%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV273^5 : 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 : 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 09:40:43 AM UTC 2026
% Result : Theorem 1.40s 1.20s
% Output : Refutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 202 ( 92 equ; 1 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 285 ( 47 ~; 33 |; 36 &; 146 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 0 ^; 60 !; 22 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cR: a > a > $o ).
thf(func_def_5,type,
sK0: ( a > $o ) > a ).
thf(func_def_6,type,
sK1: a > ( a > $o ) > a ).
thf(func_def_7,type,
sK2: a ).
thf(func_def_10,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f47,plain,
$false,
inference(equality_resolution,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: a] : ( sK2 != X0 ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: a] :
( ( sK2 != sK2 )
| ( $true != $true )
| ( sK2 != X0 ) ),
inference(superposition,[status(thm)],[f13,f31]) ).
thf(f31,plain,
! [X2: a,X0: a,X1: a] :
( ( ( cR @ X0 @ X1 )
= $true )
| ( X0 != X1 )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: a,X0: a,X1: a] :
( ( X0 != X2 )
| ( ( X0 = X1 )
!= $true )
| ( ( cR @ X0 @ X1 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: a,X0: a,X1: a] :
( ( ( X0 = X2 )
!= $true )
| ( ( X0 = X1 )
!= $true )
| ( ( cR @ X0 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f14,f18]) ).
thf(f18,plain,
! [X0: a] :
( ( sK0 @ ( (=) @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: a > $o,X1: a] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
!= $true )
| ( ! [X3: a] :
( ( ( sK0 @ X0 )
= X3 )
| ( ( ( cR @ X3 @ ( sK1 @ X3 @ X0 ) )
!= $true )
& ( $true
= ( X0 @ ( sK1 @ X3 @ X0 ) ) ) )
| ( ( X0 @ X3 )
!= $true ) )
& ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ! [X5: a] :
( ( ( cR @ ( sK0 @ X0 ) @ X5 )
= $true )
| ( ( X0 @ X5 )
!= $true ) ) ) )
& ( ( cR @ sK2 @ sK2 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
! [X0: a > $o] :
( ? [X2: a] :
( ! [X3: a] :
( ( X2 = X3 )
| ? [X4: a] :
( ( ( cR @ X3 @ X4 )
!= $true )
& ( ( X0 @ X4 )
= $true ) )
| ( ( X0 @ X3 )
!= $true ) )
& ( ( X0 @ X2 )
= $true )
& ! [X5: a] :
( ( ( cR @ X2 @ X5 )
= $true )
| ( ( X0 @ X5 )
!= $true ) ) )
=> ( ! [X3: a] :
( ( ( sK0 @ X0 )
= X3 )
| ? [X4: a] :
( ( ( cR @ X3 @ X4 )
!= $true )
& ( ( X0 @ X4 )
= $true ) )
| ( ( X0 @ X3 )
!= $true ) )
& ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ! [X5: a] :
( ( ( cR @ ( sK0 @ X0 ) @ X5 )
= $true )
| ( ( X0 @ X5 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: a > $o,X3: a] :
( ? [X4: a] :
( ( ( cR @ X3 @ X4 )
!= $true )
& ( ( X0 @ X4 )
= $true ) )
=> ( ( ( cR @ X3 @ ( sK1 @ X3 @ X0 ) )
!= $true )
& ( $true
= ( X0 @ ( sK1 @ X3 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X6: a] :
( ( cR @ X6 @ X6 )
!= $true )
=> ( ( cR @ sK2 @ sK2 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
!= $true )
| ? [X2: a] :
( ! [X3: a] :
( ( X2 = X3 )
| ? [X4: a] :
( ( ( cR @ X3 @ X4 )
!= $true )
& ( ( X0 @ X4 )
= $true ) )
| ( ( X0 @ X3 )
!= $true ) )
& ( ( X0 @ X2 )
= $true )
& ! [X5: a] :
( ( ( cR @ X2 @ X5 )
= $true )
| ( ( X0 @ X5 )
!= $true ) ) ) )
& ? [X6: a] :
( ( cR @ X6 @ X6 )
!= $true ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
!= $true )
| ? [X2: a] :
( ! [X4: a] :
( ( X2 = X4 )
| ? [X5: a] :
( ( ( cR @ X4 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) )
| ( ( X0 @ X4 )
!= $true ) )
& ( ( X0 @ X2 )
= $true )
& ! [X3: a] :
( ( $true
= ( cR @ X2 @ X3 ) )
| ( ( X0 @ X3 )
!= $true ) ) ) )
& ? [X6: a] :
( ( cR @ X6 @ X6 )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X6: a] :
( ( cR @ X6 @ X6 )
!= $true )
& ! [X0: a > $o] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ! [X3: a] :
( ( $true
= ( cR @ X2 @ X3 ) )
| ( ( X0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( X2 = X4 )
| ( ( X0 @ X4 )
!= $true )
| ? [X5: a] :
( ( ( cR @ X4 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) ) ) )
| ! [X1: a] :
( ( X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
= $true )
=> ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( $true
= ( cR @ X2 @ X3 ) ) )
& ! [X4: a] :
( ( ( ( X0 @ X4 )
= $true )
& ! [X5: a] :
( ( ( X0 @ X5 )
= $true )
=> ( ( cR @ X4 @ X5 )
= $true ) ) )
=> ( X2 = X4 ) ) ) )
=> ! [X6: a] :
( ( cR @ X6 @ X6 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > $o] :
( ? [X1: a] : ( X0 @ X1 )
=> ? [X2: a] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( cR @ X2 @ X3 ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
& ! [X5: a] :
( ( X0 @ X5 )
=> ( cR @ X4 @ X5 ) ) )
=> ( X2 = X4 ) )
& ( X0 @ X2 ) ) )
=> ! [X6: a] : ( cR @ X6 @ X6 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a > $o] :
( ? [X1: a] : ( X0 @ X1 )
=> ? [X1: a] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( cR @ X1 @ X2 ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
& ! [X2: a] :
( ( X0 @ X2 )
=> ( cR @ X3 @ X2 ) ) )
=> ( X1 = X3 ) )
& ( X0 @ X1 ) ) )
=> ! [X2: a] : ( cR @ X2 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a > $o] :
( ? [X1: a] : ( X0 @ X1 )
=> ? [X1: a] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( cR @ X1 @ X2 ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
& ! [X2: a] :
( ( X0 @ X2 )
=> ( cR @ X3 @ X2 ) ) )
=> ( X1 = X3 ) )
& ( X0 @ X1 ) ) )
=> ! [X2: a] : ( cR @ X2 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.csAQP7VjqP/DTF2THF_3330.p',cTHM542_pme) ).
thf(f14,plain,
! [X0: a > $o,X1: a,X5: a] :
( ( ( cR @ ( sK0 @ X0 ) @ X5 )
= $true )
| ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f13,plain,
( ( cR @ sK2 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV273^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n018.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:42:46 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.45 ---- Original DTF file ---
% 0.27/0.45 thf(spec,logic,$$dhol).
% 0.27/0.45 %------------------------------------------------------------------------------
% 0.27/0.45 % File : SEV273^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.45 % Domain : Set Theory (Sets of sets)
% 0.27/0.45 % Problem : TPS problem THM542
% 0.27/0.45 % Version : Especial.
% 0.27/0.45 % English : A well-ordering is reflexive.
% 0.27/0.45
% 0.27/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.45 % Source : [Bro09]
% 0.27/0.45 % Names : tps_0569 [Bro09]
% 0.27/0.45 % : THM542 [TPS]
% 0.27/0.45
% 0.27/0.45 % Status : Theorem
% 0.27/0.45 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.27/0.45 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.27/0.45 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.27/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.27/0.45 % Number of connectives : 19 ( 0 ~; 0 |; 3 &; 11 @)
% 0.27/0.45 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.27/0.45 % Maximal formula depth : 14 ( 14 avg)
% 0.27/0.45 % Number of types : 2 ( 1 usr)
% 0.27/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.27/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.27/0.45 % Number of variables : 7 ( 0 ^; 5 !; 2 ?; 7 :)
% 0.27/0.45 % SPC : TH0_THM_EQU_NAR
% 0.27/0.45
% 0.27/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.45 % : Polymorphic definitions expanded.
% 0.27/0.45 %------------------------------------------------------------------------------
% 0.27/0.45 thf(a_type,type,
% 0.27/0.45 a: $tType ).
% 0.27/0.45
% 0.27/0.45 thf(cR,type,
% 0.27/0.45 cR: a > a > $o ).
% 0.27/0.45
% 0.27/0.45 thf(cTHM542_pme,conjecture,
% 0.27/0.45 ( ! [X: a > $o] :
% 0.27/0.45 ( ? [Xz: a] : ( X @ Xz )
% 0.27/0.45 => ? [Xz: a] :
% 0.27/0.45 ( ( X @ Xz )
% 0.27/0.45 & ! [Xx: a] :
% 0.27/0.45 ( ( X @ Xx )
% 0.27/0.45 => ( cR @ Xz @ Xx ) )
% 0.27/0.45 & ! [Xy: a] :
% 0.27/0.45 ( ( ( X @ Xy )
% 0.27/0.45 & ! [Xx: a] :
% 0.27/0.45 ( ( X @ Xx )
% 0.27/0.45 => ( cR @ Xy @ Xx ) ) )
% 0.27/0.45 => ( Xy = Xz ) ) ) )
% 0.27/0.45 => ! [Xx: a] : ( cR @ Xx @ Xx ) ) ).
% 0.27/0.45
% 0.27/0.45 %------------------------------------------------------------------------------
% 0.27/0.45 ------------------------
% 1.40/1.16 ---- Embedded in THF ---
% 1.40/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.16 %%% Generated on Tue Feb 24 12:42:46 EST 2026
% 1.40/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.16 %%% Logic specification used:
% 1.40/1.16 %%% thf(spec, logic, $$dhol).
% 1.40/1.16
% 1.40/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.csAQP7VjqP/DTF2DTF3330.p
% See solution above
% 1.40/1.16 ------------------------
% 1.40/1.17 ---- Cleaned THF ---
% 1.40/1.17 thf(a_type,type,
% 1.40/1.17 a: $tType ).
% 1.40/1.17
% 1.40/1.17 thf(cR,type,
% 1.40/1.17 cR: a > a > $o ).
% 1.40/1.17
% 1.40/1.17 thf(cTHM542_pme,conjecture,
% 1.40/1.17 ( ! [X: a > $o] :
% 1.40/1.17 ( ? [Xz: a] : ( X @ Xz )
% 1.40/1.17 => ? [Xz: a] :
% 1.40/1.17 ( ( X @ Xz )
% 1.40/1.17 & ! [Xx: a] :
% 1.40/1.17 ( ( X @ Xx )
% 1.40/1.17 => ( cR @ Xz @ Xx ) )
% 1.40/1.17 & ! [Xy: a] :
% 1.40/1.17 ( ( ( X @ Xy )
% 1.40/1.17 & ! [Xx: a] :
% 1.40/1.17 ( ( X @ Xx )
% 1.40/1.17 => ( cR @ Xy @ Xx ) ) )
% 1.40/1.17 => ( Xy = Xz ) ) ) )
% 1.40/1.17 => ! [Xx: a] : ( cR @ Xx @ Xx ) ) ).
% 1.40/1.17 ------------------------
% 1.40/1.18 % (3613)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3330 for (2999ds/18Mi)
% 1.40/1.19 % (3607)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3330 for (2999ds/183Mi)
% 1.40/1.19 % (3613)Instruction limit reached!
% 1.40/1.19 % (3613)------------------------------
% 1.40/1.19 % (3613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (3613)Termination reason: Unknown
% 1.40/1.19 % (3613)Termination phase: Saturation
% 1.40/1.19
% 1.40/1.19 % (3613)Memory used [KB]: 5628
% 1.40/1.19 % (3613)Time elapsed: 0.008 s
% 1.40/1.19 % (3613)Instructions burned: 19 (million)
% 1.40/1.19 % (3613)------------------------------
% 1.40/1.19 % (3613)------------------------------
% 1.40/1.19 % (3608)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_3330 for (2999ds/4Mi)
% 1.40/1.19 % (3609)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_3330 for (2999ds/27Mi)
% 1.40/1.19 % (3610)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3330 for (2999ds/2Mi)
% 1.40/1.19 % (3611)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_3330 for (2999ds/2Mi)
% 1.40/1.19 % (3612)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_3330 for (2999ds/275Mi)
% 1.40/1.19 % (3611)Instruction limit reached!
% 1.40/1.19 % (3611)------------------------------
% 1.40/1.19 % (3611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (3611)Termination reason: Unknown
% 1.40/1.19 % (3611)Termination phase: Unused predicate definition removal
% 1.40/1.19
% 1.40/1.19 % (3611)Memory used [KB]: 895
% 1.40/1.19 % (3611)Time elapsed: 0.003 s
% 1.40/1.19 % (3611)Instructions burned: 2 (million)
% 1.40/1.19 % (3611)------------------------------
% 1.40/1.19 % (3611)------------------------------
% 1.40/1.19 % (3610)Instruction limit reached!
% 1.40/1.19 % (3610)------------------------------
% 1.40/1.19 % (3610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (3610)Termination reason: Unknown
% 1.40/1.19 % (3610)Termination phase: Saturation
% 1.40/1.19
% 1.40/1.19 % (3610)Memory used [KB]: 5500
% 1.40/1.19 % (3610)Time elapsed: 0.004 s
% 1.40/1.19 % (3610)Instructions burned: 2 (million)
% 1.40/1.19 % (3610)------------------------------
% 1.40/1.19 % (3610)------------------------------
% 1.40/1.19 % (3609)Refutation not found, incomplete strategy
% 1.40/1.19 % (3609)------------------------------
% 1.40/1.19 % (3609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (3609)Termination reason: Refutation not found, incomplete strategy
% 1.40/1.19
% 1.40/1.19
% 1.40/1.19 % (3609)Memory used [KB]: 5500
% 1.40/1.19 % (3609)Time elapsed: 0.004 s
% 1.40/1.19 % (3609)Instructions burned: 2 (million)
% 1.40/1.19 % (3609)------------------------------
% 1.40/1.19 % (3609)------------------------------
% 1.40/1.19 % (3608)Instruction limit reached!
% 1.40/1.19 % (3608)------------------------------
% 1.40/1.19 % (3608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (3608)Termination reason: Unknown
% 1.40/1.19 % (3608)Termination phase: Saturation
% 1.40/1.19
% 1.40/1.19 % (3608)Memory used [KB]: 5500
% 1.40/1.19 % (3608)Time elapsed: 0.005 s
% 1.40/1.19 % (3608)Instructions burned: 4 (million)
% 1.40/1.19 % (3608)------------------------------
% 1.40/1.19 % (3608)------------------------------
% 1.40/1.19 % (3612)First to succeed.
% 1.40/1.20 % (3607)Also succeeded, but the first one will report.
% 1.40/1.20 % (3612)Refutation found. Thanks to Tanya!
% 1.40/1.20 % SZS status Theorem for DTF2THF_3330
% 1.40/1.20 % SZS output start Proof for DTF2THF_3330
% 1.40/1.20 thf(type_def_5, type, a: $tType).
% 1.40/1.20 thf(func_def_0, type, a: $tType).
% 1.40/1.20 thf(func_def_1, type, cR: a > a > $o).
% 1.40/1.20 thf(func_def_5, type, sK0: (a > $o) > a).
% 1.40/1.20 thf(func_def_6, type, sK1: a > (a > $o) > a).
% 1.40/1.20 thf(func_def_7, type, sK2: a).
% 1.40/1.20 thf(func_def_10, type, ph4: !>[X0: $tType]:(X0)).
% 1.40/1.20 thf(f47,plain,(
% 1.40/1.20 $false),
% 1.40/1.20 inference(equality_resolution,[status(thm)],[f33])).
% 1.40/1.20 thf(f33,plain,(
% 1.40/1.20 ( ! [X0 : a] : ((sK2 != X0)) )),
% 1.40/1.20 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.40/1.20 thf(f32,plain,(
% 1.40/1.20 ( ! [X0 : a] : ((sK2 != sK2) | ($true != $true) | (sK2 != X0)) )),
% 1.40/1.20 inference(superposition,[status(thm)],[f13,f31])).
% 1.40/1.20 thf(f31,plain,(
% 1.40/1.20 ( ! [X2 : a,X0 : a,X1 : a] : (((cR @ X0 @ X1) = $true) | (X0 != X1) | (X0 != X2)) )),
% 1.40/1.20 inference(equality_proxy_clausification,[status(thm)],[f30])).
% 1.40/1.20 thf(f30,plain,(
% 1.40/1.20 ( ! [X2 : a,X0 : a,X1 : a] : ((X0 != X2) | ((X0 = X1) != $true) | ((cR @ X0 @ X1) = $true)) )),
% 1.40/1.20 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.40/1.20 thf(f29,plain,(
% 1.40/1.20 ( ! [X2 : a,X0 : a,X1 : a] : (((X0 = X2) != $true) | ((X0 = X1) != $true) | ((cR @ X0 @ X1) = $true)) )),
% 1.40/1.20 inference(superposition,[status(thm)],[f14,f18])).
% 1.40/1.20 thf(f18,plain,(
% 1.40/1.20 ( ! [X0 : a] : (((sK0 @ (= @ X0)) = X0)) )),
% 1.40/1.20 inference(leibniz_equality_elimination,[status(thm)],[f15])).
% 1.40/1.20 thf(f15,plain,(
% 1.40/1.20 ( ! [X0 : a > $o,X1 : a] : (($true = (X0 @ (sK0 @ X0))) | ((X0 @ X1) != $true)) )),
% 1.40/1.20 inference(cnf_transformation,[status(thm)],[f12])).
% 1.40/1.20 thf(f12,plain,(
% 1.40/1.20 ! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) != $true) | (! [X3 : a] : (((sK0 @ X0) = X3) | (((cR @ X3 @ (sK1 @ X3 @ X0)) != $true) & ($true = (X0 @ (sK1 @ X3 @ X0)))) | ((X0 @ X3) != $true)) & ($true = (X0 @ (sK0 @ X0))) & ! [X5 : a] : (((cR @ (sK0 @ X0) @ X5) = $true) | ((X0 @ X5) != $true)))) & ((cR @ sK2 @ sK2) != $true)),
% 1.40/1.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.40/1.20 thf(f9,plain,(
% 1.40/1.20 ! [X0 : a > $o] : (? [X2 : a] : (! [X3 : a] : ((X2 = X3) | ? [X4 : a] : (((cR @ X3 @ X4) != $true) & ((X0 @ X4) = $true)) | ((X0 @ X3) != $true)) & ((X0 @ X2) = $true) & ! [X5 : a] : (((cR @ X2 @ X5) = $true) | ((X0 @ X5) != $true))) => (! [X3 : a] : (((sK0 @ X0) = X3) | ? [X4 : a] : (((cR @ X3 @ X4) != $true) & ((X0 @ X4) = $true)) | ((X0 @ X3) != $true)) & ($true = (X0 @ (sK0 @ X0))) & ! [X5 : a] : (((cR @ (sK0 @ X0) @ X5) = $true) | ((X0 @ X5) != $true))))),
% 1.40/1.20 introduced(definition,[],[choice_axiom])).
% 1.40/1.20 thf(f10,plain,(
% 1.40/1.20 ! [X0 : a > $o,X3 : a] : (? [X4 : a] : (((cR @ X3 @ X4) != $true) & ((X0 @ X4) = $true)) => (((cR @ X3 @ (sK1 @ X3 @ X0)) != $true) & ($true = (X0 @ (sK1 @ X3 @ X0)))))),
% 1.40/1.20 introduced(definition,[],[choice_axiom])).
% 1.40/1.20 thf(f11,plain,(
% 1.40/1.20 ? [X6 : a] : ((cR @ X6 @ X6) != $true) => ((cR @ sK2 @ sK2) != $true)),
% 1.40/1.20 introduced(definition,[],[choice_axiom])).
% 1.40/1.20 thf(f8,plain,(
% 1.40/1.20 ! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) != $true) | ? [X2 : a] : (! [X3 : a] : ((X2 = X3) | ? [X4 : a] : (((cR @ X3 @ X4) != $true) & ((X0 @ X4) = $true)) | ((X0 @ X3) != $true)) & ((X0 @ X2) = $true) & ! [X5 : a] : (((cR @ X2 @ X5) = $true) | ((X0 @ X5) != $true)))) & ? [X6 : a] : ((cR @ X6 @ X6) != $true)),
% 1.40/1.20 inference(rectify,[status(thm)],[f7])).
% 1.40/1.20 thf(f7,plain,(
% 1.40/1.20 ! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) != $true) | ? [X2 : a] : (! [X4 : a] : ((X2 = X4) | ? [X5 : a] : (((cR @ X4 @ X5) != $true) & ((X0 @ X5) = $true)) | ((X0 @ X4) != $true)) & ((X0 @ X2) = $true) & ! [X3 : a] : (($true = (cR @ X2 @ X3)) | ((X0 @ X3) != $true)))) & ? [X6 : a] : ((cR @ X6 @ X6) != $true)),
% 1.40/1.20 inference(flattening,[status(thm)],[f6])).
% 1.40/1.20 thf(f6,plain,(
% 1.40/1.20 ? [X6 : a] : ((cR @ X6 @ X6) != $true) & ! [X0 : a > $o] : (? [X2 : a] : (((X0 @ X2) = $true) & ! [X3 : a] : (($true = (cR @ X2 @ X3)) | ((X0 @ X3) != $true)) & ! [X4 : a] : ((X2 = X4) | (((X0 @ X4) != $true) | ? [X5 : a] : (((cR @ X4 @ X5) != $true) & ((X0 @ X5) = $true))))) | ! [X1 : a] : ((X0 @ X1) != $true))),
% 1.40/1.20 inference(ennf_transformation,[status(thm)],[f5])).
% 1.40/1.20 thf(f5,plain,(
% 1.40/1.20 ~(! [X0 : a > $o] : (? [X1 : a] : ((X0 @ X1) = $true) => ? [X2 : a] : (((X0 @ X2) = $true) & ! [X3 : a] : (((X0 @ X3) = $true) => ($true = (cR @ X2 @ X3))) & ! [X4 : a] : ((((X0 @ X4) = $true) & ! [X5 : a] : (((X0 @ X5) = $true) => ((cR @ X4 @ X5) = $true))) => (X2 = X4)))) => ! [X6 : a] : ((cR @ X6 @ X6) = $true))),
% 1.40/1.20 inference(fool_elimination,[status(thm)],[f4])).
% 1.40/1.20 thf(f4,plain,(
% 1.40/1.20 ~(! [X0 : a > $o] : (? [X1 : a] : (X0 @ X1) => ? [X2 : a] : (! [X3 : a] : ((X0 @ X3) => (cR @ X2 @ X3)) & ! [X4 : a] : (((X0 @ X4) & ! [X5 : a] : ((X0 @ X5) => (cR @ X4 @ X5))) => (X2 = X4)) & (X0 @ X2))) => ! [X6 : a] : (cR @ X6 @ X6))),
% 1.40/1.20 inference(rectify,[status(thm)],[f2])).
% 1.40/1.20 thf(f2,negated_conjecture,(
% 1.40/1.20 ~(! [X0 : a > $o] : (? [X1 : a] : (X0 @ X1) => ? [X1 : a] : (! [X2 : a] : ((X0 @ X2) => (cR @ X1 @ X2)) & ! [X3 : a] : (((X0 @ X3) & ! [X2 : a] : ((X0 @ X2) => (cR @ X3 @ X2))) => (X1 = X3)) & (X0 @ X1))) => ! [X2 : a] : (cR @ X2 @ X2))),
% 1.40/1.20 inference(negated_conjecture,[status(cth)],[f1])).
% 1.40/1.20 thf(f1,conjecture,(
% 1.40/1.20 ! [X0 : a > $o] : (? [X1 : a] : (X0 @ X1) => ? [X1 : a] : (! [X2 : a] : ((X0 @ X2) => (cR @ X1 @ X2)) & ! [X3 : a] : (((X0 @ X3) & ! [X2 : a] : ((X0 @ X2) => (cR @ X3 @ X2))) => (X1 = X3)) & (X0 @ X1))) => ! [X2 : a] : (cR @ X2 @ X2)),
% 1.40/1.20 file('/export/starexec/sandbox/tmp/tmp.csAQP7VjqP/DTF2THF_3330.p',cTHM542_pme)).
% 1.40/1.20 thf(f14,plain,(
% 1.40/1.20 ( ! [X0 : a > $o,X1 : a,X5 : a] : (((cR @ (sK0 @ X0) @ X5) = $true) | ((X0 @ X1) != $true) | ((X0 @ X5) != $true)) )),
% 1.40/1.20 inference(cnf_transformation,[status(thm)],[f12])).
% 1.40/1.20 thf(f13,plain,(
% 1.40/1.20 ((cR @ sK2 @ sK2) != $true)),
% 1.40/1.20 inference(cnf_transformation,[status(thm)],[f12])).
% 1.40/1.20 % SZS output end Proof for DTF2THF_3330
% 1.40/1.20 % (3612)------------------------------
% 1.40/1.20 % (3612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.20 % (3612)Termination reason: Refutation
% 1.40/1.20
% 1.40/1.20 % (3612)Memory used [KB]: 5500
% 1.40/1.20 % (3612)Time elapsed: 0.007 s
% 1.40/1.20 % (3612)Instructions burned: 5 (million)
% 1.40/1.20 % (3612)------------------------------
% 1.40/1.20 % (3612)------------------------------
% 1.40/1.20 % (3606)Success in time 0.021 s
%------------------------------------------------------------------------------