%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO026^1 : 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 : n016.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 09:53:10 AM UTC 2026
% Result : Theorem 1.65s 1.30s
% Output : Refutation 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO026^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:22:06 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO026^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : Four functions from truth values to truth values
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : In Henkin semantics there are exactly four functions from truth
% 0.19/0.46 % values to truth values.
% 0.19/0.46
% 0.19/0.46 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.19/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Ben09]
% 0.19/0.46 % Names : Example 21 [BB05]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.30 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, 0.00 v5.4.0, 0.25 v5.3.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.67 v3.7.0
% 0.19/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.19/0.46 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 7 ( 7 avg)
% 0.19/0.46 % Number of connectives : 10 ( 1 ~; 0 |; 3 &; 5 @)
% 0.19/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.46 % Number of types : 1 ( 0 usr)
% 0.19/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 3 ( 1 usr; 2 con; 0-1 aty)
% 0.19/0.46 % Number of variables : 5 ( 4 ^; 1 !; 0 ?; 5 :)
% 0.19/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.46
% 0.19/0.46 % Comments :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(p_decl,type,
% 0.19/0.46 p: ( $o > $o ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf(conj,conjecture,
% 0.19/0.46 ( ( ( p
% 0.19/0.46 @ ^ [X: $o] : X )
% 0.19/0.46 & ( p
% 0.19/0.46 @ ^ [X: $o] : ~ X )
% 0.19/0.46 & ( p
% 0.19/0.46 @ ^ [X: $o] : $false )
% 0.19/0.46 & ( p
% 0.19/0.46 @ ^ [X: $o] : $true ) )
% 0.19/0.46 => ! [Y: $o > $o] : ( p @ Y ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 14:22:07 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MhiROYnFwT/DTF2DTF18565.p
% 1.47/1.27 thf(p_decl, type, p: (($o > $o) > $o)).
% 1.47/1.27 thf(conj, conjecture, (((p @ (^ [X:$o]: (X))) & ((p @ (^ [X:$o]: ((~ (X))))) & ((p @ (^ [X:$o]: ($false))) & (p @ (^ [X:$o]: ($true)))))) => (! [Y:($o > $o)]: ((p @ Y))))).
% 1.47/1.27 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MhiROYnFwT/DTF2DTF18565.p
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(p_decl,type,
% 1.47/1.28 p: ( $o > $o ) > $o ).
% 1.47/1.28
% 1.47/1.28 thf(conj,conjecture,
% 1.47/1.28 ( ( ( p
% 1.47/1.28 @ ^ [X: $o] : X )
% 1.47/1.28 & ( p
% 1.47/1.28 @ ^ [X: $o] : ~ X )
% 1.47/1.28 & ( p
% 1.47/1.28 @ ^ [X: $o] : $false )
% 1.47/1.28 & ( p
% 1.47/1.28 @ ^ [X: $o] : $true ) )
% 1.47/1.28 => ! [Y: $o > $o] : ( p @ Y ) ) ).
% 1.47/1.28 ------------------------
% 1.47/1.30 % (18725)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18565 for (2999ds/2Mi)
% 1.65/1.30 % (18722)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18565 for (2999ds/183Mi)
% 1.65/1.30 % (18725)Instruction limit reached!
% 1.65/1.30 % (18725)------------------------------
% 1.65/1.30 % (18725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (18725)Termination reason: Unknown
% 1.65/1.30 % (18725)Termination phase: Saturation
% 1.65/1.30
% 1.65/1.30 % (18725)Memory used [KB]: 5373
% 1.65/1.30 % (18725)Time elapsed: 0.002 s
% 1.65/1.30 % (18725)Instructions burned: 2 (million)
% 1.65/1.30 % (18725)------------------------------
% 1.65/1.30 % (18725)------------------------------
% 1.65/1.30 % (18722)First to succeed.
% 1.65/1.30 % (18723)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_18565 for (2999ds/4Mi)
% 1.65/1.30 % (18722)Refutation found. Thanks to Tanya!
% 1.65/1.30 % SZS status Theorem for DTF2THF_18565
% 1.65/1.30 % SZS output start Proof for DTF2THF_18565
% 1.65/1.30 thf(func_def_0, type, p: ($o > $o) > $o).
% 1.65/1.30 thf(func_def_7, type, sK0: $o > $o).
% 1.65/1.30 thf(func_def_9, type, ph2: !>[X0: $tType]:(X0)).
% 1.65/1.30 thf(f273,plain,(
% 1.65/1.30 $false),
% 1.65/1.30 inference(avatar_sat_refutation,[status(thm)],[f32,f41,f66,f81,f87,f121,f130,f136,f176,f202,f217,f267,f271])).
% 1.65/1.30 thf(f271,plain,(
% 1.65/1.30 spl1_3 | ~spl1_4 | ~spl1_7 | ~spl1_9),
% 1.65/1.30 inference(avatar_contradiction_clause,[status(thm)],[f270])).
% 1.65/1.30 thf(f270,plain,(
% 1.65/1.30 $false | (spl1_3 | ~spl1_4 | ~spl1_7 | ~spl1_9)),
% 1.65/1.30 inference(subsumption_resolution,[status(thm)],[f253,f252])).
% 1.65/1.30 thf(f252,plain,(
% 1.65/1.30 ((sK0 @ $true) != $false) | (spl1_3 | ~spl1_4)),
% 1.65/1.30 inference(superposition,[status(thm)],[f104,f251])).
% 1.65/1.30 thf(f251,plain,(
% 1.65/1.30 ($true = sK5) | (spl1_3 | ~spl1_4)),
% 1.65/1.30 inference(subsumption_resolution,[status(thm)],[f241,f35])).
% 1.65/1.30 thf(f35,plain,(
% 1.65/1.30 (sK3 != $true) | spl1_3),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.65/1.30 thf(f34,definition,(
% 1.65/1.30 spl1_3 <=> (sK3 = $true)),
% 1.65/1.30 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.65/1.30 thf(f241,plain,(
% 1.65/1.30 ($true = sK5) | (sK3 = $true) | ~spl1_4),
% 1.65/1.30 inference(binary_proxy_clausification,[status(thm)],[f240])).
% 1.65/1.30 thf(f240,plain,(
% 1.65/1.30 (sK3 != sK5) | ~spl1_4),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f238])).
% 1.65/1.30 thf(f238,plain,(
% 1.65/1.30 ($false != $false) | (sK3 != sK5) | ~spl1_4),
% 1.65/1.30 inference(constrained_superposition,[status(thm)],[f104,f40])).
% 1.65/1.30 thf(f40,plain,(
% 1.65/1.30 ($false = (sK0 @ sK3)) | ~spl1_4),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.65/1.30 thf(f38,definition,(
% 1.65/1.30 spl1_4 <=> ($false = (sK0 @ sK3))),
% 1.65/1.30 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.65/1.30 thf(f104,plain,(
% 1.65/1.30 ((sK0 @ sK5) != $false)),
% 1.65/1.30 inference(beta_eta_normalization,[status(thm)],[f103])).
% 1.65/1.30 thf(f103,plain,(
% 1.65/1.30 ((sK0 @ sK5) != ((^[Y0 : $o]: ($false)) @ sK5))),
% 1.65/1.30 inference(negative_extensionality,[status(thm)],[f59])).
% 1.65/1.30 thf(f59,plain,(
% 1.65/1.30 ((^[Y0 : $o]: ($false)) != sK0)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.65/1.30 thf(f58,plain,(
% 1.65/1.30 ((^[Y0 : $o]: ($false)) != sK0) | ($true != $true)),
% 1.65/1.30 inference(constrained_superposition,[status(thm)],[f15,f13])).
% 1.65/1.30 thf(f13,plain,(
% 1.65/1.30 ((p @ (^[Y0 : $o]: ($false))) = $true)),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.65/1.30 thf(f10,plain,(
% 1.65/1.30 ((p @ sK0) != $true) & ((p @ (^[Y0 : $o]: (Y0))) = $true) & ((p @ (^[Y0 : $o]: ($false))) = $true) & ($true = (p @ (^[Y0 : $o]: ($true)))) & ((p @ (^[Y0 : $o]: (~ Y0))) = $true)),
% 1.65/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.65/1.30 thf(f9,plain,(
% 1.65/1.30 ? [X0 : $o > $o] : ((p @ X0) != $true) => ((p @ sK0) != $true)),
% 1.65/1.30 introduced(definition,[],[choice_axiom])).
% 1.65/1.30 thf(f8,plain,(
% 1.65/1.30 ? [X0 : $o > $o] : ((p @ X0) != $true) & ((p @ (^[Y0 : $o]: (Y0))) = $true) & ((p @ (^[Y0 : $o]: ($false))) = $true) & ($true = (p @ (^[Y0 : $o]: ($true)))) & ((p @ (^[Y0 : $o]: (~ Y0))) = $true)),
% 1.65/1.30 inference(flattening,[status(thm)],[f7])).
% 1.65/1.30 thf(f7,plain,(
% 1.65/1.30 ? [X0 : $o > $o] : ((p @ X0) != $true) & (((p @ (^[Y0 : $o]: (~ Y0))) = $true) & ($true = (p @ (^[Y0 : $o]: ($true)))) & ((p @ (^[Y0 : $o]: (Y0))) = $true) & ((p @ (^[Y0 : $o]: ($false))) = $true))),
% 1.65/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.65/1.30 thf(f6,plain,(
% 1.65/1.30 ~((((p @ (^[Y0 : $o]: (~ Y0))) = $true) & ($true = (p @ (^[Y0 : $o]: ($true)))) & ((p @ (^[Y0 : $o]: (Y0))) = $true) & ((p @ (^[Y0 : $o]: ($false))) = $true)) => ! [X0 : $o > $o] : ((p @ X0) = $true))),
% 1.65/1.30 inference(rectify,[status(thm)],[f5])).
% 1.65/1.30 thf(f5,plain,(
% 1.65/1.30 ~((((p @ (^[Y0 : $o]: (~ Y0))) = $true) & ($true = (p @ (^[Y0 : $o]: ($true)))) & ((p @ (^[Y0 : $o]: (Y0))) = $true) & ((p @ (^[Y0 : $o]: ($false))) = $true)) => ! [X4 : $o > $o] : ((p @ X4) = $true))),
% 1.65/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.30 thf(f4,plain,(
% 1.65/1.30 ~(((p @ (^[X0 : $o] : ($false))) & (p @ (^[X1 : $o] : (~X1))) & (p @ (^[X2 : $o] : (X2))) & (p @ (^[X3 : $o] : ($true)))) => ! [X4 : $o > $o] : (p @ X4))),
% 1.65/1.30 inference(rectify,[status(thm)],[f2])).
% 1.65/1.30 thf(f2,negated_conjecture,(
% 1.65/1.30 ~(((p @ (^[X0 : $o] : ($false))) & (p @ (^[X0 : $o] : (~X0))) & (p @ (^[X0 : $o] : (X0))) & (p @ (^[X0 : $o] : ($true)))) => ! [X1 : $o > $o] : (p @ X1))),
% 1.65/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.30 thf(f1,conjecture,(
% 1.65/1.30 ((p @ (^[X0 : $o] : ($false))) & (p @ (^[X0 : $o] : (~X0))) & (p @ (^[X0 : $o] : (X0))) & (p @ (^[X0 : $o] : ($true)))) => ! [X1 : $o > $o] : (p @ X1)),
% 1.65/1.30 file('/export/starexec/sandbox2/tmp/tmp.MhiROYnFwT/DTF2THF_18565.p',conj)).
% 1.65/1.30 thf(f15,plain,(
% 1.65/1.30 ((p @ sK0) != $true)),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.65/1.30 thf(f253,plain,(
% 1.65/1.30 ((sK0 @ $true) = $false) | (~spl1_7 | ~spl1_9)),
% 1.65/1.30 inference(superposition,[status(thm)],[f125,f116])).
% 1.65/1.30 thf(f116,plain,(
% 1.65/1.30 (sK6 = $true) | ~spl1_7),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f114])).
% 1.65/1.30 thf(f114,definition,(
% 1.65/1.30 spl1_7 <=> (sK6 = $true)),
% 1.65/1.30 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.65/1.30 thf(f125,plain,(
% 1.65/1.30 ((sK0 @ sK6) = $false) | ~spl1_9),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f123])).
% 1.65/1.30 thf(f123,definition,(
% 1.65/1.30 spl1_9 <=> ((sK0 @ sK6) = $false)),
% 1.65/1.30 introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition])).
% 1.65/1.30 thf(f267,plain,(
% 1.65/1.30 ~spl1_8 | ~spl1_9),
% 1.65/1.30 inference(avatar_contradiction_clause,[status(thm)],[f266])).
% 1.65/1.30 thf(f266,plain,(
% 1.65/1.30 $false | (~spl1_8 | ~spl1_9)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f258])).
% 1.65/1.30 thf(f258,plain,(
% 1.65/1.30 ($true = $false) | (~spl1_8 | ~spl1_9)),
% 1.65/1.30 inference(superposition,[status(thm)],[f120,f125])).
% 1.65/1.30 thf(f120,plain,(
% 1.65/1.30 ((sK0 @ sK6) = $true) | ~spl1_8),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f118])).
% 1.65/1.30 thf(f118,definition,(
% 1.65/1.30 spl1_8 <=> ((sK0 @ sK6) = $true)),
% 1.65/1.30 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.65/1.30 thf(f217,plain,(
% 1.65/1.30 spl1_7 | spl1_2 | spl1_3 | ~spl1_8),
% 1.65/1.30 inference(avatar_split_clause,[status(thm)],[f216,f118,f34,f29,f114])).
% 1.65/1.30 thf(f29,definition,(
% 1.65/1.30 spl1_2 <=> ($true = (sK0 @ sK3))),
% 1.65/1.30 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.65/1.30 thf(f216,plain,(
% 1.65/1.30 (sK6 = $true) | (spl1_2 | spl1_3 | ~spl1_8)),
% 1.65/1.30 inference(subsumption_resolution,[status(thm)],[f209,f35])).
% 1.65/1.30 thf(f209,plain,(
% 1.65/1.30 (sK6 = $true) | (sK3 = $true) | (spl1_2 | ~spl1_8)),
% 1.65/1.30 inference(binary_proxy_clausification,[status(thm)],[f208])).
% 1.65/1.30 thf(f208,plain,(
% 1.65/1.30 (sK3 != sK6) | (spl1_2 | ~spl1_8)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.65/1.30 thf(f207,plain,(
% 1.65/1.30 ($true != $true) | (sK3 != sK6) | (spl1_2 | ~spl1_8)),
% 1.65/1.30 inference(constrained_superposition,[status(thm)],[f30,f120])).
% 1.65/1.30 thf(f30,plain,(
% 1.65/1.30 ($true != (sK0 @ sK3)) | spl1_2),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.65/1.30 thf(f202,plain,(
% 1.65/1.30 spl1_6 | spl1_7 | ~spl1_8),
% 1.65/1.30 inference(avatar_contradiction_clause,[status(thm)],[f201])).
% 1.65/1.30 thf(f201,plain,(
% 1.65/1.30 $false | (spl1_6 | spl1_7 | ~spl1_8)),
% 1.65/1.30 inference(subsumption_resolution,[status(thm)],[f200,f115])).
% 1.65/1.30 thf(f115,plain,(
% 1.65/1.30 (sK6 != $true) | spl1_7),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f114])).
% 1.65/1.30 thf(f200,plain,(
% 1.65/1.30 (sK6 = $true) | (spl1_6 | ~spl1_8)),
% 1.65/1.30 inference(subsumption_resolution,[status(thm)],[f191,f69])).
% 1.65/1.30 thf(f69,plain,(
% 1.65/1.30 (sK4 != $true) | spl1_6),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.65/1.30 thf(f68,definition,(
% 1.65/1.30 spl1_6 <=> (sK4 = $true)),
% 1.65/1.30 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.65/1.30 thf(f191,plain,(
% 1.65/1.30 (sK6 = $true) | (sK4 = $true) | ~spl1_8),
% 1.65/1.30 inference(binary_proxy_clausification,[status(thm)],[f190])).
% 1.65/1.30 thf(f190,plain,(
% 1.65/1.30 (sK4 != sK6) | ~spl1_8),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f186])).
% 1.65/1.30 thf(f186,plain,(
% 1.65/1.30 ($true != $true) | (sK4 != sK6) | ~spl1_8),
% 1.65/1.30 inference(constrained_superposition,[status(thm)],[f46,f120])).
% 1.65/1.30 thf(f46,plain,(
% 1.65/1.30 ($true != (sK0 @ sK4))),
% 1.65/1.30 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.65/1.30 thf(f45,plain,(
% 1.65/1.30 (((^[Y0 : $o]: ($true)) @ sK4) != (sK0 @ sK4))),
% 1.65/1.30 inference(negative_extensionality,[status(thm)],[f44])).
% 1.65/1.30 thf(f44,plain,(
% 1.65/1.30 ((^[Y0 : $o]: ($true)) != sK0)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.65/1.30 thf(f43,plain,(
% 1.65/1.30 ((^[Y0 : $o]: ($true)) != sK0) | ($true != $true)),
% 1.65/1.30 inference(constrained_superposition,[status(thm)],[f15,f12])).
% 1.65/1.30 thf(f12,plain,(
% 1.65/1.30 ($true = (p @ (^[Y0 : $o]: ($true))))),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.65/1.30 thf(f176,plain,(
% 1.65/1.30 ~spl1_3 | spl1_4 | ~spl1_7 | ~spl1_9),
% 1.65/1.30 inference(avatar_contradiction_clause,[status(thm)],[f175])).
% 1.65/1.30 thf(f175,plain,(
% 1.65/1.30 $false | (~spl1_3 | spl1_4 | ~spl1_7 | ~spl1_9)),
% 1.65/1.30 inference(subsumption_resolution,[status(thm)],[f138,f92])).
% 1.65/1.30 thf(f92,plain,(
% 1.65/1.30 ((sK0 @ $true) != $false) | (~spl1_3 | spl1_4)),
% 1.65/1.30 inference(superposition,[status(thm)],[f39,f36])).
% 1.65/1.30 thf(f36,plain,(
% 1.65/1.30 (sK3 = $true) | ~spl1_3),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.65/1.30 thf(f39,plain,(
% 1.65/1.30 ($false != (sK0 @ sK3)) | spl1_4),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.65/1.30 thf(f138,plain,(
% 1.65/1.30 ((sK0 @ $true) = $false) | (~spl1_7 | ~spl1_9)),
% 1.65/1.30 inference(superposition,[status(thm)],[f125,f116])).
% 1.65/1.30 thf(f136,plain,(
% 1.65/1.30 ~spl1_7 | ~spl1_10),
% 1.65/1.30 inference(avatar_contradiction_clause,[status(thm)],[f135])).
% 1.65/1.30 thf(f135,plain,(
% 1.65/1.30 $false | (~spl1_7 | ~spl1_10)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.65/1.30 thf(f132,plain,(
% 1.65/1.30 ($true = $false) | (~spl1_7 | ~spl1_10)),
% 1.65/1.30 inference(superposition,[status(thm)],[f116,f129])).
% 1.65/1.30 thf(f129,plain,(
% 1.65/1.30 (sK6 = $false) | ~spl1_10),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f127])).
% 1.65/1.30 thf(f127,definition,(
% 1.65/1.30 spl1_10 <=> (sK6 = $false)),
% 1.65/1.30 introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition])).
% 1.65/1.30 thf(f130,plain,(
% 1.65/1.30 spl1_9 | spl1_10),
% 1.65/1.30 inference(avatar_split_clause,[status(thm)],[f112,f127,f123])).
% 1.65/1.30 thf(f112,plain,(
% 1.65/1.30 (sK6 = $false) | ((sK0 @ sK6) = $false)),
% 1.65/1.30 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.65/1.30 thf(f110,plain,(
% 1.65/1.30 (sK6 != (sK0 @ sK6))),
% 1.65/1.30 inference(beta_eta_normalization,[status(thm)],[f109])).
% 1.65/1.30 thf(f109,plain,(
% 1.65/1.30 (((^[Y0 : $o]: (Y0)) @ sK6) != (sK0 @ sK6))),
% 1.65/1.30 inference(negative_extensionality,[status(thm)],[f91])).
% 1.65/1.30 thf(f91,plain,(
% 1.65/1.30 ((^[Y0 : $o]: (Y0)) != sK0)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.65/1.30 thf(f90,plain,(
% 1.65/1.30 ($true != $true) | ((^[Y0 : $o]: (Y0)) != sK0)),
% 1.65/1.30 inference(constrained_superposition,[status(thm)],[f15,f14])).
% 1.65/1.30 thf(f14,plain,(
% 1.65/1.30 ((p @ (^[Y0 : $o]: (Y0))) = $true)),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.65/1.30 thf(f121,plain,(
% 1.65/1.30 spl1_7 | spl1_8),
% 1.65/1.30 inference(avatar_split_clause,[status(thm)],[f111,f118,f114])).
% 1.65/1.30 thf(f111,plain,(
% 1.65/1.30 ((sK0 @ sK6) = $true) | (sK6 = $true)),
% 1.65/1.30 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.65/1.30 thf(f87,plain,(
% 1.65/1.30 ~spl1_2 | ~spl1_3 | ~spl1_6),
% 1.65/1.30 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 1.65/1.30 thf(f86,plain,(
% 1.65/1.30 $false | (~spl1_2 | ~spl1_3 | ~spl1_6)),
% 1.65/1.30 inference(subsumption_resolution,[status(thm)],[f85,f73])).
% 1.65/1.30 thf(f73,plain,(
% 1.65/1.30 ((sK0 @ $true) != $true) | ~spl1_6),
% 1.65/1.30 inference(superposition,[status(thm)],[f46,f70])).
% 1.65/1.30 thf(f70,plain,(
% 1.65/1.30 (sK4 = $true) | ~spl1_6),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.65/1.30 thf(f85,plain,(
% 1.65/1.30 ((sK0 @ $true) = $true) | (~spl1_2 | ~spl1_3)),
% 1.65/1.30 inference(superposition,[status(thm)],[f31,f36])).
% 1.65/1.30 thf(f31,plain,(
% 1.65/1.30 ($true = (sK0 @ sK3)) | ~spl1_2),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.65/1.30 thf(f81,plain,(
% 1.65/1.30 ~spl1_2 | ~spl1_4),
% 1.65/1.30 inference(avatar_contradiction_clause,[status(thm)],[f80])).
% 1.65/1.30 thf(f80,plain,(
% 1.65/1.30 $false | (~spl1_2 | ~spl1_4)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.65/1.30 thf(f75,plain,(
% 1.65/1.30 ($true = $false) | (~spl1_2 | ~spl1_4)),
% 1.65/1.30 inference(superposition,[status(thm)],[f40,f31])).
% 1.65/1.30 thf(f66,plain,(
% 1.65/1.30 ~spl1_1 | ~spl1_3),
% 1.65/1.30 inference(avatar_contradiction_clause,[status(thm)],[f65])).
% 1.65/1.30 thf(f65,plain,(
% 1.65/1.30 $false | (~spl1_1 | ~spl1_3)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.65/1.30 thf(f60,plain,(
% 1.65/1.30 ($true = $false) | (~spl1_1 | ~spl1_3)),
% 1.65/1.30 inference(superposition,[status(thm)],[f27,f36])).
% 1.65/1.30 thf(f27,plain,(
% 1.65/1.30 (sK3 = $false) | ~spl1_1),
% 1.65/1.30 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.65/1.30 thf(f25,definition,(
% 1.65/1.30 spl1_1 <=> (sK3 = $false)),
% 1.65/1.30 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.65/1.30 thf(f41,plain,(
% 1.65/1.30 spl1_3 | spl1_4),
% 1.65/1.30 inference(avatar_split_clause,[status(thm)],[f22,f38,f34])).
% 1.65/1.30 thf(f22,plain,(
% 1.65/1.30 (sK3 = $true) | ($false = (sK0 @ sK3))),
% 1.65/1.30 inference(not_proxy_clausification,[status(thm)],[f21])).
% 1.65/1.30 thf(f21,plain,(
% 1.65/1.30 ($false = (sK0 @ sK3)) | ($false = (~ sK3))),
% 1.65/1.30 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.65/1.30 thf(f19,plain,(
% 1.65/1.30 ((~ sK3) != (sK0 @ sK3))),
% 1.65/1.30 inference(negative_extensionality,[status(thm)],[f18])).
% 1.65/1.30 thf(f18,plain,(
% 1.65/1.30 (~ != sK0)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.65/1.30 thf(f17,plain,(
% 1.65/1.30 (~ != sK0) | ($true != $true)),
% 1.65/1.30 inference(constrained_superposition,[status(thm)],[f15,f16])).
% 1.65/1.30 thf(f16,plain,(
% 1.65/1.30 ((p @ ~) = $true)),
% 1.65/1.30 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.65/1.30 thf(f11,plain,(
% 1.65/1.30 ((p @ (^[Y0 : $o]: (~ Y0))) = $true)),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.65/1.30 thf(f32,plain,(
% 1.65/1.30 spl1_1 | spl1_2),
% 1.65/1.30 inference(avatar_split_clause,[status(thm)],[f23,f29,f25])).
% 1.65/1.30 thf(f23,plain,(
% 1.65/1.30 ($true = (sK0 @ sK3)) | (sK3 = $false)),
% 1.65/1.30 inference(not_proxy_clausification,[status(thm)],[f20])).
% 1.65/1.30 thf(f20,plain,(
% 1.65/1.30 ($true = (sK0 @ sK3)) | ($true = (~ sK3))),
% 1.65/1.30 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.65/1.30 % SZS output end Proof for DTF2THF_18565
% 1.65/1.30 % (18722)------------------------------
% 1.65/1.30 % (18722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (18722)Termination reason: Refutation
% 1.65/1.30
% 1.65/1.30 % (18722)Memory used [KB]: 5628
% 1.65/1.30 % (18722)Time elapsed: 0.006 s
% 1.65/1.30 % (18722)Instructions burned: 9 (million)
% 1.65/1.30 % (18722)------------------------------
% 1.65/1.30 % (18722)------------------------------
% 1.65/1.30 % (18721)Success in time 0.018 s
%------------------------------------------------------------------------------