%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN983^1 : TPTP v9.2.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 09:51:38 AM UTC 2026
% Result : Theorem 1.66s 1.41s
% Output : Refutation 1.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN983^1 : TPTP v9.2.1. Released v3.6.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.30 % Computer : n011.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue Feb 24 14:20:17 EST 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SYN983^1 : TPTP v9.2.1. Released v3.6.0.
% 0.17/0.40 % Domain : Syntactic
% 0.17/0.40 % Problem : Factoring application over conjunction
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English :
% 0.17/0.40
% 0.17/0.40 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.17/0.40 % : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher-Ord
% 0.17/0.40 % : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% 0.17/0.40 % Source : [Ben08]
% 0.17/0.40 % Names : BB-1 [Ben08]
% 0.17/0.40 % : E3ext [Ben99]
% 0.17/0.40 % : E3EXT [TPS]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % : Without Boolean extensionality : CounterSatisfiable
% 0.17/0.40 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 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 v6.0.0, 0.17 v5.5.0, 0.00 v5.4.0, 0.25 v5.3.0, 0.50 v4.1.0, 0.67 v4.0.0, 0.33 v3.7.0
% 0.17/0.40 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.17/0.40 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 7 ( 7 avg)
% 0.17/0.40 % Number of connectives : 6 ( 0 ~; 0 |; 2 &; 3 @)
% 0.17/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 4 ( 4 avg)
% 0.17/0.40 % Number of types : 1 ( 0 usr)
% 0.17/0.40 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 3 ( 3 usr; 2 con; 0-1 aty)
% 0.17/0.40 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.17/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.40
% 0.17/0.40 % Comments :
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(a_const,type,
% 0.17/0.40 a: $o ).
% 0.17/0.40
% 0.17/0.40 thf(b_const,type,
% 0.17/0.40 b: $o ).
% 0.17/0.40
% 0.17/0.40 thf(p_const,type,
% 0.17/0.40 p: $o > $o ).
% 0.17/0.40
% 0.17/0.40 thf(thm,conjecture,
% 0.17/0.40 ( ( ( p @ a )
% 0.17/0.40 & ( p @ b ) )
% 0.17/0.40 => ( p
% 0.17/0.40 @ ( a
% 0.17/0.40 & b ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.49/1.37 ---- Embedded in THF ---
% 1.49/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.37 %%% Generated on Tue Feb 24 14:20:18 EST 2026
% 1.49/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.37 %%% Logic specification used:
% 1.49/1.37 %%% thf(spec, logic, $$dhol).
% 1.49/1.37
% 1.49/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.J6oMaTookn/DTF2DTF15730.p
% 1.49/1.37 thf(a_const, type, a: $o).
% 1.49/1.37 thf(b_const, type, b: $o).
% 1.49/1.37 thf(p_const, type, p: ($o > $o)).
% 1.49/1.37 thf(thm, conjecture, (((p @ a) & (p @ b)) => (p @ (a & b)))).
% 1.49/1.37 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.J6oMaTookn/DTF2DTF15730.p
% 1.49/1.37 ------------------------
% 1.49/1.38 ---- Cleaned THF ---
% 1.49/1.38 thf(a_const,type,
% 1.49/1.38 a: $o ).
% 1.49/1.38
% 1.49/1.38 thf(b_const,type,
% 1.49/1.38 b: $o ).
% 1.49/1.38
% 1.49/1.38 thf(p_const,type,
% 1.49/1.38 p: $o > $o ).
% 1.49/1.38
% 1.49/1.38 thf(thm,conjecture,
% 1.49/1.38 ( ( ( p @ a )
% 1.49/1.38 & ( p @ b ) )
% 1.49/1.38 => ( p
% 1.49/1.38 @ ( a
% 1.49/1.38 & b ) ) ) ).
% 1.49/1.38 ------------------------
% 1.66/1.40 % (15831)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15730 for (3000ds/2Mi)
% 1.66/1.40 % (15830)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_15730 for (3000ds/27Mi)
% 1.66/1.40 % (15833)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_15730 for (3000ds/275Mi)
% 1.66/1.40 % (15828)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15730 for (3000ds/183Mi)
% 1.66/1.40 % (15829)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_15730 for (3000ds/4Mi)
% 1.66/1.40 % (15834)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15730 for (3000ds/18Mi)
% 1.66/1.40 % (15833)Refutation not found, incomplete strategy
% 1.66/1.40 % (15833)------------------------------
% 1.66/1.40 % (15833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (15833)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.40
% 1.66/1.40 % (15831)Refutation not found, incomplete strategy
% 1.66/1.40 % (15831)------------------------------
% 1.66/1.40 % (15831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (15831)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.40
% 1.66/1.40
% 1.66/1.40 % (15831)Memory used [KB]: 5500
% 1.66/1.40 % (15831)Time elapsed: 0.003 s
% 1.66/1.40 % (15831)Instructions burned: 1 (million)
% 1.66/1.40 % (15831)------------------------------
% 1.66/1.40 % (15831)------------------------------
% 1.66/1.40 % (15830)Refutation not found, incomplete strategy
% 1.66/1.40 % (15830)------------------------------
% 1.66/1.40 % (15830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40
% 1.66/1.40 % (15833)Memory used [KB]: 5373
% 1.66/1.40 % (15833)Time elapsed: 0.003 s
% 1.66/1.40 % (15833)Instructions burned: 1 (million)
% 1.66/1.40 % (15833)------------------------------
% 1.66/1.40 % (15833)------------------------------
% 1.66/1.40 % (15830)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.40
% 1.66/1.40
% 1.66/1.40 % (15830)Memory used [KB]: 5500
% 1.66/1.40 % (15830)Time elapsed: 0.003 s
% 1.66/1.40 % (15830)Instructions burned: 1 (million)
% 1.66/1.40 % (15830)------------------------------
% 1.66/1.40 % (15830)------------------------------
% 1.66/1.40 % (15832)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_15730 for (3000ds/2Mi)
% 1.66/1.41 % (15828)First to succeed.
% 1.66/1.41 % (15834)Also succeeded, but the first one will report.
% 1.66/1.41 % (15828)Refutation found. Thanks to Tanya!
% 1.66/1.41 % SZS status Theorem for DTF2THF_15730
% 1.66/1.41 % SZS output start Proof for DTF2THF_15730
% 1.66/1.41 thf(func_def_2, type, p: $o > $o).
% 1.66/1.41 thf(func_def_8, type, ph1: !>[X0: $tType]:(X0)).
% 1.66/1.41 thf(f61,plain,(
% 1.66/1.41 $false),
% 1.66/1.41 inference(avatar_sat_refutation,[status(thm)],[f50,f55,f60])).
% 1.66/1.41 thf(f60,plain,(
% 1.66/1.41 ~spl0_3),
% 1.66/1.41 inference(avatar_contradiction_clause,[status(thm)],[f59])).
% 1.66/1.41 thf(f59,plain,(
% 1.66/1.41 $false | ~spl0_3),
% 1.66/1.41 inference(subsumption_resolution,[status(thm)],[f58,f57])).
% 1.66/1.41 thf(f57,plain,(
% 1.66/1.41 ((p @ $false) = $true) | ~spl0_3),
% 1.66/1.41 inference(superposition,[status(thm)],[f9,f42])).
% 1.66/1.41 thf(f42,plain,(
% 1.66/1.41 (a = $false) | ~spl0_3),
% 1.66/1.41 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.66/1.41 thf(f40,definition,(
% 1.66/1.41 spl0_3 <=> (a = $false)),
% 1.66/1.41 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.66/1.41 thf(f9,plain,(
% 1.66/1.41 ((p @ a) = $true)),
% 1.66/1.41 inference(cnf_transformation,[status(thm)],[f7])).
% 1.66/1.41 thf(f7,plain,(
% 1.66/1.41 ((p @ (a & b)) != $true) & ((p @ a) = $true) & ((p @ b) = $true)),
% 1.66/1.41 inference(flattening,[status(thm)],[f6])).
% 1.66/1.41 thf(f6,plain,(
% 1.66/1.41 ((p @ (a & b)) != $true) & (((p @ b) = $true) & ((p @ a) = $true))),
% 1.66/1.41 inference(ennf_transformation,[status(thm)],[f5])).
% 1.66/1.41 thf(f5,plain,(
% 1.66/1.41 ~((((p @ b) = $true) & ((p @ a) = $true)) => ((p @ (a & b)) = $true))),
% 1.66/1.41 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.41 thf(f4,plain,(
% 1.66/1.41 ~(((p @ b) & (p @ a)) => (p @ b & a))),
% 1.66/1.41 inference(rectify,[status(thm)],[f2])).
% 1.66/1.41 thf(f2,negated_conjecture,(
% 1.66/1.41 ~(((p @ b) & (p @ a)) => (p @ b & a))),
% 1.66/1.41 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.41 thf(f1,conjecture,(
% 1.66/1.41 ((p @ b) & (p @ a)) => (p @ b & a)),
% 1.66/1.41 file('/export/starexec/sandbox/tmp/tmp.J6oMaTookn/DTF2THF_15730.p',thm)).
% 1.66/1.41 thf(f58,plain,(
% 1.66/1.41 ((p @ $false) != $true) | ~spl0_3),
% 1.66/1.41 inference(boolean_simplification,[status(thm)],[f56])).
% 1.66/1.41 thf(f56,plain,(
% 1.66/1.41 ((p @ ($false & b)) != $true) | ~spl0_3),
% 1.66/1.41 inference(superposition,[status(thm)],[f10,f42])).
% 1.66/1.41 thf(f10,plain,(
% 1.66/1.41 ((p @ (a & b)) != $true)),
% 1.66/1.41 inference(cnf_transformation,[status(thm)],[f7])).
% 1.66/1.41 thf(f55,plain,(
% 1.66/1.41 ~spl0_4),
% 1.66/1.41 inference(avatar_contradiction_clause,[status(thm)],[f54])).
% 1.66/1.41 thf(f54,plain,(
% 1.66/1.41 $false | ~spl0_4),
% 1.66/1.41 inference(subsumption_resolution,[status(thm)],[f52,f53])).
% 1.66/1.41 thf(f53,plain,(
% 1.66/1.41 ((p @ $false) != $true) | ~spl0_4),
% 1.66/1.41 inference(boolean_simplification,[status(thm)],[f51])).
% 1.66/1.41 thf(f51,plain,(
% 1.66/1.41 ((p @ (a & $false)) != $true) | ~spl0_4),
% 1.66/1.41 inference(superposition,[status(thm)],[f10,f46])).
% 1.66/1.41 thf(f46,plain,(
% 1.66/1.41 (b = $false) | ~spl0_4),
% 1.66/1.41 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.66/1.41 thf(f44,definition,(
% 1.66/1.41 spl0_4 <=> (b = $false)),
% 1.66/1.41 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.66/1.41 thf(f52,plain,(
% 1.66/1.41 ((p @ $false) = $true) | ~spl0_4),
% 1.66/1.41 inference(superposition,[status(thm)],[f8,f46])).
% 1.66/1.41 thf(f8,plain,(
% 1.66/1.41 ((p @ b) = $true)),
% 1.66/1.41 inference(cnf_transformation,[status(thm)],[f7])).
% 1.66/1.41 thf(f50,plain,(
% 1.66/1.41 spl0_4 | spl0_3),
% 1.66/1.41 inference(avatar_split_clause,[status(thm)],[f17,f40,f44])).
% 1.66/1.41 thf(f17,plain,(
% 1.66/1.41 (b = $false) | (a = $false)),
% 1.66/1.41 inference(duplicate_literal_removal,[status(thm)],[f16])).
% 1.66/1.41 thf(f16,plain,(
% 1.66/1.41 (b = $false) | (a = $false) | (b = $false)),
% 1.66/1.41 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.66/1.41 thf(f15,plain,(
% 1.66/1.41 (b = $false) | ((a & b) = $false)),
% 1.66/1.41 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.66/1.41 thf(f13,plain,(
% 1.66/1.41 (b != (a & b))),
% 1.66/1.41 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.66/1.41 thf(f12,plain,(
% 1.66/1.41 ($true != $true) | (b != (a & b))),
% 1.66/1.41 inference(constrained_superposition,[status(thm)],[f10,f8])).
% 1.66/1.41 % SZS output end Proof for DTF2THF_15730
% 1.66/1.41 % (15828)------------------------------
% 1.66/1.41 % (15828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (15828)Termination reason: Refutation
% 1.66/1.41
% 1.66/1.41 % (15828)Memory used [KB]: 5500
% 1.66/1.41 % (15828)Time elapsed: 0.004 s
% 1.66/1.41 % (15828)Instructions burned: 2 (million)
% 1.66/1.41 % (15828)------------------------------
% 1.66/1.41 % (15828)------------------------------
% 1.66/1.41 % (15827)Success in time 0.019 s
%------------------------------------------------------------------------------