%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO310^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n023.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 09:53:55 AM UTC 2026
% Result : Theorem 1.46s 1.28s
% Output : Refutation 1.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO310^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n023.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 14:28:34 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SYO310^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Syntactic
% 0.30/0.45 % Problem : TPS problem from BASIC-HO-THMS
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : tps_0835 [Bro09]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.33 v7.3.0, 0.40 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.67 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.50 v5.1.0, 0.75 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.30/0.45 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.30/0.45 % Number of atoms : 11 ( 0 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 11 ( 11 avg)
% 0.30/0.45 % Number of connectives : 18 ( 2 ~; 0 |; 4 &; 10 @)
% 0.30/0.45 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.30/0.45 % Number of types : 1 ( 0 usr)
% 0.30/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 2 ( 0 usr; 2 con; 0-0 aty)
% 0.30/0.45 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.30/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(cOMEGA_EXAMPLE,conjecture,
% 0.30/0.45 ( ? [Xop: $o > $o > $o] :
% 0.30/0.45 ( ( Xop @ $true @ $true )
% 0.30/0.45 & ( Xop @ $false @ $false )
% 0.30/0.45 & ~ ( Xop @ $false @ $true )
% 0.30/0.45 & ~ ( Xop @ $true @ $false ) )
% 0.30/0.45 & ! [Xm: $o > $o] :
% 0.30/0.45 ( ( Xm @ $true )
% 0.30/0.45 <=> ( Xm
% 0.30/0.45 @ ( $true
% 0.30/0.45 => $true ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.46/1.24 ---- Embedded in THF ---
% 1.46/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.24 %%% Generated on Tue Feb 24 14:28:35 EST 2026
% 1.46/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.24 %%% Logic specification used:
% 1.46/1.24 %%% thf(spec, logic, $$dhol).
% 1.46/1.24
% 1.46/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.CICMa7LeTi/DTF2DTF12791.p
% 1.46/1.24 thf(cOMEGA_EXAMPLE, conjecture, ((? [Xop:($o > ($o > $o))]: ((((Xop @ $true) @ $true) & (((Xop @ $false) @ $false) & ((~ (((Xop @ $false) @ $true))) & (~ (((Xop @ $true) @ $false)))))))) & (! [Xm:($o > $o)]: (((Xm @ $true) <=> (Xm @ ($true => $true))))))).
% 1.46/1.24 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.CICMa7LeTi/DTF2DTF12791.p
% 1.46/1.24 ------------------------
% 1.46/1.25 ---- Cleaned THF ---
% 1.46/1.25 thf(cOMEGA_EXAMPLE,conjecture,
% 1.46/1.25 ( ? [Xop: $o > $o > $o] :
% 1.46/1.25 ( ( Xop @ $true @ $true )
% 1.46/1.25 & ( Xop @ $false @ $false )
% 1.46/1.25 & ~ ( Xop @ $false @ $true )
% 1.46/1.25 & ~ ( Xop @ $true @ $false ) )
% 1.46/1.25 & ! [Xm: $o > $o] :
% 1.46/1.25 ( ( Xm @ $true )
% 1.46/1.25 <=> ( Xm
% 1.46/1.25 @ ( $true
% 1.46/1.25 => $true ) ) ) ) ).
% 1.46/1.25 ------------------------
% 1.46/1.27 % (13010)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12791 for (2999ds/2Mi)
% 1.46/1.27 % (13010)Instruction limit reached!
% 1.46/1.27 % (13010)------------------------------
% 1.46/1.27 % (13010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (13010)Termination reason: Unknown
% 1.46/1.27 % (13010)Termination phase: Saturation
% 1.46/1.27
% 1.46/1.27 % (13010)Memory used [KB]: 5500
% 1.46/1.27 % (13010)Time elapsed: 0.002 s
% 1.46/1.27 % (13010)Instructions burned: 2 (million)
% 1.46/1.27 % (13010)------------------------------
% 1.46/1.27 % (13010)------------------------------
% 1.46/1.27 % (13009)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_12791 for (2999ds/27Mi)
% 1.46/1.27 % (13009)Refutation not found, incomplete strategy
% 1.46/1.27 % (13009)------------------------------
% 1.46/1.27 % (13009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (13009)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.27
% 1.46/1.27
% 1.46/1.27 % (13009)Memory used [KB]: 5500
% 1.46/1.27 % (13009)Time elapsed: 0.001 s
% 1.46/1.27 % (13009)------------------------------
% 1.46/1.27 % (13009)------------------------------
% 1.46/1.27 % (13007)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12791 for (2999ds/183Mi)
% 1.46/1.27 % (13008)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_12791 for (2999ds/4Mi)
% 1.46/1.27 % (13011)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_12791 for (2999ds/2Mi)
% 1.46/1.27 % (13012)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_12791 for (2999ds/275Mi)
% 1.46/1.27 % (13013)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12791 for (2999ds/18Mi)
% 1.46/1.27 % (13011)Instruction limit reached!
% 1.46/1.27 % (13011)------------------------------
% 1.46/1.27 % (13011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.27 % (13011)Termination reason: Unknown
% 1.46/1.27 % (13011)Termination phase: Saturation
% 1.46/1.27
% 1.46/1.27 % (13011)Memory used [KB]: 895
% 1.46/1.27 % (13011)Time elapsed: 0.003 s
% 1.46/1.27 % (13011)Instructions burned: 2 (million)
% 1.46/1.27 % (13011)------------------------------
% 1.46/1.27 % (13011)------------------------------
% 1.46/1.28 % (13014)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12791 for (2999ds/3Mi)
% 1.46/1.28 % (13007)First to succeed.
% 1.46/1.28 % (13014)Instruction limit reached!
% 1.46/1.28 % (13014)------------------------------
% 1.46/1.28 % (13014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (13014)Termination reason: Unknown
% 1.46/1.28 % (13014)Termination phase: Saturation
% 1.46/1.28
% 1.46/1.28 % (13014)Memory used [KB]: 5500
% 1.46/1.28 % (13014)Time elapsed: 0.002 s
% 1.46/1.28 % (13014)Instructions burned: 3 (million)
% 1.46/1.28 % (13014)------------------------------
% 1.46/1.28 % (13014)------------------------------
% 1.46/1.28 % (13008)Also succeeded, but the first one will report.
% 1.46/1.28 % (13015)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_12791 for (2999ds/37Mi)
% 1.46/1.28 % (13007)Refutation found. Thanks to Tanya!
% 1.46/1.28 % SZS status Theorem for DTF2THF_12791
% 1.46/1.28 % SZS output start Proof for DTF2THF_12791
% 1.46/1.28 thf(func_def_4, type, sK0: $o > $o).
% 1.46/1.28 thf(func_def_7, type, ph2: !>[X0: $tType]:(X0)).
% 1.46/1.28 thf(f62,plain,(
% 1.46/1.28 $false),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.46/1.28 thf(f61,plain,(
% 1.46/1.28 ($false = $true)),
% 1.46/1.28 inference(equality_proxy_clausification,[status(thm)],[f60])).
% 1.46/1.28 thf(f60,plain,(
% 1.46/1.28 (($true = $false) = $true)),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.46/1.28 thf(f59,plain,(
% 1.46/1.28 ($false = $true) | (($true = $false) = $true)),
% 1.46/1.28 inference(equality_proxy_clausification,[status(thm)],[f58])).
% 1.46/1.28 thf(f58,plain,(
% 1.46/1.28 (($false = $true) = $true) | (($true = $false) = $true)),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.46/1.28 thf(f57,plain,(
% 1.46/1.28 (($false = $true) = $true) | (($true = $false) = $true) | ($true != $true)),
% 1.46/1.28 inference(boolean_simplification,[status(thm)],[f56])).
% 1.46/1.28 thf(f56,plain,(
% 1.46/1.28 (($true = $false) = $true) | (($false = $true) = $true) | (($true = $true) != $true)),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.46/1.28 thf(f55,plain,(
% 1.46/1.28 (($false = $true) = $true) | (($true = $true) != $true) | (($true = $false) = $true) | ($true != $true)),
% 1.46/1.28 inference(boolean_simplification,[status(thm)],[f54])).
% 1.46/1.28 thf(f54,plain,(
% 1.46/1.28 (($false = $true) = $true) | (($true = $false) = $true) | (($false = $false) != $true) | (($true = $true) != $true)),
% 1.46/1.28 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.46/1.28 thf(f15,plain,(
% 1.46/1.28 (((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 = Y0)))) @ $true @ $true) != $true) | (((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 = Y0)))) @ $true @ $false) = $true) | (((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 = Y0)))) @ $false @ $false) != $true) | (((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 = Y0)))) @ $false @ $true) = $true)),
% 1.46/1.28 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.46/1.28 thf(f12,plain,(
% 1.46/1.28 ( ! [X0 : $o > $o > $o] : (((X0 @ $true @ $false) = $true) | ((X0 @ $false @ $true) = $true) | ((X0 @ $false @ $false) != $true) | ((X0 @ $true @ $true) != $true)) )),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f11])).
% 1.46/1.28 thf(f11,plain,(
% 1.46/1.28 ( ! [X0 : $o > $o > $o] : (((X0 @ $false @ $true) = $true) | ((X0 @ $false @ $false) != $true) | ((sK0 @ $true) != (sK0 @ $true)) | ((X0 @ $true @ $true) != $true) | ((X0 @ $true @ $false) = $true)) )),
% 1.46/1.28 inference(boolean_simplification,[status(thm)],[f10])).
% 1.46/1.28 thf(f10,plain,(
% 1.46/1.28 ( ! [X0 : $o > $o > $o] : (((sK0 @ $true) != (sK0 @ ($true => $true))) | ((X0 @ $false @ $true) = $true) | ((X0 @ $true @ $false) = $true) | ((X0 @ $false @ $false) != $true) | ((X0 @ $true @ $true) != $true)) )),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.28 thf(f9,plain,(
% 1.46/1.28 ! [X0 : $o > $o > $o] : (((X0 @ $false @ $false) != $true) | ((X0 @ $true @ $false) = $true) | ((X0 @ $false @ $true) = $true) | ((X0 @ $true @ $true) != $true)) | ((sK0 @ $true) != (sK0 @ ($true => $true)))),
% 1.46/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.46/1.28 thf(f8,plain,(
% 1.46/1.28 ? [X1 : $o > $o] : ((X1 @ $true) != (X1 @ ($true => $true))) => ((sK0 @ $true) != (sK0 @ ($true => $true)))),
% 1.46/1.28 introduced(definition,[],[choice_axiom])).
% 1.46/1.28 thf(f7,plain,(
% 1.46/1.28 ! [X0 : $o > $o > $o] : (((X0 @ $false @ $false) != $true) | ((X0 @ $true @ $false) = $true) | ((X0 @ $false @ $true) = $true) | ((X0 @ $true @ $true) != $true)) | ? [X1 : $o > $o] : ((X1 @ $true) != (X1 @ ($true => $true)))),
% 1.46/1.28 inference(ennf_transformation,[status(thm)],[f6])).
% 1.46/1.28 thf(f6,plain,(
% 1.46/1.28 ~(! [X1 : $o > $o] : ((X1 @ $true) = (X1 @ ($true => $true))) & ? [X0 : $o > $o > $o] : (((X0 @ $true @ $true) = $true) & ((X0 @ $true @ $false) != $true) & ((X0 @ $false @ $true) != $true) & ((X0 @ $false @ $false) = $true)))),
% 1.46/1.28 inference(flattening,[status(thm)],[f5])).
% 1.46/1.28 thf(f5,plain,(
% 1.46/1.28 ~(? [X0 : $o > $o > $o] : (((X0 @ $true @ $true) = $true) & ((X0 @ $false @ $false) = $true) & ~((X0 @ $true @ $false) = $true) & ~((X0 @ $false @ $true) = $true)) & ! [X1 : $o > $o] : ((X1 @ $true) = (X1 @ ($true => $true))))),
% 1.46/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.28 thf(f4,plain,(
% 1.46/1.28 ~(? [X0 : $o > $o > $o] : ((X0 @ $true @ $true) & (X0 @ $false @ $false) & ~(X0 @ $true @ $false) & ~(X0 @ $false @ $true)) & ! [X1 : $o > $o] : ((X1 @ $true => $true) <=> (X1 @ $true)))),
% 1.46/1.28 inference(rectify,[status(thm)],[f2])).
% 1.46/1.28 thf(f2,negated_conjecture,(
% 1.46/1.28 ~(? [X0 : $o > $o > $o] : ((X0 @ $true @ $true) & (X0 @ $false @ $false) & ~(X0 @ $true @ $false) & ~(X0 @ $false @ $true)) & ! [X1 : $o > $o] : ((X1 @ $true => $true) <=> (X1 @ $true)))),
% 1.46/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.28 thf(f1,conjecture,(
% 1.46/1.28 ? [X0 : $o > $o > $o] : ((X0 @ $true @ $true) & (X0 @ $false @ $false) & ~(X0 @ $true @ $false) & ~(X0 @ $false @ $true)) & ! [X1 : $o > $o] : ((X1 @ $true => $true) <=> (X1 @ $true))),
% 1.46/1.28 file('/export/starexec/sandbox2/tmp/tmp.CICMa7LeTi/DTF2THF_12791.p',cOMEGA_EXAMPLE)).
% 1.46/1.28 % SZS output end Proof for DTF2THF_12791
% 1.46/1.28 % (13007)------------------------------
% 1.46/1.28 % (13007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (13007)Termination reason: Refutation
% 1.46/1.28
% 1.46/1.28 % (13007)Memory used [KB]: 5500
% 1.46/1.28 % (13007)Time elapsed: 0.005 s
% 1.46/1.28 % (13007)Instructions burned: 3 (million)
% 1.46/1.28 % (13007)------------------------------
% 1.46/1.28 % (13007)------------------------------
% 1.46/1.28 % (13006)Success in time 0.02 s
%------------------------------------------------------------------------------