%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO020^1 : 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 : n005.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 1.49s 1.27s
% Output : Refutation 1.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO020^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:21:29 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO020^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : De Morgan by Leibnitz
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.18/0.45 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Ben09]
% 0.18/0.45 % Names : Example 20b [BB05]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % : Without Boolean extensionality : CounterSatisfiable
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.00 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 1 def)
% 0.18/0.45 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.18/0.45 % Number of connectives : 10 ( 3 ~; 1 |; 1 &; 4 @)
% 0.18/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 7 ( 4 avg)
% 0.18/0.45 % Number of types : 1 ( 0 usr)
% 0.18/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.18/0.45 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments :
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(leibeq_decl,type,
% 0.18/0.45 leibeq: $o > $o > $o ).
% 0.18/0.45
% 0.18/0.45 thf(leibeq,definition,
% 0.18/0.45 ( leibeq
% 0.18/0.45 = ( ^ [X: $o,Y: $o] :
% 0.18/0.45 ! [P: $o > $o] :
% 0.18/0.45 ( ( P @ X )
% 0.18/0.45 => ( P @ Y ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(conj,conjecture,
% 0.18/0.45 ! [X: $o,Y: $o] :
% 0.18/0.45 ( leibeq
% 0.18/0.45 @ ( X
% 0.18/0.45 & Y )
% 0.18/0.45 @ ~ ( ~ X
% 0.18/0.45 | ~ Y ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.24 %%% Generated on Tue Feb 24 14:21:30 EST 2026
% 1.49/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.24 %%% Logic specification used:
% 1.49/1.24 %%% thf(spec, logic, $$dhol).
% 1.49/1.24
% 1.49/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3J0t0lPhRN/DTF2DTF9325.p
% 1.49/1.24 thf(leibeq_decl, type, leibeq: ($o > ($o > $o))).
% 1.49/1.24 thf(leibeq, definition, (leibeq = (^ [X:$o,Y:$o]: ((! [P:($o > $o)]: (((P @ X) => (P @ Y)))))))).
% 1.49/1.24 thf(conj, conjecture, (! [X:$o,Y:$o]: (((leibeq @ (X & Y)) @ (~ (((~ (X)) | (~ (Y))))))))).
% 1.49/1.24 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.3J0t0lPhRN/DTF2DTF9325.p
% 1.49/1.24 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(leibeq_decl,type,
% 1.49/1.25 leibeq: $o > $o > $o ).
% 1.49/1.25
% 1.49/1.25 thf(leibeq,definition,
% 1.49/1.25 ( leibeq
% 1.49/1.25 = ( ^ [X: $o,Y: $o] :
% 1.49/1.25 ! [P: $o > $o] :
% 1.49/1.25 ( ( P @ X )
% 1.49/1.25 => ( P @ Y ) ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(conj,conjecture,
% 1.49/1.25 ! [X: $o,Y: $o] :
% 1.49/1.25 ( leibeq
% 1.49/1.25 @ ( X
% 1.49/1.25 & Y )
% 1.49/1.25 @ ~ ( ~ X
% 1.49/1.25 | ~ Y ) ) ).
% 1.49/1.25 ------------------------
% 1.49/1.26 % (9619)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9325 for (2999ds/18Mi)
% 1.49/1.26 % (9617)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_9325 for (2999ds/2Mi)
% 1.49/1.27 % (9617)Instruction limit reached!
% 1.49/1.27 % (9617)------------------------------
% 1.49/1.27 % (9617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (9617)Termination reason: Unknown
% 1.49/1.27 % (9617)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (9617)Memory used [KB]: 5500
% 1.49/1.27 % (9617)Time elapsed: 0.002 s
% 1.49/1.27 % (9617)Instructions burned: 2 (million)
% 1.49/1.27 % (9617)------------------------------
% 1.49/1.27 % (9617)------------------------------
% 1.49/1.27 % (9619)First to succeed.
% 1.49/1.27 % (9619)Refutation found. Thanks to Tanya!
% 1.49/1.27 % SZS status Theorem for DTF2THF_9325
% 1.49/1.27 % SZS output start Proof for DTF2THF_9325
% 1.49/1.27 thf(func_def_0, type, leibeq: $o > $o > $o).
% 1.49/1.27 thf(func_def_16, type, sK3: $o > $o).
% 1.49/1.27 thf(func_def_17, type, ph4: !>[X0: $tType]:(X0)).
% 1.49/1.27 thf(f109,plain,(
% 1.49/1.27 $false),
% 1.49/1.27 inference(avatar_sat_refutation,[status(thm)],[f93,f104])).
% 1.49/1.27 thf(f104,plain,(
% 1.49/1.27 ~spl2_1),
% 1.49/1.27 inference(avatar_contradiction_clause,[status(thm)],[f103])).
% 1.49/1.27 thf(f103,plain,(
% 1.49/1.27 $false | ~spl2_1),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.49/1.27 thf(f102,plain,(
% 1.49/1.27 ($true = $false) | ~spl2_1),
% 1.49/1.27 inference(forward_demodulation,[status(thm)],[f98,f101])).
% 1.49/1.27 thf(f101,plain,(
% 1.49/1.27 ($false = (sK3 @ sK1)) | ~spl2_1),
% 1.49/1.27 inference(boolean_simplification,[status(thm)],[f100])).
% 1.49/1.27 thf(f100,plain,(
% 1.49/1.27 ($false = (sK3 @ (~ (~ sK1)))) | ~spl2_1),
% 1.49/1.27 inference(boolean_simplification,[status(thm)],[f99])).
% 1.49/1.27 thf(f99,plain,(
% 1.49/1.27 ((sK3 @ (~ ((~ sK1) | $false))) = $false) | ~spl2_1),
% 1.49/1.27 inference(boolean_simplification,[status(thm)],[f97])).
% 1.49/1.27 thf(f97,plain,(
% 1.49/1.27 ((sK3 @ (~ ((~ sK1) | (~ $true)))) = $false) | ~spl2_1),
% 1.49/1.27 inference(backward_demodulation,[status(thm)],[f18,f73])).
% 1.49/1.27 thf(f73,plain,(
% 1.49/1.27 (sK0 = $true) | ~spl2_1),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.49/1.27 thf(f71,definition,(
% 1.49/1.27 spl2_1 <=> (sK0 = $true)),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.49/1.27 thf(f18,plain,(
% 1.49/1.27 ($false = (sK3 @ (~ ((~ sK1) | (~ sK0)))))),
% 1.49/1.27 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.49/1.27 thf(f17,plain,(
% 1.49/1.27 ($false = ((sK3 @ (sK0 & sK1)) => (sK3 @ (~ ((~ sK1) | (~ sK0))))))),
% 1.49/1.27 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.49/1.27 thf(f16,plain,(
% 1.49/1.27 (((^[Y0 : $o > $o]: ((Y0 @ (sK0 & sK1)) => (Y0 @ (~ ((~ sK1) | (~ sK0)))))) @ sK3) = $false)),
% 1.49/1.27 inference(sigma_clausification,[status(thm)],[f15])).
% 1.49/1.27 thf(f15,plain,(
% 1.49/1.27 ($true != (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (sK0 & sK1)) => (Y0 @ (~ ((~ sK1) | (~ sK0))))))))),
% 1.49/1.27 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.49/1.27 thf(f14,plain,(
% 1.49/1.27 ($true != ((^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (sK0 & sK1) @ (~ ((~ sK1) | (~ sK0)))))),
% 1.49/1.27 inference(definition_unfolding,[status(thm)],[f13,f12])).
% 1.49/1.27 thf(f12,plain,(
% 1.49/1.27 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f8])).
% 1.49/1.27 thf(f8,plain,(
% 1.49/1.27 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f7])).
% 1.49/1.27 thf(f7,plain,(
% 1.49/1.27 ((^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.49/1.27 inference(rectify,[status(thm)],[f1])).
% 1.49/1.27 thf(f1,axiom,(
% 1.49/1.27 ((^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.3J0t0lPhRN/DTF2THF_9325.p',leibeq)).
% 1.49/1.27 thf(f13,plain,(
% 1.49/1.27 ($true != (leibeq @ (sK0 & sK1) @ (~ ((~ sK1) | (~ sK0)))))),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.27 thf(f11,plain,(
% 1.49/1.27 ($true != (leibeq @ (sK0 & sK1) @ (~ ((~ sK1) | (~ sK0)))))),
% 1.49/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 1.49/1.27 thf(f10,plain,(
% 1.49/1.27 ? [X0 : $o,X1 : $o] : ($true != (leibeq @ (X0 & X1) @ (~ ((~ X1) | (~ X0))))) => ($true != (leibeq @ (sK0 & sK1) @ (~ ((~ sK1) | (~ sK0)))))),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f9,plain,(
% 1.49/1.27 ? [X0 : $o,X1 : $o] : ($true != (leibeq @ (X0 & X1) @ (~ ((~ X1) | (~ X0)))))),
% 1.49/1.27 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.27 thf(f6,plain,(
% 1.49/1.27 ~! [X0 : $o,X1 : $o] : ($true = (leibeq @ (X0 & X1) @ (~ ((~ X1) | (~ X0)))))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f5])).
% 1.49/1.27 thf(f5,plain,(
% 1.49/1.27 ~! [X0 : $o,X1 : $o] : (leibeq @ X1 & X0 @ ~(~X0 | ~X1))),
% 1.49/1.27 inference(rectify,[status(thm)],[f3])).
% 1.49/1.27 thf(f3,negated_conjecture,(
% 1.49/1.27 ~! [X0 : $o,X1 : $o] : (leibeq @ X1 & X0 @ ~(~X0 | ~X1))),
% 1.49/1.27 inference(negated_conjecture,[status(cth)],[f2])).
% 1.49/1.27 thf(f2,conjecture,(
% 1.49/1.27 ! [X0 : $o,X1 : $o] : (leibeq @ X1 & X0 @ ~(~X0 | ~X1))),
% 1.49/1.27 file('/export/starexec/sandbox/tmp/tmp.3J0t0lPhRN/DTF2THF_9325.p',conj)).
% 1.49/1.27 thf(f98,plain,(
% 1.49/1.27 ($true = (sK3 @ sK1)) | ~spl2_1),
% 1.49/1.27 inference(boolean_simplification,[status(thm)],[f96])).
% 1.49/1.27 thf(f96,plain,(
% 1.49/1.27 ($true = (sK3 @ ($true & sK1))) | ~spl2_1),
% 1.49/1.27 inference(backward_demodulation,[status(thm)],[f19,f73])).
% 1.49/1.27 thf(f19,plain,(
% 1.49/1.27 ($true = (sK3 @ (sK0 & sK1)))),
% 1.49/1.27 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.49/1.27 thf(f93,plain,(
% 1.49/1.27 spl2_1),
% 1.49/1.27 inference(avatar_split_clause,[status(thm)],[f39,f71])).
% 1.49/1.27 thf(f39,plain,(
% 1.49/1.27 (sK0 = $true)),
% 1.49/1.27 inference(duplicate_literal_removal,[status(thm)],[f38])).
% 1.49/1.27 thf(f38,plain,(
% 1.49/1.27 (sK0 = $true) | (sK0 = $true)),
% 1.49/1.27 inference(not_proxy_clausification,[status(thm)],[f35])).
% 1.49/1.27 thf(f35,plain,(
% 1.49/1.27 (sK0 = $true) | ($false = (~ sK0))),
% 1.49/1.27 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.49/1.27 thf(f34,plain,(
% 1.49/1.27 (sK0 = $true) | ($false = ((~ sK1) | (~ sK0)))),
% 1.49/1.27 inference(not_proxy_clausification,[status(thm)],[f33])).
% 1.49/1.27 thf(f33,plain,(
% 1.49/1.27 ($true = (~ ((~ sK1) | (~ sK0)))) | (sK0 = $true)),
% 1.49/1.27 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.49/1.27 thf(f23,plain,(
% 1.49/1.27 ((sK0 & sK1) = $true) | ($true = (~ ((~ sK1) | (~ sK0))))),
% 1.49/1.27 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.49/1.27 thf(f22,plain,(
% 1.49/1.27 ((sK0 & sK1) != (~ ((~ sK1) | (~ sK0))))),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.49/1.27 thf(f20,plain,(
% 1.49/1.27 ($true = $false) | ((sK0 & sK1) != (~ ((~ sK1) | (~ sK0))))),
% 1.49/1.27 inference(constrained_superposition,[status(thm)],[f18,f19])).
% 1.49/1.27 % SZS output end Proof for DTF2THF_9325
% 1.49/1.27 % (9619)------------------------------
% 1.49/1.27 % (9619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (9619)Termination reason: Refutation
% 1.49/1.27
% 1.49/1.27 % (9619)Memory used [KB]: 5500
% 1.49/1.27 % (9619)Time elapsed: 0.004 s
% 1.49/1.27 % (9619)Instructions burned: 3 (million)
% 1.49/1.27 % (9619)------------------------------
% 1.49/1.27 % (9619)------------------------------
% 1.49/1.27 % (9612)Success in time 0.013 s
%------------------------------------------------------------------------------