%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO377^5 : 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 : n026.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 09:54:05 AM UTC 2026
% Result : Theorem 1.48s 1.27s
% Output : Refutation 1.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO377^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n026.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:29:25 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SYO377^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Syntactic
% 0.31/0.46 % Problem : TPS problem from EXTENSIONALITY
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0831 [Bro09]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 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, 0.33 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.00 v5.3.0, 0.25 v4.1.0, 0.67 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.31/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.31/0.46 % Number of connectives : 12 ( 0 ~; 0 |; 2 &; 5 @)
% 0.31/0.46 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.31/0.46 % Number of types : 1 ( 0 usr)
% 0.31/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 2 ( 2 usr; 2 con; 0-0 aty)
% 0.31/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(b,type,
% 0.31/0.46 b: $o ).
% 0.31/0.46
% 0.31/0.46 thf(a,type,
% 0.31/0.46 a: $o ).
% 0.31/0.46
% 0.31/0.46 thf(cEXT_IMP_EMB2,conjecture,
% 0.31/0.46 ( ! [Xx: $o,Xy: $o] :
% 0.31/0.46 ( ( Xx
% 0.31/0.46 <=> Xy )
% 0.31/0.46 => ! [Xq: $o > $o] :
% 0.31/0.46 ( ( Xq @ Xx )
% 0.31/0.46 => ( Xq @ Xy ) ) )
% 0.31/0.46 => ! [Xp: $o > $o] :
% 0.31/0.46 ( ( ( Xp @ a )
% 0.31/0.46 & ( Xp @ b ) )
% 0.31/0.46 => ( Xp
% 0.31/0.46 @ ( a
% 0.31/0.46 & b ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.24 %%% Generated on Tue Feb 24 14:29:26 EST 2026
% 1.48/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.24 %%% Logic specification used:
% 1.48/1.24 %%% thf(spec, logic, $$dhol).
% 1.48/1.24
% 1.48/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Ve0LM0imNA/DTF2DTF31661.p
% 1.48/1.24 thf(b, type, b: $o).
% 1.48/1.24 thf(a, type, a: $o).
% 1.48/1.24 thf(cEXT_IMP_EMB2, conjecture, ((! [Xx:$o,Xy:$o]: (((Xx <=> Xy) => (! [Xq:($o > $o)]: (((Xq @ Xx) => (Xq @ Xy))))))) => (! [Xp:($o > $o)]: ((((Xp @ a) & (Xp @ b)) => (Xp @ (a & b))))))).
% 1.48/1.24 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Ve0LM0imNA/DTF2DTF31661.p
% 1.48/1.24 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.26 thf(b,type,
% 1.48/1.26 b: $o ).
% 1.48/1.26
% 1.48/1.26 thf(a,type,
% 1.48/1.26 a: $o ).
% 1.48/1.26
% 1.48/1.26 thf(cEXT_IMP_EMB2,conjecture,
% 1.48/1.26 ( ! [Xx: $o,Xy: $o] :
% 1.48/1.26 ( ( Xx
% 1.48/1.26 <=> Xy )
% 1.48/1.26 => ! [Xq: $o > $o] :
% 1.48/1.26 ( ( Xq @ Xx )
% 1.48/1.26 => ( Xq @ Xy ) ) )
% 1.48/1.26 => ! [Xp: $o > $o] :
% 1.48/1.26 ( ( ( Xp @ a )
% 1.48/1.26 & ( Xp @ b ) )
% 1.48/1.26 => ( Xp
% 1.48/1.26 @ ( a
% 1.48/1.26 & b ) ) ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.27 % (31880)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_31661 for (2999ds/27Mi)
% 1.48/1.27 % (31878)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31661 for (2999ds/183Mi)
% 1.48/1.27 % (31880)Refutation not found, incomplete strategy
% 1.48/1.27 % (31880)------------------------------
% 1.48/1.27 % (31880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (31880)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.27
% 1.48/1.27
% 1.48/1.27 % (31880)Memory used [KB]: 5500
% 1.48/1.27 % (31880)Time elapsed: 0.002 s
% 1.48/1.27 % (31880)Instructions burned: 1 (million)
% 1.48/1.27 % (31880)------------------------------
% 1.48/1.27 % (31880)------------------------------
% 1.48/1.27 % (31878)First to succeed.
% 1.48/1.27 % (31878)Refutation found. Thanks to Tanya!
% 1.48/1.27 % SZS status Theorem for DTF2THF_31661
% 1.48/1.27 % SZS output start Proof for DTF2THF_31661
% 1.48/1.27 thf(func_def_6, type, sK0: $o > $o).
% 1.48/1.27 thf(func_def_9, type, ph2: !>[X0: $tType]:(X0)).
% 1.48/1.27 thf(f53,plain,(
% 1.48/1.27 $false),
% 1.48/1.27 inference(avatar_sat_refutation,[status(thm)],[f42,f47,f52])).
% 1.48/1.27 thf(f52,plain,(
% 1.48/1.27 ~spl1_1),
% 1.48/1.27 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.48/1.27 thf(f51,plain,(
% 1.48/1.27 $false | ~spl1_1),
% 1.48/1.27 inference(subsumption_resolution,[status(thm)],[f50,f49])).
% 1.48/1.27 thf(f49,plain,(
% 1.48/1.27 ((sK0 @ $false) = $true) | ~spl1_1),
% 1.48/1.27 inference(superposition,[status(thm)],[f10,f36])).
% 1.48/1.27 thf(f36,plain,(
% 1.48/1.27 (b = $false) | ~spl1_1),
% 1.48/1.27 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.48/1.27 thf(f34,definition,(
% 1.48/1.27 spl1_1 <=> (b = $false)),
% 1.48/1.27 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.48/1.27 thf(f10,plain,(
% 1.48/1.27 ((sK0 @ b) = $true)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.27 thf(f9,plain,(
% 1.48/1.27 ! [X0 : $o,X1 : $o] : ((X0 != X1) | ! [X2 : $o > $o] : (((X2 @ X1) = $true) | ((X2 @ X0) != $true))) & (((sK0 @ (a & b)) != $true) & ((sK0 @ a) = $true) & ((sK0 @ b) = $true))),
% 1.48/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.48/1.27 thf(f8,plain,(
% 1.48/1.27 ? [X3 : $o > $o] : (((X3 @ (a & b)) != $true) & ((X3 @ a) = $true) & ((X3 @ b) = $true)) => (((sK0 @ (a & b)) != $true) & ((sK0 @ a) = $true) & ((sK0 @ b) = $true))),
% 1.48/1.27 introduced(definition,[],[choice_axiom])).
% 1.48/1.27 thf(f7,plain,(
% 1.48/1.27 ! [X0 : $o,X1 : $o] : ((X0 != X1) | ! [X2 : $o > $o] : (((X2 @ X1) = $true) | ((X2 @ X0) != $true))) & ? [X3 : $o > $o] : (((X3 @ (a & b)) != $true) & ((X3 @ a) = $true) & ((X3 @ b) = $true))),
% 1.48/1.27 inference(flattening,[status(thm)],[f6])).
% 1.48/1.27 thf(f6,plain,(
% 1.48/1.27 ? [X3 : $o > $o] : (((X3 @ (a & b)) != $true) & (((X3 @ a) = $true) & ((X3 @ b) = $true))) & ! [X0 : $o,X1 : $o] : ((X0 != X1) | ! [X2 : $o > $o] : (((X2 @ X1) = $true) | ((X2 @ X0) != $true)))),
% 1.48/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.27 thf(f5,plain,(
% 1.48/1.27 ~(! [X1 : $o,X0 : $o] : ((X0 = X1) => ! [X2 : $o > $o] : (((X2 @ X0) = $true) => ((X2 @ X1) = $true))) => ! [X3 : $o > $o] : ((((X3 @ a) = $true) & ((X3 @ b) = $true)) => ((X3 @ (a & b)) = $true)))),
% 1.48/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.27 thf(f4,plain,(
% 1.48/1.27 ~(! [X0 : $o,X1 : $o] : ((X0 <=> X1) => ! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1))) => ! [X3 : $o > $o] : (((X3 @ a) & (X3 @ b)) => (X3 @ b & a)))),
% 1.48/1.27 inference(rectify,[status(thm)],[f2])).
% 1.48/1.27 thf(f2,negated_conjecture,(
% 1.48/1.27 ~(! [X0 : $o,X1 : $o] : ((X0 <=> X1) => ! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1))) => ! [X3 : $o > $o] : (((X3 @ a) & (X3 @ b)) => (X3 @ b & a)))),
% 1.48/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.27 thf(f1,conjecture,(
% 1.48/1.27 ! [X0 : $o,X1 : $o] : ((X0 <=> X1) => ! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1))) => ! [X3 : $o > $o] : (((X3 @ a) & (X3 @ b)) => (X3 @ b & a))),
% 1.48/1.27 file('/export/starexec/sandbox2/tmp/tmp.Ve0LM0imNA/DTF2THF_31661.p',cEXT_IMP_EMB2)).
% 1.48/1.27 thf(f50,plain,(
% 1.48/1.27 ((sK0 @ $false) != $true) | ~spl1_1),
% 1.48/1.27 inference(boolean_simplification,[status(thm)],[f48])).
% 1.48/1.27 thf(f48,plain,(
% 1.48/1.27 ((sK0 @ (a & $false)) != $true) | ~spl1_1),
% 1.48/1.27 inference(superposition,[status(thm)],[f12,f36])).
% 1.48/1.27 thf(f12,plain,(
% 1.48/1.27 ((sK0 @ (a & b)) != $true)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.27 thf(f47,plain,(
% 1.48/1.27 ~spl1_2),
% 1.48/1.27 inference(avatar_contradiction_clause,[status(thm)],[f46])).
% 1.48/1.27 thf(f46,plain,(
% 1.48/1.27 $false | ~spl1_2),
% 1.48/1.27 inference(subsumption_resolution,[status(thm)],[f45,f44])).
% 1.48/1.27 thf(f44,plain,(
% 1.48/1.27 ((sK0 @ $false) = $true) | ~spl1_2),
% 1.48/1.27 inference(superposition,[status(thm)],[f11,f40])).
% 1.48/1.27 thf(f40,plain,(
% 1.48/1.27 (a = $false) | ~spl1_2),
% 1.48/1.27 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.48/1.27 thf(f38,definition,(
% 1.48/1.27 spl1_2 <=> (a = $false)),
% 1.48/1.27 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.48/1.27 thf(f11,plain,(
% 1.48/1.27 ((sK0 @ a) = $true)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.27 thf(f45,plain,(
% 1.48/1.27 ((sK0 @ $false) != $true) | ~spl1_2),
% 1.48/1.27 inference(boolean_simplification,[status(thm)],[f43])).
% 1.48/1.27 thf(f43,plain,(
% 1.48/1.27 ((sK0 @ ($false & b)) != $true) | ~spl1_2),
% 1.48/1.27 inference(superposition,[status(thm)],[f12,f40])).
% 1.48/1.27 thf(f42,plain,(
% 1.48/1.27 spl1_1 | spl1_2),
% 1.48/1.27 inference(avatar_split_clause,[status(thm)],[f21,f38,f34])).
% 1.48/1.27 thf(f21,plain,(
% 1.48/1.27 (a = $false) | (b = $false)),
% 1.48/1.27 inference(duplicate_literal_removal,[status(thm)],[f20])).
% 1.48/1.27 thf(f20,plain,(
% 1.48/1.27 (a = $false) | (b = $false) | (a = $false)),
% 1.48/1.27 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.48/1.27 thf(f19,plain,(
% 1.48/1.27 (a = $false) | ((a & b) = $false)),
% 1.48/1.27 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.48/1.27 thf(f17,plain,(
% 1.48/1.27 (a != (a & b))),
% 1.48/1.27 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.48/1.27 thf(f15,plain,(
% 1.48/1.27 ($true != $true) | (a != (a & b))),
% 1.48/1.27 inference(constrained_superposition,[status(thm)],[f12,f11])).
% 1.48/1.27 % SZS output end Proof for DTF2THF_31661
% 1.48/1.27 % (31878)------------------------------
% 1.48/1.27 % (31878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (31878)Termination reason: Refutation
% 1.48/1.27
% 1.48/1.27 % (31878)Memory used [KB]: 5500
% 1.48/1.27 % (31878)Time elapsed: 0.003 s
% 1.48/1.27 % (31878)Instructions burned: 2 (million)
% 1.48/1.27 % (31878)------------------------------
% 1.48/1.27 % (31878)------------------------------
% 1.48/1.27 % (31877)Success in time 0.013 s
%------------------------------------------------------------------------------