF3916.p
% 1.34/1.29 ------------------------
% 1.53/1.30 ---- Cleaned THF ---
% 1.53/1.30 thf(a,type,
% 1.53/1.30 a: $o ).
% 1.53/1.30
% 1.53/1.30 thf(b,type,
% 1.53/1.30 b: $o ).
% 1.53/1.30
% 1.53/1.30 thf(p,type,
% 1.53/1.30 p: $o > $o ).
% 1.53/1.30
% 1.53/1.30 thf(conj,conjecture,
% 1.53/1.30 ( ( p
% 1.53/1.30 @ ( a
% 1.53/1.30 & b ) )
% 1.53/1.30 => ( p
% 1.53/1.30 @ ( b
% 1.53/1.30 & a ) ) ) ).
% 1.53/1.30 ------------------------
% 1.53/1.32 % (4019)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_3916 for (3000ds/275Mi)
% 1.53/1.32 % (4020)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3916 for (3000ds/18Mi)
% 1.53/1.32 % (4017)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3916 for (3000ds/2Mi)
% 1.53/1.32 % (4016)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_3916 for (3000ds/27Mi)
% 1.53/1.32 % (4018)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_3916 for (3000ds/2Mi)
% 1.53/1.32 % (4014)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3916 for (3000ds/183Mi)
% 1.53/1.32 % (4015)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_3916 for (3000ds/4Mi)
% 1.53/1.32 % (4018)First to succeed.
% 1.53/1.32 % (4019)Refutation not found, incomplete strategy
% 1.53/1.32 % (4019)------------------------------
% 1.53/1.32 % (4019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (4017)Refutation not found, incomplete strategy
% 1.53/1.32 % (4017)------------------------------
% 1.53/1.32 % (4017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (4019)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.32
% 1.53/1.32
% 1.53/1.32 % (4019)Memory used [KB]: 5373
% 1.53/1.32 % (4019)Time elapsed: 0.002 s
% 1.53/1.32 % (4019)Instructions burned: 1 (million)
% 1.53/1.32 % (4019)------------------------------
% 1.53/1.32 % (4019)------------------------------
% 1.53/1.32 % (4017)Termination reason: Refutation not found, incomplete strategy
% 1.53/1.32
% 1.53/1.32
% 1.53/1.32 % (4017)Memory used [KB]: 5500
% 1.53/1.32 % (4017)Time elapsed: 0.003 s
% 1.53/1.32 % (4017)Instructions burned: 1 (million)
% 1.53/1.32 % (4014)Also succeeded, but the first one will report.
% 1.53/1.32 % (4017)------------------------------
% 1.53/1.32 % (4017)------------------------------
% 1.53/1.32 % (4020)Also succeeded, but the first one will report.
% 1.53/1.32 % (4018)Refutation found. Thanks to Tanya!
% 1.53/1.32 % SZS status Theorem for DTF2THF_3916
% 1.53/1.32 % SZS output start Proof for DTF2THF_3916
% 1.53/1.32 thf(func_def_2, type, p: $o > $o).
% 1.53/1.32 thf(f9,plain,(
% 1.53/1.32 $false),
% 1.53/1.32 inference(trivial_inequality_removal,[status(thm)],[f8])).
% 1.53/1.32 thf(f8,plain,(
% 1.53/1.32 ($true = $false)),
% 1.53/1.32 inference(boolean_simplification,[status(thm)],[f7])).
% 1.53/1.32 thf(f7,plain,(
% 1.53/1.32 ($true = (~ $true))),
% 1.53/1.32 inference(boolean_simplification,[status(thm)],[f6])).
% 1.53/1.32 thf(f6,plain,(
% 1.53/1.32 ($true = (~ ((p @ (b & a)) => (p @ (b & a)))))),
% 1.53/1.32 inference(cnf_transformation,[status(thm)],[f5])).
% 1.53/1.32 thf(f5,plain,(
% 1.53/1.32 ($true = (~ ((p @ (b & a)) => (p @ (b & a)))))),
% 1.53/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.32 thf(f4,plain,(
% 1.53/1.32 ~((p @ a & b) => (p @ a & b))),
% 1.53/1.32 inference(rectify,[status(thm)],[f2])).
% 1.53/1.32 thf(f2,negated_conjecture,(
% 1.53/1.32 ~((p @ a & b) => (p @ a & b))),
% 1.53/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.32 thf(f1,conjecture,(
% 1.53/1.32 (p @ a & b) => (p @ a & b)),
% 1.53/1.32 file('/export/starexec/sandbox2/tmp/tmp.kEVCTjdGh3/DTF2THF_3916.p',conj)).
% 1.53/1.32 % SZS output end Proof for DTF2THF_3916
% 1.53/1.32 % (4018)------------------------------
% 1.53/1.32 % (4018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.32 % (4018)Termination reason: Refutation
% 1.53/1.32
% 1.53/1.32 % (4018)Memory used [KB]: 5373
% 1.53/1.32 % (4018)Time elapsed: 0.003 s
% 1.53/1.32 % (4018)Instructions burned: 1 (million)
% 1.53/1.32 % (4018)------------------------------
% 1.53/1.32 % (4018)------------------------------
% 1.53/1.32 % (4013)Success in time 0.017 s
%------------------------------------------------------------------------------