%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU951^5 : 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 : n004.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 09:37:50 AM UTC 2026
% Result : Theorem 0.22s 1.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 43 ( 10 ~; 3 |; 2 &; 23 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 29 ( 0 ^; 23 !; 6 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
h: ( a > $o ) > b ).
thf(func_def_6,type,
sK0: ( b > a > $o ) > a > $o ).
thf(func_def_9,type,
inv_h_2: b > a > $o ).
thf(func_def_10,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f15,plain,
$false,
inference(equality_resolution,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: a > $o] :
( ( sK0 @ inv_h_2 )
!= X0 ),
inference(superposition,[status(thm)],[f7,f9]) ).
thf(f9,plain,
! [X0: a > $o] :
( ( inv_h_2 @ ( h @ X0 ) )
= X0 ),
inference(injectivity,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: a > $o,X1: a > $o] :
( ( ( h @ X0 )
!= ( h @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( X0 = X1 )
| ( ( h @ X0 )
!= ( h @ X1 ) ) )
& ! [X2: b > a > $o,X4: b] :
( ( X2 @ X4 )
!= ( sK0 @ X2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f4,f5]) ).
thf(f5,plain,
! [X2: b > a > $o] :
( ? [X3: a > $o] :
! [X4: b] :
( ( X2 @ X4 )
!= X3 )
=> ! [X4: b] :
( ( X2 @ X4 )
!= ( sK0 @ X2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f4,plain,
( ! [X0: a > $o,X1: a > $o] :
( ( X0 = X1 )
| ( ( h @ X0 )
!= ( h @ X1 ) ) )
& ! [X2: b > a > $o] :
? [X3: a > $o] :
! [X4: b] :
( ( X2 @ X4 )
!= X3 ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a > $o,X0: a > $o] :
( ( ( h @ X0 )
= ( h @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: b > a > $o] :
! [X3: a > $o] :
? [X4: b] :
( ( X2 @ X4 )
= X3 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: a > $o,X0: a > $o] :
( ( ( h @ X0 )
= ( h @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: b > a > $o] :
! [X3: a > $o] :
? [X4: b] :
( ( X2 @ X4 )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.NAecehNtg5/DTF2THF_31680.p',cTHM574_pme) ).
thf(f7,plain,
! [X2: b > a > $o,X4: b] :
( ( X2 @ X4 )
!= ( sK0 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU951^5 : 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 : n004.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 12:36:56 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.39 ---- Original DTF file ---
% 0.19/0.39 thf(spec,logic,$$dhol).
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 % File : SEU951^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.39 % Domain : Set Theory (Functions)
% 0.19/0.39 % Problem : TPS problem THM574
% 0.19/0.39 % Version : Especial.
% 0.19/0.39 % English : Challenge from Dana Scott stemming from injective Cantor Theorem.
% 0.19/0.39
% 0.19/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.39 % Source : [Bro09]
% 0.19/0.39 % Names : tps_0577 [Bro09]
% 0.19/0.39 % : THM574 [TPS]
% 0.19/0.39
% 0.19/0.39 % Status : Theorem
% 0.19/0.39 % Rating : 0.56 v9.1.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.43 v7.4.0, 0.78 v7.2.0, 0.75 v7.1.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 1.00 v4.0.0
% 0.19/0.39 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.39 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.19/0.39 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.39 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 3 @)
% 0.19/0.39 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.39 % Maximal formula depth : 5 ( 5 avg)
% 0.19/0.39 % Number of types : 3 ( 2 usr)
% 0.19/0.39 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.39 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.19/0.39 % Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% 0.19/0.39 % SPC : TH0_THM_EQU_NAR
% 0.19/0.39
% 0.19/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.39 % : Polymorphic definitions expanded.
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 thf(a_type,type,
% 0.19/0.39 a: $tType ).
% 0.19/0.39
% 0.19/0.39 thf(b_type,type,
% 0.19/0.39 b: $tType ).
% 0.19/0.39
% 0.19/0.39 thf(h,type,
% 0.19/0.39 h: ( a > $o ) > b ).
% 0.19/0.39
% 0.19/0.39 thf(cTHM574_pme,conjecture,
% 0.19/0.39 ( ! [Xx: a > $o,Xy: a > $o] :
% 0.19/0.39 ( ( ( h @ Xx )
% 0.19/0.39 = ( h @ Xy ) )
% 0.19/0.39 => ( Xx = Xy ) )
% 0.19/0.39 => ? [Xg: b > a > $o] :
% 0.19/0.39 ! [Y: a > $o] :
% 0.19/0.39 ? [X: b] :
% 0.19/0.39 ( ( Xg @ X )
% 0.19/0.39 = Y ) ) ).
% 0.19/0.39
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 ------------------------
% 0.22/1.30 ---- Embedded in THF ---
% 0.22/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.22/1.30 %%% Generated on Tue Feb 24 12:36:57 EST 2026
% 0.22/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.22/1.30 %%% Logic specification used:
% 0.22/1.30 %%% thf(spec, logic, $$dhol).
% 0.22/1.30
% 0.22/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.NAecehNtg5/DTF2DTF31680.p
% See solution above
% 0.22/1.30 ------------------------
% 0.22/1.31 ---- Cleaned THF ---
% 0.22/1.31 thf(a_type,type,
% 0.22/1.31 a: $tType ).
% 0.22/1.31
% 0.22/1.31 thf(b_type,type,
% 0.22/1.31 b: $tType ).
% 0.22/1.31
% 0.22/1.31 thf(h,type,
% 0.22/1.31 h: ( a > $o ) > b ).
% 0.22/1.31
% 0.22/1.31 thf(cTHM574_pme,conjecture,
% 0.22/1.31 ( ! [Xx: a > $o,Xy: a > $o] :
% 0.22/1.31 ( ( ( h @ Xx )
% 0.22/1.31 = ( h @ Xy ) )
% 0.22/1.31 => ( Xx = Xy ) )
% 0.22/1.31 => ? [Xg: b > a > $o] :
% 0.22/1.31 ! [Y: a > $o] :
% 0.22/1.31 ? [X: b] :
% 0.22/1.31 ( ( Xg @ X )
% 0.22/1.31 = Y ) ) ).
% 0.22/1.31 ------------------------
% 0.22/1.33 % (31778)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_31680 for (3000ds/4Mi)
% 0.22/1.33 % (31777)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31680 for (3000ds/183Mi)
% 0.22/1.33 % (31781)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_31680 for (3000ds/2Mi)
% 0.22/1.33 % (31783)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31680 for (3000ds/18Mi)
% 0.22/1.33 % (31779)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_31680 for (3000ds/27Mi)
% 0.22/1.33 % (31782)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_31680 for (3000ds/275Mi)
% 0.22/1.33 % (31780)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31680 for (3000ds/2Mi)
% 0.22/1.33 % (31781)Instruction limit reached!
% 0.22/1.33 % (31781)------------------------------
% 0.22/1.33 % (31781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (31781)Termination reason: Unknown
% 0.22/1.33 % (31781)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (31781)Memory used [KB]: 5373
% 0.22/1.33 % (31781)Time elapsed: 0.003 s
% 0.22/1.33 % (31781)Instructions burned: 2 (million)
% 0.22/1.33 % (31781)------------------------------
% 0.22/1.33 % (31781)------------------------------
% 0.22/1.33 % (31782)Refutation not found, incomplete strategy
% 0.22/1.33 % (31782)------------------------------
% 0.22/1.33 % (31782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (31779)Refutation not found, incomplete strategy
% 0.22/1.33 % (31779)------------------------------
% 0.22/1.33 % (31779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (31779)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.33
% 0.22/1.33
% 0.22/1.33 % (31779)Memory used [KB]: 5500
% 0.22/1.33 % (31779)Time elapsed: 0.003 s
% 0.22/1.33 % (31779)Instructions burned: 1 (million)
% 0.22/1.33 % (31779)------------------------------
% 0.22/1.33 % (31779)------------------------------
% 0.22/1.33 % (31782)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.33
% 0.22/1.33
% 0.22/1.33 % (31782)Memory used [KB]: 5373
% 0.22/1.33 % (31782)Time elapsed: 0.003 s
% 0.22/1.33 % (31782)Instructions burned: 1 (million)
% 0.22/1.33 % (31782)------------------------------
% 0.22/1.33 % (31782)------------------------------
% 0.22/1.33 % (31780)First to succeed.
% 0.22/1.33 % (31778)Instruction limit reached!
% 0.22/1.33 % (31778)------------------------------
% 0.22/1.33 % (31778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (31778)Termination reason: Unknown
% 0.22/1.33 % (31778)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (31778)Memory used [KB]: 5500
% 0.22/1.33 % (31780)Refutation found. Thanks to Tanya!
% 0.22/1.33 % SZS status Theorem for DTF2THF_31680
% 0.22/1.33 % SZS output start Proof for DTF2THF_31680
% 0.22/1.33 thf(type_def_5, type, a: $tType).
% 0.22/1.33 thf(type_def_7, type, b: $tType).
% 0.22/1.33 thf(func_def_0, type, a: $tType).
% 0.22/1.33 thf(func_def_1, type, b: $tType).
% 0.22/1.33 thf(func_def_2, type, h: (a > $o) > b).
% 0.22/1.33 thf(func_def_6, type, sK0: (b > a > $o) > a > $o).
% 0.22/1.33 thf(func_def_9, type, inv_h_2: b > a > $o).
% 0.22/1.33 thf(func_def_10, type, ph3: !>[X0: $tType]:(X0)).
% 0.22/1.33 thf(f15,plain,(
% 0.22/1.33 $false),
% 0.22/1.33 inference(equality_resolution,[status(thm)],[f14])).
% 0.22/1.33 thf(f14,plain,(
% 0.22/1.33 ( ! [X0 : a > $o] : (((sK0 @ inv_h_2) != X0)) )),
% 0.22/1.33 inference(superposition,[status(thm)],[f7,f9])).
% 0.22/1.33 thf(f9,plain,(
% 0.22/1.33 ( ! [X0 : a > $o] : (((inv_h_2 @ (h @ X0)) = X0)) )),
% 0.22/1.33 inference(injectivity,[status(thm)],[f8])).
% 0.22/1.33 thf(f8,plain,(
% 0.22/1.33 ( ! [X0 : a > $o,X1 : a > $o] : (((h @ X0) != (h @ X1)) | (X0 = X1)) )),
% 0.22/1.33 inference(cnf_transformation,[status(thm)],[f6])).
% 0.22/1.33 thf(f6,plain,(
% 0.22/1.33 ! [X0 : a > $o,X1 : a > $o] : ((X0 = X1) | ((h @ X0) != (h @ X1))) & ! [X2 : b > a > $o] : ! [X4 : b] : ((X2 @ X4) != (sK0 @ X2))),
% 0.22/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f4,f5])).
% 0.22/1.33 thf(f5,plain,(
% 0.22/1.33 ! [X2 : b > a > $o] : (? [X3 : a > $o] : ! [X4 : b] : ((X2 @ X4) != X3) => ! [X4 : b] : ((X2 @ X4) != (sK0 @ X2)))),
% 0.22/1.33 introduced(definition,[],[choice_axiom])).
% 0.22/1.33 thf(f4,plain,(
% 0.22/1.33 ! [X0 : a > $o,X1 : a > $o] : ((X0 = X1) | ((h @ X0) != (h @ X1))) & ! [X2 : b > a > $o] : ? [X3 : a > $o] : ! [X4 : b] : ((X2 @ X4) != X3)),
% 0.22/1.33 inference(ennf_transformation,[status(thm)],[f2])).
% 0.22/1.33 thf(f2,negated_conjecture,(
% 0.22/1.33 ~(! [X1 : a > $o,X0 : a > $o] : (((h @ X0) = (h @ X1)) => (X0 = X1)) => ? [X2 : b > a > $o] : ! [X3 : a > $o] : ? [X4 : b] : ((X2 @ X4) = X3))),
% 0.22/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/1.33 thf(f1,conjecture,(
% 0.22/1.33 ! [X1 : a > $o,X0 : a > $o] : (((h @ X0) = (h @ X1)) => (X0 = X1)) => ? [X2 : b > a > $o] : ! [X3 : a > $o] : ? [X4 : b] : ((X2 @ X4) = X3)),
% 0.22/1.33 file('/export/starexec/sandbox/tmp/tmp.NAecehNtg5/DTF2THF_31680.p',cTHM574_pme)).
% 0.22/1.33 thf(f7,plain,(
% 0.22/1.33 ( ! [X2 : b > a > $o,X4 : b] : (((X2 @ X4) != (sK0 @ X2))) )),
% 0.22/1.33 inference(cnf_transformation,[status(thm)],[f6])).
% 0.22/1.33 % SZS output end Proof for DTF2THF_31680
% 0.22/1.33 % (31780)------------------------------
% 0.22/1.33 % (31780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (31780)Termination reason: Refutation
% 0.22/1.33
% 0.22/1.33 % (31780)Memory used [KB]: 5500
% 0.22/1.33 % (31780)Time elapsed: 0.003 s
% 0.22/1.33 % (31780)Instructions burned: 1 (million)
% 0.22/1.33 % (31780)------------------------------
% 0.22/1.33 % (31780)------------------------------
% 0.22/1.33 % (31776)Success in time 0.018 s
%------------------------------------------------------------------------------