%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU894^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 09:37:41 AM UTC 2026
% Result : Theorem 0.84s 0.89s
% Output : Refutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 114 ( 81 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 227 ( 30 ~; 17 |; 39 &; 118 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 86 ( 12 ^; 46 !; 28 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_6,type,
sK0: $i > $i ).
thf(func_def_7,type,
sK1: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_8,type,
sK2: ( $i > $i ) > $i ).
thf(func_def_10,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f21,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( sK2 @ sK0 )
!= ( sK2 @ sK0 ) ),
inference(superposition,[status(thm)],[f13,f15]) ).
thf(f15,plain,
! [X1: $i > $i] :
( ( sK2 @ X1 )
= ( X1 @ ( sK2 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( $true
!= ( X2 @ sK0 ) )
| ( ( ( X2
@ ^ [Y0: $i] : ( sK0 @ ( sK1 @ X2 @ Y0 ) ) )
!= $true )
& ( ( X2 @ ( sK1 @ X2 ) )
= $true ) )
| ( ( X2 @ X1 )
= $true ) )
& ( ( sK2 @ X1 )
= ( X1 @ ( sK2 @ X1 ) ) )
& ! [X5: $i] :
( ( ( X1 @ X5 )
!= X5 )
| ( ( sK2 @ X1 )
= X5 ) )
& ! [X6: $i] :
( ( sK0 @ X6 )
!= X6 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i > $i] :
! [X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( ( X2 @ X0 )
!= $true )
| ? [X3: $i > $i] :
( ( $true
!= ( X2
@ ^ [Y0: $i] : ( X0 @ ( X3 @ Y0 ) ) ) )
& ( ( X2 @ X3 )
= $true ) )
| ( ( X2 @ X1 )
= $true ) )
& ? [X4: $i] :
( ( ( X1 @ X4 )
= X4 )
& ! [X5: $i] :
( ( ( X1 @ X5 )
!= X5 )
| ( X4 = X5 ) ) )
& ! [X6: $i] :
( ( X0 @ X6 )
!= X6 ) )
=> ! [X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( $true
!= ( X2 @ sK0 ) )
| ? [X3: $i > $i] :
( ( ( X2
@ ^ [Y0: $i] : ( sK0 @ ( X3 @ Y0 ) ) )
!= $true )
& ( ( X2 @ X3 )
= $true ) )
| ( ( X2 @ X1 )
= $true ) )
& ? [X4: $i] :
( ( ( X1 @ X4 )
= X4 )
& ! [X5: $i] :
( ( ( X1 @ X5 )
!= X5 )
| ( X4 = X5 ) ) )
& ! [X6: $i] :
( ( sK0 @ X6 )
!= X6 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X2: ( $i > $i ) > $o] :
( ? [X3: $i > $i] :
( ( ( X2
@ ^ [Y0: $i] : ( sK0 @ ( X3 @ Y0 ) ) )
!= $true )
& ( ( X2 @ X3 )
= $true ) )
=> ( ( ( X2
@ ^ [Y0: $i] : ( sK0 @ ( sK1 @ X2 @ Y0 ) ) )
!= $true )
& ( ( X2 @ ( sK1 @ X2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X1: $i > $i] :
( ? [X4: $i] :
( ( ( X1 @ X4 )
= X4 )
& ! [X5: $i] :
( ( ( X1 @ X5 )
!= X5 )
| ( X4 = X5 ) ) )
=> ( ( ( sK2 @ X1 )
= ( X1 @ ( sK2 @ X1 ) ) )
& ! [X5: $i] :
( ( ( X1 @ X5 )
!= X5 )
| ( ( sK2 @ X1 )
= X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i > $i] :
! [X1: $i > $i] :
( ! [X2: ( $i > $i ) > $o] :
( ( ( X2 @ X0 )
!= $true )
| ? [X3: $i > $i] :
( ( $true
!= ( X2
@ ^ [Y0: $i] : ( X0 @ ( X3 @ Y0 ) ) ) )
& ( ( X2 @ X3 )
= $true ) )
| ( ( X2 @ X1 )
= $true ) )
& ? [X4: $i] :
( ( ( X1 @ X4 )
= X4 )
& ! [X5: $i] :
( ( ( X1 @ X5 )
!= X5 )
| ( X4 = X5 ) ) )
& ! [X6: $i] :
( ( X0 @ X6 )
!= X6 ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: $i > $i] :
! [X1: $i > $i] :
( ! [X6: $i] :
( ( X0 @ X6 )
!= X6 )
& ! [X2: ( $i > $i ) > $o] :
( ( ( X2 @ X1 )
= $true )
| ( ( X2 @ X0 )
!= $true )
| ? [X3: $i > $i] :
( ( $true
!= ( X2
@ ^ [Y0: $i] : ( X0 @ ( X3 @ Y0 ) ) ) )
& ( ( X2 @ X3 )
= $true ) ) )
& ? [X4: $i] :
( ( ( X1 @ X4 )
= X4 )
& ! [X5: $i] :
( ( ( X1 @ X5 )
!= X5 )
| ( X4 = X5 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i > $i] :
? [X1: $i > $i] :
( ( ! [X2: ( $i > $i ) > $o] :
( ( ( ( X2 @ X0 )
= $true )
& ! [X3: $i > $i] :
( ( ( X2 @ X3 )
= $true )
=> ( $true
= ( X2
@ ^ [Y0: $i] : ( X0 @ ( X3 @ Y0 ) ) ) ) ) )
=> ( ( X2 @ X1 )
= $true ) )
& ? [X4: $i] :
( ( ( X1 @ X4 )
= X4 )
& ! [X5: $i] :
( ( ( X1 @ X5 )
= X5 )
=> ( X4 = X5 ) ) ) )
=> ? [X6: $i] :
( ( X0 @ X6 )
= X6 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $i] :
? [X1: $i > $i] :
( ( ! [X2: ( $i > $i ) > $o] :
( ( ( ( X2 @ X0 )
= $true )
& ! [X3: $i > $i] :
( ( ( X2 @ X3 )
= $true )
=> ( $true
= ( X2
@ ^ [Y0: $i] : ( X0 @ ( X3 @ Y0 ) ) ) ) ) )
=> ( ( X2 @ X1 )
= $true ) )
& ? [X5: $i] :
( ! [X6: $i] :
( ( ( X1 @ X6 )
= X6 )
=> ( X5 = X6 ) )
& ( ( X1 @ X5 )
= X5 ) ) )
=> ? [X7: $i] :
( ( X0 @ X7 )
= X7 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $i] :
? [X1: $i > $i] :
( ( ! [X2: ( $i > $i ) > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : ( X0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) )
& ? [X5: $i] :
( ! [X6: $i] :
( ( ( X1 @ X6 )
= X6 )
=> ( X5 = X6 ) )
& ( ( X1 @ X5 )
= X5 ) ) )
=> ? [X7: $i] :
( ( X0 @ X7 )
= X7 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $i] :
? [X1: $i > $i] :
( ( ! [X2: ( $i > $i ) > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : ( X0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) )
& ? [X5: $i] :
( ! [X6: $i] :
( ( ( X1 @ X6 )
= X6 )
=> ( X5 = X6 ) )
& ( ( X1 @ X5 )
= X5 ) ) )
=> ? [X6: $i] :
( ( X0 @ X6 )
= X6 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $i] :
? [X1: $i > $i] :
( ( ! [X2: ( $i > $i ) > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i > $i] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i] : ( X0 @ ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) )
& ? [X5: $i] :
( ! [X6: $i] :
( ( ( X1 @ X6 )
= X6 )
=> ( X5 = X6 ) )
& ( ( X1 @ X5 )
= X5 ) ) )
=> ? [X6: $i] :
( ( X0 @ X6 )
= X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.oaItS3Lxpp/DTF2THF_30798.p',cTHM15_0_pme) ).
thf(f13,plain,
! [X6: $i] :
( ( sK0 @ X6 )
!= X6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU894^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.24 % Computer : n012.cluster.edu
% 0.08/0.24 % Model : x86_64 x86_64
% 0.08/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.24 % Memory : 8042.1875MB
% 0.08/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 12:36:00 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.31 ---- Original DTF file ---
% 0.08/0.31 thf(spec,logic,$$dhol).
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 % File : SEU894^5 : TPTP v9.2.1. Released v4.0.0.
% 0.08/0.31 % Domain : Set Theory
% 0.08/0.31 % Problem : TPS problem THM15-0
% 0.08/0.31 % Version : Especial.
% 0.08/0.31 % English :
% 0.08/0.31
% 0.08/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.08/0.31 % Source : [Bro09]
% 0.08/0.31 % Names : tps_0364 [Bro09]
% 0.08/0.31 % : THM15-0 [TPS]
% 0.08/0.31
% 0.08/0.31 % Status : Theorem
% 0.08/0.31 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.08/0.31 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.08/0.31 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.08/0.31 % Maximal formula atoms : 4 ( 4 avg)
% 0.08/0.31 % Number of connectives : 16 ( 0 ~; 0 |; 3 &; 9 @)
% 0.08/0.31 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.08/0.31 % Maximal formula depth : 14 ( 14 avg)
% 0.08/0.31 % Number of types : 2 ( 0 usr)
% 0.08/0.31 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.08/0.31 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.08/0.31 % Number of variables : 8 ( 1 ^; 4 !; 3 ?; 8 :)
% 0.08/0.31 % SPC : TH0_THM_EQU_NAR
% 0.08/0.31
% 0.08/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.08/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.08/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.08/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.08/0.31 % : Polymorphic definitions expanded.
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 thf(cTHM15_0_pme,conjecture,
% 0.08/0.31 ! [F: $i > $i] :
% 0.08/0.31 ? [G: $i > $i] :
% 0.08/0.31 ( ( ! [P: ( $i > $i ) > $o] :
% 0.08/0.31 ( ( ( P @ F )
% 0.08/0.31 & ! [H: $i > $i] :
% 0.08/0.31 ( ( P @ H )
% 0.08/0.31 => ( P
% 0.08/0.31 @ ^ [T: $i] : ( F @ ( H @ T ) ) ) ) )
% 0.08/0.31 => ( P @ G ) )
% 0.08/0.31 & ? [X: $i] :
% 0.08/0.31 ( ( ( G @ X )
% 0.08/0.31 = X )
% 0.08/0.31 & ! [Y: $i] :
% 0.08/0.31 ( ( ( G @ Y )
% 0.08/0.31 = Y )
% 0.08/0.31 => ( X = Y ) ) ) )
% 0.08/0.31 => ? [Y: $i] :
% 0.08/0.31 ( ( F @ Y )
% 0.08/0.31 = Y ) ) ).
% 0.08/0.31
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 ------------------------
% 0.84/0.87 ---- Embedded in THF ---
% 0.84/0.87 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.84/0.87 %%% Generated on Tue Feb 24 12:36:01 EST 2026
% 0.84/0.87 %%% using '$$dhol' embedding, version 1.3.0.
% 0.84/0.87 %%% Logic specification used:
% 0.84/0.87 %%% thf(spec, logic, $$dhol).
% 0.84/0.87
% 0.84/0.87 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.oaItS3Lxpp/DTF2DTF30798.p
% See solution above
% 0.84/0.87 ------------------------
% 0.84/0.87 ---- Cleaned THF ---
% 0.84/0.87 thf(cTHM15_0_pme,conjecture,
% 0.84/0.87 ! [F: $i > $i] :
% 0.84/0.87 ? [G: $i > $i] :
% 0.84/0.87 ( ( ! [P: ( $i > $i ) > $o] :
% 0.84/0.87 ( ( ( P @ F )
% 0.84/0.87 & ! [H: $i > $i] :
% 0.84/0.87 ( ( P @ H )
% 0.84/0.87 => ( P
% 0.84/0.87 @ ^ [T: $i] : ( F @ ( H @ T ) ) ) ) )
% 0.84/0.87 => ( P @ G ) )
% 0.84/0.87 & ? [X: $i] :
% 0.84/0.87 ( ( ( G @ X )
% 0.84/0.87 = X )
% 0.84/0.87 & ! [Y: $i] :
% 0.84/0.87 ( ( ( G @ Y )
% 0.84/0.87 = Y )
% 0.84/0.87 => ( X = Y ) ) ) )
% 0.84/0.87 => ? [Y: $i] :
% 0.84/0.87 ( ( F @ Y )
% 0.84/0.87 = Y ) ) ).
% 0.84/0.87 ------------------------
% 0.84/0.88 % (30999)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_30798 for (3000ds/4Mi)
% 0.84/0.88 % (30998)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30798 for (3000ds/183Mi)
% 0.84/0.88 % (31000)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_30798 for (3000ds/27Mi)
% 0.84/0.88 % (31001)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30798 for (3000ds/2Mi)
% 0.84/0.88 % (31002)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_30798 for (3000ds/2Mi)
% 0.84/0.88 % (31003)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_30798 for (3000ds/275Mi)
% 0.84/0.88 % (31004)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30798 for (3000ds/18Mi)
% 0.84/0.88 % (31001)Instruction limit reached!
% 0.84/0.88 % (31001)------------------------------
% 0.84/0.88 % (31001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.84/0.88 % (31001)Termination reason: Unknown
% 0.84/0.88 % (31001)Termination phase: Saturation
% 0.84/0.88
% 0.84/0.88 % (31001)Memory used [KB]: 895
% 0.84/0.88 % (31001)Time elapsed: 0.002 s
% 0.84/0.88 % (31001)Instructions burned: 2 (million)
% 0.84/0.88 % (31001)------------------------------
% 0.84/0.88 % (31001)------------------------------
% 0.84/0.88 % (31002)Instruction limit reached!
% 0.84/0.88 % (31002)------------------------------
% 0.84/0.88 % (31002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.84/0.88 % (31002)Termination reason: Unknown
% 0.84/0.88 % (31002)Termination phase: Saturation
% 0.84/0.88
% 0.84/0.88 % (31002)Memory used [KB]: 895
% 0.84/0.88 % (31002)Time elapsed: 0.002 s
% 0.84/0.88 % (31002)Instructions burned: 2 (million)
% 0.84/0.88 % (31002)------------------------------
% 0.84/0.88 % (31002)------------------------------
% 0.84/0.89 % (31000)First to succeed.
% 0.84/0.89 % (31003)Also succeeded, but the first one will report.
% 0.84/0.89 % (30998)Also succeeded, but the first one will report.
% 0.84/0.89 % (31000)Refutation found. Thanks to Tanya!
% 0.84/0.89 % SZS status Theorem for DTF2THF_30798
% 0.84/0.89 % SZS output start Proof for DTF2THF_30798
% 0.84/0.89 thf(func_def_1, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.84/0.89 thf(func_def_6, type, sK0: $i > $i).
% 0.84/0.89 thf(func_def_7, type, sK1: (($i > $i) > $o) > $i > $i).
% 0.84/0.89 thf(func_def_8, type, sK2: ($i > $i) > $i).
% 0.84/0.89 thf(func_def_10, type, ph4: !>[X0: $tType]:(X0)).
% 0.84/0.89 thf(f21,plain,(
% 0.84/0.89 $false),
% 0.84/0.89 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 0.84/0.89 thf(f20,plain,(
% 0.84/0.89 ((sK2 @ sK0) != (sK2 @ sK0))),
% 0.84/0.89 inference(superposition,[status(thm)],[f13,f15])).
% 0.84/0.89 thf(f15,plain,(
% 0.84/0.89 ( ! [X1 : $i > $i] : (((sK2 @ X1) = (X1 @ (sK2 @ X1)))) )),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f12])).
% 0.84/0.89 thf(f12,plain,(
% 0.84/0.89 ! [X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : (($true != (X2 @ sK0)) | (((X2 @ (^[Y0 : $i]: (sK0 @ (sK1 @ X2 @ Y0)))) != $true) & ((X2 @ (sK1 @ X2)) = $true)) | ((X2 @ X1) = $true)) & (((sK2 @ X1) = (X1 @ (sK2 @ X1))) & ! [X5 : $i] : (((X1 @ X5) != X5) | ((sK2 @ X1) = X5))) & ! [X6 : $i] : ((sK0 @ X6) != X6))),
% 0.84/0.89 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 0.84/0.89 thf(f9,plain,(
% 0.84/0.89 ? [X0 : $i > $i] : ! [X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : (((X2 @ X0) != $true) | ? [X3 : $i > $i] : (($true != (X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0))))) & ((X2 @ X3) = $true)) | ((X2 @ X1) = $true)) & ? [X4 : $i] : (((X1 @ X4) = X4) & ! [X5 : $i] : (((X1 @ X5) != X5) | (X4 = X5))) & ! [X6 : $i] : ((X0 @ X6) != X6)) => ! [X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : (($true != (X2 @ sK0)) | ? [X3 : $i > $i] : (((X2 @ (^[Y0 : $i]: (sK0 @ (X3 @ Y0)))) != $true) & ((X2 @ X3) = $true)) | ((X2 @ X1) = $true)) & ? [X4 : $i] : (((X1 @ X4) = X4) & ! [X5 : $i] : (((X1 @ X5) != X5) | (X4 = X5))) & ! [X6 : $i] : ((sK0 @ X6) != X6))),
% 0.84/0.89 introduced(definition,[],[choice_axiom])).
% 0.84/0.89 thf(f10,plain,(
% 0.84/0.89 ! [X2 : ($i > $i) > $o] : (? [X3 : $i > $i] : (((X2 @ (^[Y0 : $i]: (sK0 @ (X3 @ Y0)))) != $true) & ((X2 @ X3) = $true)) => (((X2 @ (^[Y0 : $i]: (sK0 @ (sK1 @ X2 @ Y0)))) != $true) & ((X2 @ (sK1 @ X2)) = $true)))),
% 0.84/0.89 introduced(definition,[],[choice_axiom])).
% 0.84/0.89 thf(f11,plain,(
% 0.84/0.89 ! [X1 : $i > $i] : (? [X4 : $i] : (((X1 @ X4) = X4) & ! [X5 : $i] : (((X1 @ X5) != X5) | (X4 = X5))) => (((sK2 @ X1) = (X1 @ (sK2 @ X1))) & ! [X5 : $i] : (((X1 @ X5) != X5) | ((sK2 @ X1) = X5))))),
% 0.84/0.89 introduced(definition,[],[choice_axiom])).
% 0.84/0.89 thf(f8,plain,(
% 0.84/0.89 ? [X0 : $i > $i] : ! [X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : (((X2 @ X0) != $true) | ? [X3 : $i > $i] : (($true != (X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0))))) & ((X2 @ X3) = $true)) | ((X2 @ X1) = $true)) & ? [X4 : $i] : (((X1 @ X4) = X4) & ! [X5 : $i] : (((X1 @ X5) != X5) | (X4 = X5))) & ! [X6 : $i] : ((X0 @ X6) != X6))),
% 0.84/0.89 inference(flattening,[status(thm)],[f7])).
% 0.84/0.89 thf(f7,plain,(
% 0.84/0.89 ? [X0 : $i > $i] : ! [X1 : $i > $i] : (! [X6 : $i] : ((X0 @ X6) != X6) & (! [X2 : ($i > $i) > $o] : (((X2 @ X1) = $true) | (((X2 @ X0) != $true) | ? [X3 : $i > $i] : (($true != (X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0))))) & ((X2 @ X3) = $true)))) & ? [X4 : $i] : (((X1 @ X4) = X4) & ! [X5 : $i] : (((X1 @ X5) != X5) | (X4 = X5)))))),
% 0.84/0.89 inference(ennf_transformation,[status(thm)],[f6])).
% 0.84/0.89 thf(f6,plain,(
% 0.84/0.89 ~! [X0 : $i > $i] : ? [X1 : $i > $i] : ((! [X2 : ($i > $i) > $o] : ((((X2 @ X0) = $true) & ! [X3 : $i > $i] : (((X2 @ X3) = $true) => ($true = (X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0))))))) => ((X2 @ X1) = $true)) & ? [X4 : $i] : (((X1 @ X4) = X4) & ! [X5 : $i] : (((X1 @ X5) = X5) => (X4 = X5)))) => ? [X6 : $i] : ((X0 @ X6) = X6))),
% 0.84/0.89 inference(rectify,[status(thm)],[f5])).
% 0.84/0.89 thf(f5,plain,(
% 0.84/0.89 ~! [X0 : $i > $i] : ? [X1 : $i > $i] : ((! [X2 : ($i > $i) > $o] : ((((X2 @ X0) = $true) & ! [X3 : $i > $i] : (((X2 @ X3) = $true) => ($true = (X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0))))))) => ((X2 @ X1) = $true)) & ? [X5 : $i] : (! [X6 : $i] : (((X1 @ X6) = X6) => (X5 = X6)) & ((X1 @ X5) = X5))) => ? [X7 : $i] : ((X0 @ X7) = X7))),
% 0.84/0.89 inference(fool_elimination,[status(thm)],[f4])).
% 0.84/0.89 thf(f4,plain,(
% 0.84/0.89 ~! [X0 : $i > $i] : ? [X1 : $i > $i] : ((! [X2 : ($i > $i) > $o] : (((X2 @ X0) & ! [X3 : $i > $i] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : (X0 @ (X3 @ X4)))))) => (X2 @ X1)) & ? [X5 : $i] : (! [X6 : $i] : (((X1 @ X6) = X6) => (X5 = X6)) & ((X1 @ X5) = X5))) => ? [X7 : $i] : ((X0 @ X7) = X7))),
% 0.84/0.89 inference(rectify,[status(thm)],[f2])).
% 0.84/0.89 thf(f2,negated_conjecture,(
% 0.84/0.89 ~! [X0 : $i > $i] : ? [X1 : $i > $i] : ((! [X2 : ($i > $i) > $o] : (((X2 @ X0) & ! [X3 : $i > $i] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : (X0 @ (X3 @ X4)))))) => (X2 @ X1)) & ? [X5 : $i] : (! [X6 : $i] : (((X1 @ X6) = X6) => (X5 = X6)) & ((X1 @ X5) = X5))) => ? [X6 : $i] : ((X0 @ X6) = X6))),
% 0.84/0.89 inference(negated_conjecture,[status(cth)],[f1])).
% 0.84/0.89 thf(f1,conjecture,(
% 0.84/0.89 ! [X0 : $i > $i] : ? [X1 : $i > $i] : ((! [X2 : ($i > $i) > $o] : (((X2 @ X0) & ! [X3 : $i > $i] : ((X2 @ X3) => (X2 @ (^[X4 : $i] : (X0 @ (X3 @ X4)))))) => (X2 @ X1)) & ? [X5 : $i] : (! [X6 : $i] : (((X1 @ X6) = X6) => (X5 = X6)) & ((X1 @ X5) = X5))) => ? [X6 : $i] : ((X0 @ X6) = X6))),
% 0.84/0.89 file('/export/starexec/sandbox2/tmp/tmp.oaItS3Lxpp/DTF2THF_30798.p',cTHM15_0_pme)).
% 0.84/0.89 thf(f13,plain,(
% 0.84/0.89 ( ! [X6 : $i] : (((sK0 @ X6) != X6)) )),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f12])).
% 0.84/0.89 % SZS output end Proof for DTF2THF_30798
% 0.84/0.89 % (31000)------------------------------
% 0.84/0.89 % (31000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.84/0.89 % (31000)Termination reason: Refutation
% 0.84/0.89
% 0.84/0.89 % (31000)Memory used [KB]: 5500
% 0.84/0.89 % (31000)Time elapsed: 0.003 s
% 0.84/0.89 % (31000)Instructions burned: 2 (million)
% 0.84/0.89 % (31000)------------------------------
% 0.84/0.89 % (31000)------------------------------
% 0.84/0.89 % (30997)Success in time 0.011 s
%------------------------------------------------------------------------------