%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO552^1 : 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 : n018.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 09:54:32 AM UTC 2026
% Result : Theorem 0.34s 1.64s
% Output : Refutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 9 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 36 ( 8 ~; 0 |; 0 &; 27 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 11 !; 9 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( $i > $i > $i ) > $i ).
thf(func_def_4,type,
sK1: ( $i > $i > $i ) > $i ).
thf(func_def_6,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f10,plain,
$false,
inference(equality_resolution,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $i > $i] :
( ( sK0 @ X0 )
!= ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $i > $i] :
( ( sK0 @ X0 )
!= ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
! [X0: $i > $i > $i] :
( ? [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
!= X1 )
=> ( ( sK0 @ X0 )
!= ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: $i > $i > $i] :
? [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
!= X1 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i > $i > $i] :
? [X2: $i,X1: $i] :
( ( X0 @ X2 @ X1 )
!= X2 ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $i > $i] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
= X2 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $i > $i] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $i > $i] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
= X1 ),
file('/export/starexec/sandbox/tmp/tmp.WazQZ52EQP/DTF2THF_30624.p',claim) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO552^1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Feb 24 14:33:31 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SYO552^1 : TPTP v9.2.1. Released v5.2.0.
% 0.33/0.49 % Domain : Syntactic
% 0.33/0.49 % Problem : The first projection exists
% 0.33/0.49 % Version : Especial.
% 0.33/0.49 % English : There is a binary function that returns its first argument
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.33/0.49 % Source : [Bro11]
% 0.33/0.49 % Names : PROJ1 [Bro11]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % 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
% 0.33/0.49 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.33/0.49 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 1 ( 1 avg)
% 0.33/0.49 % Number of connectives : 2 ( 0 ~; 0 |; 0 &; 2 @)
% 0.33/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 4 ( 4 avg)
% 0.33/0.49 % Number of types : 1 ( 0 usr)
% 0.33/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.33/0.49 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.33/0.49 % SPC : TH0_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : This simple problem tests higher-order instantiations.
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(claim,conjecture,
% 0.33/0.49 ? [F: $i > $i > $i] :
% 0.33/0.49 ! [X: $i,Y: $i] :
% 0.33/0.49 ( ( F @ X @ Y )
% 0.33/0.49 = X ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 0.34/1.60 ---- Embedded in THF ---
% 0.34/1.61 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.34/1.61 %%% Generated on Tue Feb 24 14:33:32 EST 2026
% 0.34/1.61 %%% using '$$dhol' embedding, version 1.3.0.
% 0.34/1.61 %%% Logic specification used:
% 0.34/1.61 %%% thf(spec, logic, $$dhol).
% 0.34/1.61
% 0.34/1.61 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WazQZ52EQP/DTF2DTF30624.p
% See solution above
% 0.34/1.61 ------------------------
% 0.34/1.61 ---- Cleaned THF ---
% 0.34/1.62 thf(claim,conjecture,
% 0.34/1.62 ? [F: $i > $i > $i] :
% 0.34/1.62 ! [X: $i,Y: $i] :
% 0.34/1.62 ( ( F @ X @ Y )
% 0.34/1.62 = X ) ).
% 0.34/1.62 ------------------------
% 0.34/1.64 % (30724)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30624 for (3000ds/2Mi)
% 0.34/1.64 % (30723)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_30624 for (3000ds/27Mi)
% 0.34/1.64 % (30727)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30624 for (3000ds/18Mi)
% 0.34/1.64 % (30725)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_30624 for (3000ds/2Mi)
% 0.34/1.64 % (30722)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_30624 for (3000ds/4Mi)
% 0.34/1.64 % (30721)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30624 for (3000ds/183Mi)
% 0.34/1.64 % (30724)Refutation not found, incomplete strategy
% 0.34/1.64 % (30724)------------------------------
% 0.34/1.64 % (30724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.64 % (30723)Refutation not found, incomplete strategy
% 0.34/1.64 % (30723)------------------------------
% 0.34/1.64 % (30723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.64 % (30723)Termination reason: Refutation not found, incomplete strategy
% 0.34/1.64
% 0.34/1.64
% 0.34/1.64 % (30723)Memory used [KB]: 5373
% 0.34/1.64 % (30723)Time elapsed: 0.003 s
% 0.34/1.64 % (30723)Instructions burned: 1 (million)
% 0.34/1.64 % (30723)------------------------------
% 0.34/1.64 % (30723)------------------------------
% 0.34/1.64 % (30724)Termination reason: Refutation not found, incomplete strategy
% 0.34/1.64
% 0.34/1.64
% 0.34/1.64 % (30724)Memory used [KB]: 5373
% 0.34/1.64 % (30724)Time elapsed: 0.003 s
% 0.34/1.64 % (30725)Instruction limit reached!
% 0.34/1.64 % (30725)------------------------------
% 0.34/1.64 % (30725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.64 % (30724)Instructions burned: 1 (million)
% 0.34/1.64 % (30724)------------------------------
% 0.34/1.64 % (30724)------------------------------
% 0.34/1.64 % (30726)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_30624 for (3000ds/275Mi)
% 0.34/1.64 % (30721)First to succeed.
% 0.34/1.64 % (30725)Termination reason: Unknown
% 0.34/1.64 % (30725)Termination phase: Saturation
% 0.34/1.64
% 0.34/1.64 % (30725)Memory used [KB]: 5500
% 0.34/1.64 % (30725)Time elapsed: 0.003 s
% 0.34/1.64 % (30725)Instructions burned: 2 (million)
% 0.34/1.64 % (30725)------------------------------
% 0.34/1.64 % (30725)------------------------------
% 0.34/1.64 % (30722)Also succeeded, but the first one will report.
% 0.34/1.64 % (30726)Refutation not found, incomplete strategy
% 0.34/1.64 % (30726)------------------------------
% 0.34/1.64 % (30726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.64 % (30726)Termination reason: Refutation not found, incomplete strategy
% 0.34/1.64
% 0.34/1.64
% 0.34/1.64 % (30726)Memory used [KB]: 5373
% 0.34/1.64 % (30726)Time elapsed: 0.002 s
% 0.34/1.64 % (30726)Instructions burned: 1 (million)
% 0.34/1.64 % (30726)------------------------------
% 0.34/1.64 % (30726)------------------------------
% 0.34/1.64 % (30721)Refutation found. Thanks to Tanya!
% 0.34/1.64 % SZS status Theorem for DTF2THF_30624
% 0.34/1.64 % SZS output start Proof for DTF2THF_30624
% 0.34/1.64 thf(func_def_3, type, sK0: ($i > $i > $i) > $i).
% 0.34/1.64 thf(func_def_4, type, sK1: ($i > $i > $i) > $i).
% 0.34/1.64 thf(func_def_6, type, ph3: !>[X0: $tType]:(X0)).
% 0.34/1.64 thf(f10,plain,(
% 0.34/1.64 $false),
% 0.34/1.64 inference(equality_resolution,[status(thm)],[f9])).
% 0.34/1.64 thf(f9,plain,(
% 0.34/1.64 ( ! [X0 : $i > $i > $i] : (((sK0 @ X0) != (X0 @ (sK0 @ X0) @ (sK1 @ X0)))) )),
% 0.34/1.64 inference(cnf_transformation,[status(thm)],[f8])).
% 0.34/1.64 thf(f8,plain,(
% 0.34/1.64 ! [X0 : $i > $i > $i] : ((sK0 @ X0) != (X0 @ (sK0 @ X0) @ (sK1 @ X0)))),
% 0.34/1.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 0.34/1.64 thf(f7,plain,(
% 0.34/1.64 ! [X0 : $i > $i > $i] : (? [X1 : $i,X2 : $i] : ((X0 @ X1 @ X2) != X1) => ((sK0 @ X0) != (X0 @ (sK0 @ X0) @ (sK1 @ X0))))),
% 0.34/1.64 introduced(definition,[],[choice_axiom])).
% 0.34/1.64 thf(f6,plain,(
% 0.34/1.64 ! [X0 : $i > $i > $i] : ? [X1 : $i,X2 : $i] : ((X0 @ X1 @ X2) != X1)),
% 0.34/1.64 inference(rectify,[status(thm)],[f5])).
% 0.34/1.64 thf(f5,plain,(
% 0.34/1.64 ! [X0 : $i > $i > $i] : ? [X2 : $i,X1 : $i] : ((X0 @ X2 @ X1) != X2)),
% 0.34/1.64 inference(ennf_transformation,[status(thm)],[f4])).
% 0.34/1.64 thf(f4,plain,(
% 0.34/1.64 ~? [X0 : $i > $i > $i] : ! [X1 : $i,X2 : $i] : ((X0 @ X2 @ X1) = X2)),
% 0.34/1.64 inference(rectify,[status(thm)],[f2])).
% 0.34/1.64 thf(f2,negated_conjecture,(
% 0.34/1.64 ~? [X0 : $i > $i > $i] : ! [X2 : $i,X1 : $i] : ((X0 @ X1 @ X2) = X1)),
% 0.34/1.64 inference(negated_conjecture,[status(cth)],[f1])).
% 0.34/1.64 thf(f1,conjecture,(
% 0.34/1.64 ? [X0 : $i > $i > $i] : ! [X2 : $i,X1 : $i] : ((X0 @ X1 @ X2) = X1)),
% 0.34/1.64 file('/export/starexec/sandbox/tmp/tmp.WazQZ52EQP/DTF2THF_30624.p',claim)).
% 0.34/1.64 % SZS output end Proof for DTF2THF_30624
% 0.34/1.64 % (30721)------------------------------
% 0.34/1.64 % (30721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.34/1.64 % (30721)Termination reason: Refutation
% 0.34/1.64
% 0.34/1.64 % (30721)Memory used [KB]: 5373
% 0.34/1.64 % (30721)Time elapsed: 0.002 s
% 0.34/1.64 % (30721)Instructions burned: 1 (million)
% 0.34/1.64 % (30721)------------------------------
% 0.34/1.64 % (30721)------------------------------
% 0.34/1.64 % (30720)Success in time 0.018 s
%------------------------------------------------------------------------------