%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : CAT039^1 : TPTP v9.2.1. Released v9.2.0.
% 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 08:40:55 AM UTC 2026
% Result : Theorem 1.88s 1.53s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 18 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 102 ( 9 ~; 0 |; 4 &; 84 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-5 aty)
% Number of variables : 16 ( 0 ^; 12 !; 4 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
obj: $tType ).
thf(type_def_7,type,
mor: $tType ).
thf(func_def_0,type,
isPer:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > $o ) ).
thf(func_def_2,type,
obj: $tType ).
thf(func_def_3,type,
objStar: obj > obj > $o ).
thf(func_def_4,type,
mor: $tType ).
thf(func_def_5,type,
morStar: obj > obj > mor > mor > $o ).
thf(func_def_6,type,
id: obj > mor ).
thf(func_def_7,type,
comp: obj > obj > obj > mor > mor > mor ).
thf(func_def_10,type,
sK0: obj ).
thf(func_def_11,type,
sK1: obj ).
thf(f46,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f45,f41]) ).
thf(f41,plain,
! [X0: obj] :
( ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: obj] :
( ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: obj] : ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: obj] : ( morStar @ X2 @ X2 @ ( id @ X2 ) @ ( id @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.98VnGS3ci7/DTF2THF_11563.p',id_tp_ax) ).
thf(f45,plain,
( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK0 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f40,f39]) ).
thf(f39,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK1 ) )
!= $true )
& ( sK1 = sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f32,f36]) ).
thf(f36,plain,
( ? [X0: obj,X1: obj] :
( ( ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X1 ) )
!= $true )
& ( X0 = X1 ) )
=> ( ( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK1 ) )
!= $true )
& ( sK1 = sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
? [X0: obj,X1: obj] :
( ( ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X1 ) )
!= $true )
& ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ! [X0: obj,X1: obj] :
( ( X0 = X1 )
=> ( ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ! [X0: obj,X1: obj] :
( ( X0 = X1 )
=> ( morStar @ X0 @ X0 @ ( id @ X0 ) @ ( id @ X1 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,negated_conjecture,
~ ! [X2: obj,X3: obj] :
( ( X2 = X3 )
=> ( morStar @ X2 @ X2 @ ( id @ X2 ) @ ( id @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f9,conjecture,
! [X2: obj,X3: obj] :
( ( X2 = X3 )
=> ( morStar @ X2 @ X2 @ ( id @ X2 ) @ ( id @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.98VnGS3ci7/DTF2THF_11563.p',conj) ).
thf(f40,plain,
( ( morStar @ sK0 @ sK0 @ ( id @ sK0 ) @ ( id @ sK1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT039^1 : TPTP v9.2.1. Released v9.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n001.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 04:09:20 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.49 ---- Original DTF file ---
% 0.32/0.49 thf(spec,logic,$$dhol).
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 % File : CAT039^1 : TPTP v9.2.1. Released v9.2.0.
% 0.32/0.49 % Domain : Category Theory
% 0.32/0.49 % Problem : Simple problem from category theory dhol_1
% 0.32/0.49 % Version : Especial.
% 0.32/0.49 % English :
% 0.32/0.49
% 0.32/0.49 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.32/0.49 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.32/0.49 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.32/0.49 % Source : [Rot25]
% 0.32/0.49 % Names : CategoryTheory/category-theory-lemmas-dhol_1.p [Rot25]
% 0.32/0.49
% 0.32/0.49 % Status : Theorem
% 0.32/0.49 % Rating : ? v9.2.0
% 0.32/0.49 % Syntax : Number of formulae : 8 ( 3 unt; 4 typ; 0 def)
% 0.32/0.49 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.32/0.49 % Maximal formula atoms : 2 ( 1 avg)
% 0.32/0.49 % Number of connectives : 53 ( 0 ~; 0 |; 0 &; 52 @)
% 0.32/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 8 ( 5 avg)
% 0.32/0.49 % Number of types : 1 ( 1 usr)
% 0.32/0.49 % Number of type decls : 4 ( 0 !>P; 2 !>D)
% 0.32/0.49 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 4 ( 3 usr; 0 con; 1-5 aty)
% 0.32/0.49 % Number of variables : 19 ( 0 ^; 15 !; 0 ?; 19 :)
% 0.32/0.49 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.49 % SPC : DH0_THM_EQU_NAR
% 0.32/0.49
% 0.32/0.49 % Comments :
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(obj_type,type,
% 0.32/0.49 obj: $tType ).
% 0.32/0.49
% 0.32/0.49 thf(mor_type,type,
% 0.32/0.49 mor: obj > obj > $tType ).
% 0.32/0.49
% 0.32/0.49 thf(id_type,type,
% 0.32/0.49 id:
% 0.32/0.49 !>[X: obj] : ( mor @ X @ X ) ).
% 0.32/0.49
% 0.32/0.49 thf(comp_type,type,
% 0.32/0.49 comp:
% 0.32/0.49 !>[X: obj,Y: obj,Z: obj] : ( ( mor @ X @ Y ) > ( mor @ Y @ Z ) > ( mor @ X @ Z ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(ax1,axiom,
% 0.32/0.49 ! [X: obj,Y: obj,M: mor @ X @ Y] :
% 0.32/0.49 ( ( comp @ X @ X @ Y @ ( id @ X ) @ M )
% 0.32/0.49 = M ) ).
% 0.32/0.49
% 0.32/0.49 thf(ax2,axiom,
% 0.32/0.49 ! [X: obj,Y: obj,M: mor @ X @ Y] :
% 0.32/0.49 ( ( comp @ X @ Y @ Y @ M @ ( id @ Y ) )
% 0.32/0.49 = M ) ).
% 0.32/0.49
% 0.32/0.49 thf(ax3,axiom,
% 0.32/0.49 ! [X: obj,Y: obj,Z: obj,A: obj,F: mor @ X @ Y,G: mor @ Y @ Z,H: mor @ Z @ A] :
% 0.32/0.49 ( ( comp @ X @ Y @ A @ F @ ( comp @ Y @ Z @ A @ G @ H ) )
% 0.32/0.49 = ( comp @ X @ Z @ A @ ( comp @ X @ Y @ Z @ F @ G ) @ H ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(conj,conjecture,
% 0.32/0.49 ! [X: obj,Y: obj] :
% 0.32/0.49 ( ( X = Y )
% 0.32/0.49 => ( ( id @ X )
% 0.32/0.49 = ( id @ Y ) ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 1.68/1.49 ---- Embedded in THF ---
% 1.68/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.49 %%% Generated on Tue Feb 24 04:09:21 EST 2026
% 1.68/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.49 %%% Logic specification used:
% 1.68/1.49 %%% thf(spec, logic, $$dhol).
% 1.68/1.49
% 1.68/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.98VnGS3ci7/DTF2DTF11563.p
% See solution above
% 1.68/1.49 ------------------------
% 1.88/1.50 ---- Cleaned THF ---
% 1.88/1.50 thf(is_per_type,type,
% 1.88/1.50 isPer:
% 1.88/1.50 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.88/1.50
% 1.88/1.50 thf(is_per,definition,
% 1.88/1.50 ! [A: $tType,AStar: A > A > $o] :
% 1.88/1.50 ( ( isPer @ A @ AStar )
% 1.88/1.50 <=> ( ! [X: A,Y: A] :
% 1.88/1.50 ( ( AStar @ X @ Y )
% 1.88/1.50 => ( AStar @ Y @ X ) )
% 1.88/1.50 & ! [X: A,Y: A,Z: A] :
% 1.88/1.50 ( ( AStar @ X @ Y )
% 1.88/1.50 => ( ( AStar @ Y @ Z )
% 1.88/1.50 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.88/1.50
% 1.88/1.50 thf(obj_type,type,
% 1.88/1.50 obj: $tType ).
% 1.88/1.50
% 1.88/1.50 thf(objStar,type,
% 1.88/1.50 objStar: obj > obj > $o ).
% 1.88/1.50
% 1.88/1.50 thf(objStar_is_eq,axiom,
% 1.88/1.50 ! [X: obj,Y: obj] :
% 1.88/1.50 ( ( objStar @ X @ Y )
% 1.88/1.50 <=> ( X = Y ) ) ).
% 1.88/1.50
% 1.88/1.50 thf(mor_type,type,
% 1.88/1.50 mor: $tType ).
% 1.88/1.50
% 1.88/1.50 thf(morStar,type,
% 1.88/1.50 morStar: obj > obj > mor > mor > $o ).
% 1.88/1.50
% 1.88/1.50 thf('\'morStar\'_is_per',axiom,
% 1.88/1.50 ! [C: obj,C0: obj] : ( isPer @ mor @ ( morStar @ C @ C0 ) ) ).
% 1.88/1.50
% 1.88/1.50 thf(id_type,type,
% 1.88/1.50 id: obj > mor ).
% 1.88/1.50
% 1.88/1.50 thf(id_tp_ax,axiom,
% 1.88/1.50 ! [X: obj] : ( morStar @ X @ X @ ( id @ X ) @ ( id @ X ) ) ).
% 1.88/1.50
% 1.88/1.50 thf(comp_type,type,
% 1.88/1.50 comp: obj > obj > obj > mor > mor > mor ).
% 1.88/1.50
% 1.88/1.50 thf(comp_tp_ax,axiom,
% 1.88/1.50 ! [X: obj,Y: obj,Z: obj,D: mor,D_prime: mor] :
% 1.88/1.50 ( ( morStar @ X @ Y @ D @ D_prime )
% 1.88/1.50 => ! [D0: mor,D0_prime: mor] :
% 1.88/1.50 ( ( morStar @ Y @ Z @ D0 @ D0_prime )
% 1.88/1.50 => ( morStar @ X @ Z @ ( comp @ X @ Y @ Z @ D @ D0 ) @ ( comp @ X @ Y @ Z @ D_prime @ D0_prime ) ) ) ) ).
% 1.88/1.50
% 1.88/1.50 thf(ax1,axiom,
% 1.88/1.50 ! [X: obj,Y: obj,M: mor] :
% 1.88/1.50 ( ( morStar @ X @ Y @ M @ M )
% 1.88/1.50 => ( morStar @ X @ Y @ ( comp @ X @ X @ Y @ ( id @ X ) @ M ) @ M ) ) ).
% 1.88/1.50
% 1.88/1.50 thf(ax2,axiom,
% 1.88/1.50 ! [X: obj,Y: obj,M: mor] :
% 1.88/1.50 ( ( morStar @ X @ Y @ M @ M )
% 1.88/1.50 => ( morStar @ X @ Y @ ( comp @ X @ Y @ Y @ M @ ( id @ Y ) ) @ M ) ) ).
% 1.88/1.50
% 1.88/1.50 thf(ax3,axiom,
% 1.88/1.50 ! [X: obj,Y: obj,Z: obj,A: obj,F: mor,G: mor,H: mor] :
% 1.88/1.50 ( ( morStar @ X @ Y @ F @ F )
% 1.88/1.50 => ( ( morStar @ Y @ Z @ G @ G )
% 1.88/1.50 => ( ( morStar @ Z @ A @ H @ H )
% 1.88/1.50 => ( morStar @ X @ A @ ( comp @ X @ Y @ A @ F @ ( comp @ Y @ Z @ A @ G @ H ) ) @ ( comp @ X @ Z @ A @ ( comp @ X @ Y @ Z @ F @ G ) @ H ) ) ) ) ) ).
% 1.88/1.50
% 1.88/1.50 thf(conj,conjecture,
% 1.88/1.50 ! [X: obj,Y: obj] :
% 1.88/1.50 ( ( X = Y )
% 1.88/1.50 => ( morStar @ X @ X @ ( id @ X ) @ ( id @ Y ) ) ) ).
% 1.88/1.50 ------------------------
% 1.88/1.52 % (11675)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_11563 for (2999ds/4Mi)
% 1.88/1.52 % (11674)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11563 for (2999ds/183Mi)
% 1.88/1.52 % (11677)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11563 for (2999ds/2Mi)
% 1.88/1.52 % (11676)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_11563 for (2999ds/27Mi)
% 1.88/1.52 % (11678)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_11563 for (2999ds/2Mi)
% 1.88/1.52 % (11680)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11563 for (2999ds/18Mi)
% 1.88/1.52 % (11679)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_11563 for (2999ds/275Mi)
% 1.88/1.52 % (11677)Instruction limit reached!
% 1.88/1.52 % (11677)------------------------------
% 1.88/1.52 % (11677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.52 % (11677)Termination reason: Unknown
% 1.88/1.52 % (11677)Termination phase: Preprocessing 2
% 1.88/1.52 % (11678)Instruction limit reached!
% 1.88/1.52 % (11678)------------------------------
% 1.88/1.52 % (11678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.52 % (11678)Termination reason: Unknown
% 1.88/1.52 % (11678)Termination phase: Property scanning
% 1.88/1.52
% 1.88/1.52 % (11678)Memory used [KB]: 1023
% 1.88/1.52 % (11678)Time elapsed: 0.003 s
% 1.88/1.52 % (11678)Instructions burned: 3 (million)
% 1.88/1.52 % (11678)------------------------------
% 1.88/1.52 % (11678)------------------------------
% 1.88/1.52
% 1.88/1.52 % (11677)Memory used [KB]: 1023
% 1.88/1.52 % (11677)Time elapsed: 0.003 s
% 1.88/1.52 % (11677)Instructions burned: 3 (million)
% 1.88/1.52 % (11677)------------------------------
% 1.88/1.52 % (11677)------------------------------
% 1.88/1.52 % (11675)Instruction limit reached!
% 1.88/1.52 % (11675)------------------------------
% 1.88/1.52 % (11675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.52 % (11675)Termination reason: Unknown
% 1.88/1.52 % (11675)Termination phase: Property scanning
% 1.88/1.52
% 1.88/1.52 % (11675)Memory used [KB]: 1023
% 1.88/1.52 % (11675)Time elapsed: 0.004 s
% 1.88/1.52 % (11675)Instructions burned: 5 (million)
% 1.88/1.52 % (11675)------------------------------
% 1.88/1.52 % (11675)------------------------------
% 1.88/1.52 % (11679)First to succeed.
% 1.88/1.52 % (11674)Also succeeded, but the first one will report.
% 1.88/1.53 % (11679)Refutation found. Thanks to Tanya!
% 1.88/1.53 % SZS status Theorem for DTF2THF_11563
% 1.88/1.53 % SZS output start Proof for DTF2THF_11563
% 1.88/1.53 thf(type_def_6, type, obj: $tType).
% 1.88/1.53 thf(type_def_7, type, mor: $tType).
% 1.88/1.53 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.88/1.53 thf(func_def_2, type, obj: $tType).
% 1.88/1.53 thf(func_def_3, type, objStar: obj > obj > $o).
% 1.88/1.53 thf(func_def_4, type, mor: $tType).
% 1.88/1.53 thf(func_def_5, type, morStar: obj > obj > mor > mor > $o).
% 1.88/1.53 thf(func_def_6, type, id: obj > mor).
% 1.88/1.53 thf(func_def_7, type, comp: obj > obj > obj > mor > mor > mor).
% 1.88/1.53 thf(func_def_10, type, sK0: obj).
% 1.88/1.53 thf(func_def_11, type, sK1: obj).
% 1.88/1.53 thf(f46,plain,(
% 1.88/1.53 $false),
% 1.88/1.53 inference(subsumption_resolution,[status(thm)],[f45,f41])).
% 1.88/1.53 thf(f41,plain,(
% 1.88/1.53 ( ! [X0 : obj] : (((morStar @ X0 @ X0 @ (id @ X0) @ (id @ X0)) = $true)) )),
% 1.88/1.53 inference(cnf_transformation,[status(thm)],[f25])).
% 1.88/1.53 thf(f25,plain,(
% 1.88/1.53 ! [X0 : obj] : ((morStar @ X0 @ X0 @ (id @ X0) @ (id @ X0)) = $true)),
% 1.88/1.53 inference(fool_elimination,[status(thm)],[f24])).
% 1.88/1.53 thf(f24,plain,(
% 1.88/1.53 ! [X0 : obj] : (morStar @ X0 @ X0 @ (id @ X0) @ (id @ X0))),
% 1.88/1.53 inference(rectify,[status(thm)],[f4])).
% 1.88/1.53 thf(f4,axiom,(
% 1.88/1.53 ! [X2 : obj] : (morStar @ X2 @ X2 @ (id @ X2) @ (id @ X2))),
% 1.88/1.53 file('/export/starexec/sandbox/tmp/tmp.98VnGS3ci7/DTF2THF_11563.p',id_tp_ax)).
% 1.88/1.53 thf(f45,plain,(
% 1.88/1.53 ((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK0)) != $true)),
% 1.88/1.53 inference(definition_unfolding,[status(thm)],[f40,f39])).
% 1.88/1.53 thf(f39,plain,(
% 1.88/1.53 (sK1 = sK0)),
% 1.88/1.53 inference(cnf_transformation,[status(thm)],[f37])).
% 1.88/1.53 thf(f37,plain,(
% 1.88/1.53 ((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK1)) != $true) & (sK1 = sK0)),
% 1.88/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f32,f36])).
% 1.88/1.53 thf(f36,plain,(
% 1.88/1.53 ? [X0 : obj,X1 : obj] : (((morStar @ X0 @ X0 @ (id @ X0) @ (id @ X1)) != $true) & (X0 = X1)) => (((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK1)) != $true) & (sK1 = sK0))),
% 1.88/1.53 introduced(definition,[],[choice_axiom])).
% 1.88/1.53 thf(f32,plain,(
% 1.88/1.53 ? [X0 : obj,X1 : obj] : (((morStar @ X0 @ X0 @ (id @ X0) @ (id @ X1)) != $true) & (X0 = X1))),
% 1.88/1.53 inference(ennf_transformation,[status(thm)],[f17])).
% 1.88/1.53 thf(f17,plain,(
% 1.88/1.53 ~! [X0 : obj,X1 : obj] : ((X0 = X1) => ((morStar @ X0 @ X0 @ (id @ X0) @ (id @ X1)) = $true))),
% 1.88/1.53 inference(fool_elimination,[status(thm)],[f16])).
% 1.88/1.53 thf(f16,plain,(
% 1.88/1.53 ~! [X0 : obj,X1 : obj] : ((X0 = X1) => (morStar @ X0 @ X0 @ (id @ X0) @ (id @ X1)))),
% 1.88/1.53 inference(rectify,[status(thm)],[f10])).
% 1.88/1.53 thf(f10,negated_conjecture,(
% 1.88/1.53 ~! [X2 : obj,X3 : obj] : ((X2 = X3) => (morStar @ X2 @ X2 @ (id @ X2) @ (id @ X3)))),
% 1.88/1.53 inference(negated_conjecture,[status(cth)],[f9])).
% 1.88/1.53 thf(f9,conjecture,(
% 1.88/1.53 ! [X2 : obj,X3 : obj] : ((X2 = X3) => (morStar @ X2 @ X2 @ (id @ X2) @ (id @ X3)))),
% 1.88/1.53 file('/export/starexec/sandbox/tmp/tmp.98VnGS3ci7/DTF2THF_11563.p',conj)).
% 1.88/1.53 thf(f40,plain,(
% 1.88/1.53 ((morStar @ sK0 @ sK0 @ (id @ sK0) @ (id @ sK1)) != $true)),
% 1.88/1.53 inference(cnf_transformation,[status(thm)],[f37])).
% 1.88/1.53 % SZS output end Proof for DTF2THF_11563
% 1.88/1.53 % (11679)------------------------------
% 1.88/1.53 % (11679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.53 % (11679)Termination reason: Refutation
% 1.88/1.53
% 1.88/1.53 % (11679)Memory used [KB]: 5500
% 1.88/1.53 % (11679)Time elapsed: 0.005 s
% 1.88/1.53 % (11679)Instructions burned: 5 (million)
% 1.88/1.53 % (11679)------------------------------
% 1.88/1.53 % (11679)------------------------------
% 1.88/1.53 % (11673)Success in time 0.02 s
%------------------------------------------------------------------------------