%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET045^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 09:31:04 AM UTC 2026
% Result : Theorem 1.54s 1.30s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 7 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 6 ~; 0 |; 0 &; 10 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 6 !; 4 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
cA: b ).
thf(func_def_6,type,
sK0: ( a > b ) > a ).
thf(func_def_8,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f8,plain,
$false,
inference(equality_resolution,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: a > b] :
( cA
!= ( X0 @ ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: a > b] :
( cA
!= ( X0 @ ( sK0 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f4,f5]) ).
thf(f5,plain,
! [X0: a > b] :
( ? [X1: a] :
( ( X0 @ X1 )
!= cA )
=> ( cA
!= ( X0 @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f4,plain,
! [X0: a > b] :
? [X1: a] :
( ( X0 @ X1 )
!= cA ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: a > b] :
! [X1: a] :
( ( X0 @ X1 )
= cA ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: a > b] :
! [X1: a] :
( ( X0 @ X1 )
= cA ),
file('/export/starexec/sandbox/tmp/tmp.wU82cFdbli/DTF2THF_22626.p',cTTTP5243) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET045^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n001.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 11:51:05 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SET045^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.39 % Domain : Set Theory
% 0.18/0.39 % Problem : TPS problem TTTP5243
% 0.18/0.39 % Version : Especial.
% 0.18/0.39 % English : Comprehension Theorem.
% 0.18/0.39
% 0.18/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.39 % Source : [Bro09]
% 0.18/0.39 % Names : tps_0027 [Bro09]
% 0.18/0.39 % : TTTP5243 [TPS]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.18/0.39 % Syntax : Number of formulae : 4 ( 1 unt; 3 typ; 0 def)
% 0.18/0.39 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 1 ( 1 avg)
% 0.18/0.39 % Number of connectives : 1 ( 0 ~; 0 |; 0 &; 1 @)
% 0.18/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 3 ( 3 avg)
% 0.18/0.39 % Number of types : 2 ( 2 usr)
% 0.18/0.39 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 2 ( 1 usr; 1 con; 0-2 aty)
% 0.18/0.39 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.18/0.39 % SPC : TH0_THM_EQU_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(b_type,type,
% 0.18/0.39 b: $tType ).
% 0.18/0.39
% 0.18/0.39 thf(a_type,type,
% 0.18/0.39 a: $tType ).
% 0.18/0.39
% 0.18/0.39 thf(cA,type,
% 0.18/0.39 cA: b ).
% 0.18/0.39
% 0.18/0.39 thf(cTTTP5243,conjecture,
% 0.18/0.39 ? [U: a > b] :
% 0.18/0.39 ! [V: a] :
% 0.18/0.39 ( ( U @ V )
% 0.18/0.39 = cA ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.37/1.27 ---- Embedded in THF ---
% 1.37/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.27 %%% Generated on Tue Feb 24 11:51:06 EST 2026
% 1.37/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.27 %%% Logic specification used:
% 1.37/1.27 %%% thf(spec, logic, $$dhol).
% 1.37/1.27
% 1.37/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.wU82cFdbli/DTF2DTF22626.p
% See solution above
% 1.37/1.27 ------------------------
% 1.37/1.28 ---- Cleaned THF ---
% 1.37/1.28 thf(b_type,type,
% 1.37/1.28 b: $tType ).
% 1.37/1.28
% 1.37/1.28 thf(a_type,type,
% 1.37/1.28 a: $tType ).
% 1.37/1.28
% 1.37/1.28 thf(cA,type,
% 1.37/1.28 cA: b ).
% 1.37/1.28
% 1.37/1.28 thf(cTTTP5243,conjecture,
% 1.37/1.28 ? [U: a > b] :
% 1.37/1.28 ! [V: a] :
% 1.37/1.28 ( ( U @ V )
% 1.37/1.28 = cA ) ).
% 1.37/1.28 ------------------------
% 1.54/1.30 % (22729)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_22626 for (3000ds/2Mi)
% 1.54/1.30 % (22728)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22626 for (3000ds/2Mi)
% 1.54/1.30 % (22727)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_22626 for (3000ds/27Mi)
% 1.54/1.30 % (22726)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_22626 for (3000ds/4Mi)
% 1.54/1.30 % (22730)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_22626 for (3000ds/275Mi)
% 1.54/1.30 % (22731)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22626 for (3000ds/18Mi)
% 1.54/1.30 % (22725)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22626 for (3000ds/183Mi)
% 1.54/1.30 % (22730)Refutation not found, incomplete strategy
% 1.54/1.30 % (22730)------------------------------
% 1.54/1.30 % (22730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (22728)Refutation not found, incomplete strategy
% 1.54/1.30 % (22728)------------------------------
% 1.54/1.30 % (22728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (22728)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.30
% 1.54/1.30
% 1.54/1.30 % (22728)Memory used [KB]: 5373
% 1.54/1.30 % (22727)Refutation not found, incomplete strategy
% 1.54/1.30 % (22727)------------------------------
% 1.54/1.30 % (22727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (22728)Time elapsed: 0.002 s
% 1.54/1.30 % (22728)Instructions burned: 1 (million)
% 1.54/1.30 % (22727)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.30
% 1.54/1.30
% 1.54/1.30 % (22728)------------------------------
% 1.54/1.30 % (22728)------------------------------
% 1.54/1.30 % (22727)Memory used [KB]: 5373
% 1.54/1.30 % (22727)Time elapsed: 0.002 s
% 1.54/1.30 % (22727)Instructions burned: 1 (million)
% 1.54/1.30 % (22727)------------------------------
% 1.54/1.30 % (22727)------------------------------
% 1.54/1.30 % (22725)First to succeed.
% 1.54/1.30 % (22730)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.30
% 1.54/1.30
% 1.54/1.30 % (22730)Memory used [KB]: 5373
% 1.54/1.30 % (22730)Time elapsed: 0.002 s
% 1.54/1.30 % (22730)Instructions burned: 1 (million)
% 1.54/1.30 % (22730)------------------------------
% 1.54/1.30 % (22730)------------------------------
% 1.54/1.30 % (22729)Instruction limit reached!
% 1.54/1.30 % (22729)------------------------------
% 1.54/1.30 % (22729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (22729)Termination reason: Unknown
% 1.54/1.30 % (22729)Termination phase: Saturation
% 1.54/1.30
% 1.54/1.30 % (22729)Memory used [KB]: 5500
% 1.54/1.30 % (22729)Time elapsed: 0.003 s
% 1.54/1.30 % (22729)Instructions burned: 2 (million)
% 1.54/1.30 % (22729)------------------------------
% 1.54/1.30 % (22729)------------------------------
% 1.54/1.30 % (22731)Also succeeded, but the first one will report.
% 1.54/1.30 % (22726)Also succeeded, but the first one will report.
% 1.54/1.30 % (22725)Refutation found. Thanks to Tanya!
% 1.54/1.30 % SZS status Theorem for DTF2THF_22626
% 1.54/1.30 % SZS output start Proof for DTF2THF_22626
% 1.54/1.30 thf(type_def_5, type, b: $tType).
% 1.54/1.30 thf(type_def_6, type, a: $tType).
% 1.54/1.30 thf(func_def_0, type, b: $tType).
% 1.54/1.30 thf(func_def_1, type, a: $tType).
% 1.54/1.30 thf(func_def_2, type, cA: b).
% 1.54/1.30 thf(func_def_6, type, sK0: (a > b) > a).
% 1.54/1.30 thf(func_def_8, type, ph2: !>[X0: $tType]:(X0)).
% 1.54/1.30 thf(f8,plain,(
% 1.54/1.30 $false),
% 1.54/1.30 inference(equality_resolution,[status(thm)],[f7])).
% 1.54/1.30 thf(f7,plain,(
% 1.54/1.30 ( ! [X0 : a > b] : ((cA != (X0 @ (sK0 @ X0)))) )),
% 1.54/1.30 inference(cnf_transformation,[status(thm)],[f6])).
% 1.54/1.30 thf(f6,plain,(
% 1.54/1.30 ! [X0 : a > b] : (cA != (X0 @ (sK0 @ X0)))),
% 1.54/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f4,f5])).
% 1.54/1.30 thf(f5,plain,(
% 1.54/1.30 ! [X0 : a > b] : (? [X1 : a] : ((X0 @ X1) != cA) => (cA != (X0 @ (sK0 @ X0))))),
% 1.54/1.30 introduced(definition,[],[choice_axiom])).
% 1.54/1.30 thf(f4,plain,(
% 1.54/1.30 ! [X0 : a > b] : ? [X1 : a] : ((X0 @ X1) != cA)),
% 1.54/1.30 inference(ennf_transformation,[status(thm)],[f2])).
% 1.54/1.30 thf(f2,negated_conjecture,(
% 1.54/1.30 ~? [X0 : a > b] : ! [X1 : a] : ((X0 @ X1) = cA)),
% 1.54/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.30 thf(f1,conjecture,(
% 1.54/1.30 ? [X0 : a > b] : ! [X1 : a] : ((X0 @ X1) = cA)),
% 1.54/1.30 file('/export/starexec/sandbox/tmp/tmp.wU82cFdbli/DTF2THF_22626.p',cTTTP5243)).
% 1.54/1.30 % SZS output end Proof for DTF2THF_22626
% 1.54/1.30 % (22725)------------------------------
% 1.54/1.30 % (22725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (22725)Termination reason: Refutation
% 1.54/1.30
% 1.54/1.30 % (22725)Memory used [KB]: 5373
% 1.54/1.30 % (22725)Time elapsed: 0.003 s
% 1.54/1.30 % (22725)Instructions burned: 1 (million)
% 1.54/1.30 % (22725)------------------------------
% 1.54/1.30 % (22725)------------------------------
% 1.54/1.30 % (22724)Success in time 0.017 s
%------------------------------------------------------------------------------