%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM781^2 : TPTP v9.2.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 09:24:41 AM UTC 2026
% Result : Theorem 1.48s 1.24s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 0 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 12 ( 6 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(func_def_0,type,
a: $tType ).
tff(func_def_1,type,
vEPSILON:
!>[X0: $tType] : sTfun(sTfun(X0,$o),X0) ).
tff(func_def_2,type,
sK0: a ).
tff(func_def_3,type,
sK1: a ).
tff(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
tff(f10,plain,
sK0 != sK0,
inference(definition_unfolding,[status(thm)],[f8,f9]) ).
tff(f9,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f7]) ).
tff(f7,plain,
( ( sK1 = sK0 )
& ( sK1 != sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6]) ).
tff(f6,plain,
( ? [X0: a,X1: a] :
( ( X0 = X1 )
& ( X0 != X1 ) )
=> ( ( sK1 = sK0 )
& ( sK1 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f5,plain,
? [X0: a,X1: a] :
( ( X0 = X1 )
& ( X0 != X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
tff(f4,plain,
? [X1: a,X0: a] :
( ( X0 = X1 )
& ( X0 != X1 ) ),
inference(ennf_transformation,[status(thm)],[f3]) ).
tff(f3,plain,
~ ! [X1: a,X0: a] :
( ( X0 = X1 )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X1: a,X0: a] :
( ( X0 = X1 )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
! [X1: a,X0: a] :
( ( X0 = X1 )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.wHoTmyhjTY/DTF2THF_25947.p',cES_eq_) ).
tff(f8,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM781^2 : TPTP v9.2.1. Released v5.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n014.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 11:13:57 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : NUM781^2 : TPTP v9.2.1. Released v5.1.0.
% 0.30/0.47 % Domain : Number Theory
% 0.30/0.47 % Problem : Landau theorem 79
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Bro09]
% 0.30/0.47 % Names : tps_0053 [Bro09]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0
% 0.30/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.30/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.30/0.47 % Number of connectives : 1 ( 0 ~; 0 |; 0 &; 0 @)
% 0.30/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 4 ( 4 avg)
% 0.30/0.47 % Number of types : 1 ( 1 usr)
% 0.30/0.47 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.47 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.47 % : TPS problem from TTTP-NATS-THMS
% 0.30/0.47 % :
% 0.30/0.47 % : Renamed from SYO343^5
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(a_type,type,
% 0.30/0.47 a: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(cES_eq_,conjecture,
% 0.30/0.47 ! [A: a,B: a] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ( B = A ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.48/1.21 ---- Embedded in THF ---
% 1.48/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.22 %%% Generated on Tue Feb 24 11:13:58 EST 2026
% 1.48/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.22 %%% Logic specification used:
% 1.48/1.22 %%% thf(spec, logic, $$dhol).
% 1.48/1.22
% 1.48/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.wHoTmyhjTY/DTF2DTF25947.p
% See solution above
% 1.48/1.22 ------------------------
% 1.48/1.23 ---- Cleaned THF ---
% 1.48/1.23 thf(a_type,type,
% 1.48/1.23 a: $tType ).
% 1.48/1.23
% 1.48/1.23 thf(cES_eq_,conjecture,
% 1.48/1.23 ! [A: a,B: a] :
% 1.48/1.23 ( ( A = B )
% 1.48/1.23 => ( B = A ) ) ).
% 1.48/1.23 ------------------------
% 1.48/1.24 % (26277)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_25947 for (3000ds/27Mi)
% 1.48/1.24 % (26277)First to succeed.
% 1.48/1.24 % (26275)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25947 for (3000ds/183Mi)
% 1.48/1.24 % (26275)Also succeeded, but the first one will report.
% 1.48/1.24 % (26277)Refutation found. Thanks to Tanya!
% 1.48/1.24 % SZS status Theorem for DTF2THF_25947
% 1.48/1.24 % SZS output start Proof for DTF2THF_25947
% 1.48/1.24 tff(type_def_5, type, a: $tType).
% 1.48/1.24 tff(func_def_0, type, a: $tType).
% 1.48/1.24 tff(func_def_1, type, vEPSILON: !>[X0: $tType]:(sTfun(sTfun(X0,$o),X0))).
% 1.48/1.24 tff(func_def_2, type, sK0: a).
% 1.48/1.24 tff(func_def_3, type, sK1: a).
% 1.48/1.24 tff(f11,plain,(
% 1.48/1.24 $false),
% 1.48/1.24 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 1.48/1.24 tff(f10,plain,(
% 1.48/1.24 sK0 != sK0),
% 1.48/1.24 inference(definition_unfolding,[status(thm)],[f8,f9])).
% 1.48/1.24 tff(f9,plain,(
% 1.48/1.24 sK1 = sK0),
% 1.48/1.24 inference(cnf_transformation,[status(thm)],[f7])).
% 1.48/1.24 tff(f7,plain,(
% 1.48/1.24 sK1 = sK0 & sK1 != sK0),
% 1.48/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6])).
% 1.48/1.24 tff(f6,plain,(
% 1.48/1.24 ? [X0 : a,X1 : a] : (X0 = X1 & X0 != X1) => (sK1 = sK0 & sK1 != sK0)),
% 1.48/1.24 introduced(definition,[],[choice_axiom])).
% 1.48/1.24 tff(f5,plain,(
% 1.48/1.24 ? [X0 : a,X1 : a] : (X0 = X1 & X0 != X1)),
% 1.48/1.24 inference(rectify,[status(thm)],[f4])).
% 1.48/1.24 tff(f4,plain,(
% 1.48/1.24 ? [X1 : a,X0 : a] : (X0 = X1 & X0 != X1)),
% 1.48/1.24 inference(ennf_transformation,[status(thm)],[f3])).
% 1.48/1.24 tff(f3,plain,(
% 1.48/1.24 ~! [X1 : a,X0 : a] : (X0 = X1 => X0 = X1)),
% 1.48/1.24 inference(rectify,[status(thm)],[f2])).
% 1.48/1.24 tff(f2,negated_conjecture,(
% 1.48/1.24 ~! [X1 : a,X0 : a] : (X0 = X1 => X0 = X1)),
% 1.48/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.24 tff(f1,conjecture,(
% 1.48/1.24 ! [X1 : a,X0 : a] : (X0 = X1 => X0 = X1)),
% 1.48/1.24 file('/export/starexec/sandbox/tmp/tmp.wHoTmyhjTY/DTF2THF_25947.p',cES_eq_)).
% 1.48/1.24 tff(f8,plain,(
% 1.48/1.24 sK1 != sK0),
% 1.48/1.24 inference(cnf_transformation,[status(thm)],[f7])).
% 1.48/1.24 % SZS output end Proof for DTF2THF_25947
% 1.48/1.24 % (26277)------------------------------
% 1.48/1.24 % (26277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.24 % (26277)Termination reason: Refutation
% 1.48/1.24
% 1.48/1.24 % (26277)Memory used [KB]: 5373
% 1.48/1.24 % (26277)Time elapsed: 0.002 s
% 1.48/1.24 % (26277)------------------------------
% 1.48/1.24 % (26277)------------------------------
% 1.48/1.24 % (26274)Success in time 0.01 s
%------------------------------------------------------------------------------