%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO551^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 09:54:31 AM UTC 2026
% Result : Theorem 1.92s 1.62s
% Output : Refutation 1.92s
% 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 : 20 ( 6 ~; 0 |; 0 &; 13 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 6 !; 4 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(func_def_5,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f8,plain,
$false,
inference(equality_resolution,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: ( $i > $i ) > $i > $i] :
( ( sK0 @ X0 )
!= ( X0 @ ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: ( $i > $i ) > $i > $i] :
( ( sK0 @ X0 )
!= ( X0 @ ( sK0 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f4,f5]) ).
thf(f5,plain,
! [X0: ( $i > $i ) > $i > $i] :
( ? [X1: $i > $i] :
( ( X0 @ X1 )
!= X1 )
=> ( ( sK0 @ X0 )
!= ( X0 @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f4,plain,
! [X0: ( $i > $i ) > $i > $i] :
? [X1: $i > $i] :
( ( X0 @ X1 )
!= X1 ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $i ) > $i > $i] :
! [X1: $i > $i] :
( ( X0 @ X1 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $i ) > $i > $i] :
! [X1: $i > $i] :
( ( X0 @ X1 )
= X1 ),
file('/export/starexec/sandbox/tmp/tmp.5r6ILacBHu/DTF2THF_23310.p',claim) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO551^1 : TPTP v9.2.1. Released v5.2.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:33:23 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SYO551^1 : TPTP v9.2.1. Released v5.2.0.
% 0.20/0.48 % Domain : Syntactic
% 0.20/0.48 % Problem : The identity function on functions from $i to $i exists
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bro11]
% 0.20/0.48 % Names : IDii [Bro11]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.20/0.48 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.20/0.48 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.48 % Number of connectives : 1 ( 0 ~; 0 |; 0 &; 1 @)
% 0.20/0.48 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 3 ( 3 avg)
% 0.20/0.48 % Number of types : 1 ( 0 usr)
% 0.20/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.48 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This simple problem tests higher-order instantiations.
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(claim,conjecture,
% 0.20/0.48 ? [F: ( $i > $i ) > $i > $i] :
% 0.20/0.48 ! [X: $i > $i] :
% 0.20/0.48 ( ( F @ X )
% 0.20/0.48 = X ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.75/1.59 ---- Embedded in THF ---
% 1.75/1.59 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.75/1.59 %%% Generated on Tue Feb 24 14:33:24 EST 2026
% 1.75/1.59 %%% using '$$dhol' embedding, version 1.3.0.
% 1.75/1.59 %%% Logic specification used:
% 1.75/1.59 %%% thf(spec, logic, $$dhol).
% 1.75/1.59
% 1.75/1.59 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5r6ILacBHu/DTF2DTF23310.p
% See solution above
% 1.75/1.59 ------------------------
% 1.92/1.60 ---- Cleaned THF ---
% 1.92/1.60 thf(claim,conjecture,
% 1.92/1.60 ? [F: ( $i > $i ) > $i > $i] :
% 1.92/1.60 ! [X: $i > $i] :
% 1.92/1.60 ( ( F @ X )
% 1.92/1.60 = X ) ).
% 1.92/1.60 ------------------------
% 1.92/1.62 % (23410)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_23310 for (3000ds/27Mi)
% 1.92/1.62 % (23408)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23310 for (3000ds/183Mi)
% 1.92/1.62 % (23409)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_23310 for (3000ds/4Mi)
% 1.92/1.62 % (23414)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23310 for (3000ds/18Mi)
% 1.92/1.62 % (23411)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23310 for (3000ds/2Mi)
% 1.92/1.62 % (23410)Refutation not found, incomplete strategy
% 1.92/1.62 % (23410)------------------------------
% 1.92/1.62 % (23410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.62 % (23410)Termination reason: Refutation not found, incomplete strategy
% 1.92/1.62
% 1.92/1.62 % (23408)First to succeed.
% 1.92/1.62 % (23412)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_23310 for (3000ds/2Mi)
% 1.92/1.62 % (23413)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_23310 for (3000ds/275Mi)
% 1.92/1.62
% 1.92/1.62 % (23410)Memory used [KB]: 5373
% 1.92/1.62 % (23410)Time elapsed: 0.003 s
% 1.92/1.62 % (23410)Instructions burned: 1 (million)
% 1.92/1.62 % (23410)------------------------------
% 1.92/1.62 % (23410)------------------------------
% 1.92/1.62 % (23411)Refutation not found, incomplete strategy
% 1.92/1.62 % (23411)------------------------------
% 1.92/1.62 % (23411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.62 % (23411)Termination reason: Refutation not found, incomplete strategy
% 1.92/1.62
% 1.92/1.62
% 1.92/1.62 % (23411)Memory used [KB]: 5373
% 1.92/1.62 % (23411)Time elapsed: 0.002 s
% 1.92/1.62 % (23411)Instructions burned: 1 (million)
% 1.92/1.62 % (23411)------------------------------
% 1.92/1.62 % (23411)------------------------------
% 1.92/1.62 % (23414)Also succeeded, but the first one will report.
% 1.92/1.62 % (23413)Refutation not found, incomplete strategy
% 1.92/1.62 % (23413)------------------------------
% 1.92/1.62 % (23413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.62 % (23413)Termination reason: Refutation not found, incomplete strategy
% 1.92/1.62
% 1.92/1.62
% 1.92/1.62 % (23413)Memory used [KB]: 5373
% 1.92/1.62 % (23413)Time elapsed: 0.002 s
% 1.92/1.62 % (23413)Instructions burned: 1 (million)
% 1.92/1.62 % (23413)------------------------------
% 1.92/1.62 % (23413)------------------------------
% 1.92/1.62 % (23412)Instruction limit reached!
% 1.92/1.62 % (23412)------------------------------
% 1.92/1.62 % (23412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.62 % (23412)Termination reason: Unknown
% 1.92/1.62 % (23412)Termination phase: Saturation
% 1.92/1.62
% 1.92/1.62 % (23412)Memory used [KB]: 5500
% 1.92/1.62 % (23412)Time elapsed: 0.003 s
% 1.92/1.62 % (23412)Instructions burned: 2 (million)
% 1.92/1.62 % (23412)------------------------------
% 1.92/1.62 % (23412)------------------------------
% 1.92/1.62 % (23409)Also succeeded, but the first one will report.
% 1.92/1.62 % (23408)Refutation found. Thanks to Tanya!
% 1.92/1.62 % SZS status Theorem for DTF2THF_23310
% 1.92/1.62 % SZS output start Proof for DTF2THF_23310
% 1.92/1.62 thf(func_def_3, type, sK0: (($i > $i) > $i > $i) > $i > $i).
% 1.92/1.62 thf(func_def_5, type, ph2: !>[X0: $tType]:(X0)).
% 1.92/1.62 thf(f8,plain,(
% 1.92/1.62 $false),
% 1.92/1.62 inference(equality_resolution,[status(thm)],[f7])).
% 1.92/1.62 thf(f7,plain,(
% 1.92/1.62 ( ! [X0 : ($i > $i) > $i > $i] : (((sK0 @ X0) != (X0 @ (sK0 @ X0)))) )),
% 1.92/1.62 inference(cnf_transformation,[status(thm)],[f6])).
% 1.92/1.62 thf(f6,plain,(
% 1.92/1.62 ! [X0 : ($i > $i) > $i > $i] : ((sK0 @ X0) != (X0 @ (sK0 @ X0)))),
% 1.92/1.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f4,f5])).
% 1.92/1.62 thf(f5,plain,(
% 1.92/1.62 ! [X0 : ($i > $i) > $i > $i] : (? [X1 : $i > $i] : ((X0 @ X1) != X1) => ((sK0 @ X0) != (X0 @ (sK0 @ X0))))),
% 1.92/1.62 introduced(definition,[],[choice_axiom])).
% 1.92/1.62 thf(f4,plain,(
% 1.92/1.62 ! [X0 : ($i > $i) > $i > $i] : ? [X1 : $i > $i] : ((X0 @ X1) != X1)),
% 1.92/1.62 inference(ennf_transformation,[status(thm)],[f2])).
% 1.92/1.62 thf(f2,negated_conjecture,(
% 1.92/1.62 ~? [X0 : ($i > $i) > $i > $i] : ! [X1 : $i > $i] : ((X0 @ X1) = X1)),
% 1.92/1.62 inference(negated_conjecture,[status(cth)],[f1])).
% 1.92/1.62 thf(f1,conjecture,(
% 1.92/1.62 ? [X0 : ($i > $i) > $i > $i] : ! [X1 : $i > $i] : ((X0 @ X1) = X1)),
% 1.92/1.62 file('/export/starexec/sandbox/tmp/tmp.5r6ILacBHu/DTF2THF_23310.p',claim)).
% 1.92/1.62 % SZS output end Proof for DTF2THF_23310
% 1.92/1.62 % (23408)------------------------------
% 1.92/1.62 % (23408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.92/1.62 % (23408)Termination reason: Refutation
% 1.92/1.62
% 1.92/1.62 % (23408)Memory used [KB]: 5373
% 1.92/1.62 % (23408)Time elapsed: 0.003 s
% 1.92/1.62 % (23408)Instructions burned: 1 (million)
% 1.92/1.62 % (23408)------------------------------
% 1.92/1.62 % (23408)------------------------------
% 1.92/1.62 % (23407)Success in time 0.019 s
%------------------------------------------------------------------------------