%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV015^5 : 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 : n025.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 09:40:04 AM UTC 2026
% Result : Theorem 1.31s 1.14s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 190 ( 80 equ; 0 cnn)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 300 ( 43 ~; 25 |; 38 &; 176 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 0 ^; 72 !; 16 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > a > $o ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_6,type,
sK2: a ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
$true != $true,
inference(superposition,[status(thm)],[f24,f12]) ).
thf(f12,plain,
( ( sK0 @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( sK0 = sK0 )
& ! [X1: a,X2: a,X3: a] :
( ( $true
!= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X3 @ X2 )
!= $true )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
& ! [X4: a,X5: a] :
( ( $true
!= ( sK0 @ X4 @ X5 ) )
| ( $true
= ( sK0 @ X5 @ X4 ) ) )
& ( ( sK0 @ sK2 @ sK2 )
!= $true )
& ( ( sK0 @ sK2 @ sK1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o] :
( ( X0 = X0 )
& ! [X1: a,X2: a,X3: a] :
( ( ( X0 @ X1 @ X3 )
!= $true )
| ( ( X0 @ X3 @ X2 )
!= $true )
| ( ( X0 @ X1 @ X2 )
= $true ) )
& ! [X4: a,X5: a] :
( ( $true
!= ( X0 @ X4 @ X5 ) )
| ( $true
= ( X0 @ X5 @ X4 ) ) )
& ? [X6: a,X7: a] :
( ( $true
!= ( X0 @ X7 @ X7 ) )
& ( ( X0 @ X7 @ X6 )
= $true ) ) )
=> ( ( sK0 = sK0 )
& ! [X3: a,X2: a,X1: a] :
( ( $true
!= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X3 @ X2 )
!= $true )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
& ! [X5: a,X4: a] :
( ( $true
!= ( sK0 @ X4 @ X5 ) )
| ( $true
= ( sK0 @ X5 @ X4 ) ) )
& ? [X7: a,X6: a] :
( ( ( sK0 @ X7 @ X7 )
!= $true )
& ( ( sK0 @ X7 @ X6 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X7: a,X6: a] :
( ( ( sK0 @ X7 @ X7 )
!= $true )
& ( ( sK0 @ X7 @ X6 )
= $true ) )
=> ( ( ( sK0 @ sK2 @ sK2 )
!= $true )
& ( ( sK0 @ sK2 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o] :
( ( X0 = X0 )
& ! [X1: a,X2: a,X3: a] :
( ( ( X0 @ X1 @ X3 )
!= $true )
| ( ( X0 @ X3 @ X2 )
!= $true )
| ( ( X0 @ X1 @ X2 )
= $true ) )
& ! [X4: a,X5: a] :
( ( $true
!= ( X0 @ X4 @ X5 ) )
| ( $true
= ( X0 @ X5 @ X4 ) ) )
& ? [X6: a,X7: a] :
( ( $true
!= ( X0 @ X7 @ X7 ) )
& ( ( X0 @ X7 @ X6 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > $o] :
( ( X0 = X0 )
& ! [X4: a,X3: a,X5: a] :
( ( $true
!= ( X0 @ X4 @ X5 ) )
| ( $true
!= ( X0 @ X5 @ X3 ) )
| ( $true
= ( X0 @ X4 @ X3 ) ) )
& ! [X2: a,X1: a] :
( ( ( X0 @ X2 @ X1 )
!= $true )
| ( ( X0 @ X1 @ X2 )
= $true ) )
& ? [X7: a,X6: a] :
( ( $true
!= ( X0 @ X6 @ X6 ) )
& ( $true
= ( X0 @ X6 @ X7 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > a > $o] :
( ? [X7: a,X6: a] :
( ( $true
!= ( X0 @ X6 @ X6 ) )
& ( $true
= ( X0 @ X6 @ X7 ) ) )
& ( X0 = X0 )
& ! [X3: a,X5: a,X4: a] :
( ( $true
= ( X0 @ X4 @ X3 ) )
| ( $true
!= ( X0 @ X4 @ X5 ) )
| ( $true
!= ( X0 @ X5 @ X3 ) ) )
& ! [X2: a,X1: a] :
( ( ( X0 @ X2 @ X1 )
!= $true )
| ( ( X0 @ X1 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > $o] :
( ( ( X0 = X0 )
& ! [X3: a,X5: a,X4: a] :
( ( ( $true
= ( X0 @ X4 @ X5 ) )
& ( $true
= ( X0 @ X5 @ X3 ) ) )
=> ( $true
= ( X0 @ X4 @ X3 ) ) )
& ! [X1: a,X2: a] :
( ( ( X0 @ X2 @ X1 )
= $true )
=> ( ( X0 @ X1 @ X2 )
= $true ) ) )
=> ! [X6: a,X7: a] :
( ( $true
= ( X0 @ X6 @ X7 ) )
=> ( $true
= ( X0 @ X6 @ X6 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ( ! [X1: a,X2: a] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) )
& ( X0 = X0 )
& ! [X3: a,X4: a,X5: a] :
( ( ( X0 @ X5 @ X3 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X4 @ X3 ) ) )
=> ! [X6: a,X7: a] :
( ( X0 @ X6 @ X7 )
=> ( X0 @ X6 @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ( ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ( X0 = X0 )
& ! [X3: a,X1: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X1 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ( ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ( X0 = X0 )
& ! [X3: a,X1: a,X2: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.psLSMevQuT/DTF2THF_19662.p',cTHM520_pme) ).
thf(f24,plain,
! [X0: a] :
( ( sK0 @ sK2 @ X0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: a] :
( ( $true != $true )
| ( ( sK0 @ sK2 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f21,f14]) ).
thf(f14,plain,
! [X4: a,X5: a] :
( ( $true
= ( sK0 @ X5 @ X4 ) )
| ( $true
!= ( sK0 @ X4 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f21,plain,
! [X0: a] :
( $true
!= ( sK0 @ X0 @ sK2 ) ),
inference(subsumption_resolution,[status(thm)],[f20,f14]) ).
thf(f20,plain,
! [X0: a] :
( ( ( sK0 @ sK2 @ X0 )
!= $true )
| ( $true
!= ( sK0 @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: a] :
( ( $true != $true )
| ( ( sK0 @ sK2 @ X0 )
!= $true )
| ( $true
!= ( sK0 @ X0 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f13,f15]) ).
thf(f15,plain,
! [X2: a,X3: a,X1: a] :
( ( $true
= ( sK0 @ X1 @ X2 ) )
| ( ( sK0 @ X3 @ X2 )
!= $true )
| ( $true
!= ( sK0 @ X1 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f13,plain,
( ( sK0 @ sK2 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV015^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:38:42 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.41 thf(spec,logic,$$dhol).
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % File : SEV015^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.41 % Domain : Set Theory (Relations)
% 0.15/0.41 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 0.15/0.41 % Version : Especial.
% 0.15/0.41 % English :
% 0.15/0.41
% 0.15/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.41 % Source : [Bro09]
% 0.15/0.41 % Names : tps_0926 [Bro09]
% 0.15/0.41
% 0.15/0.41 % Status : Theorem
% 0.15/0.41 % Rating : 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.15/0.41 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.15/0.41 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 1 ( 1 avg)
% 0.15/0.41 % Number of connectives : 21 ( 0 ~; 0 |; 3 &; 14 @)
% 0.15/0.41 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 12 ( 12 avg)
% 0.15/0.41 % Number of types : 2 ( 1 usr)
% 0.15/0.41 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.15/0.41 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.15/0.41 % SPC : TH0_THM_EQU_NAR
% 0.15/0.41
% 0.15/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 thf(a_type,type,
% 0.15/0.41 a: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(cTHM520_pme,conjecture,
% 0.15/0.41 ! [Xp: a > a > $o] :
% 0.15/0.41 ( ( ! [Xx: a,Xy: a] :
% 0.15/0.41 ( ( Xp @ Xx @ Xy )
% 0.15/0.41 => ( Xp @ Xy @ Xx ) )
% 0.15/0.41 & ! [Xx: a,Xy: a,Xz: a] :
% 0.15/0.41 ( ( ( Xp @ Xx @ Xy )
% 0.15/0.41 & ( Xp @ Xy @ Xz ) )
% 0.15/0.41 => ( Xp @ Xx @ Xz ) )
% 0.15/0.41 & ( Xp = Xp ) )
% 0.15/0.41 => ! [Xx: a,Xy: a] :
% 0.15/0.41 ( ( Xp @ Xx @ Xy )
% 0.15/0.41 => ( Xp @ Xx @ Xx ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 ------------------------
% 1.11/1.11 ---- Embedded in THF ---
% 1.11/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.11/1.11 %%% Generated on Tue Feb 24 12:38:43 EST 2026
% 1.11/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.11/1.11 %%% Logic specification used:
% 1.11/1.11 %%% thf(spec, logic, $$dhol).
% 1.11/1.11
% 1.11/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.psLSMevQuT/DTF2DTF19662.p
% See solution above
% 1.11/1.11 ------------------------
% 1.31/1.12 ---- Cleaned THF ---
% 1.31/1.12 thf(a_type,type,
% 1.31/1.12 a: $tType ).
% 1.31/1.12
% 1.31/1.12 thf(cTHM520_pme,conjecture,
% 1.31/1.12 ! [Xp: a > a > $o] :
% 1.31/1.12 ( ( ! [Xx: a,Xy: a] :
% 1.31/1.12 ( ( Xp @ Xx @ Xy )
% 1.31/1.12 => ( Xp @ Xy @ Xx ) )
% 1.31/1.12 & ! [Xx: a,Xy: a,Xz: a] :
% 1.31/1.12 ( ( ( Xp @ Xx @ Xy )
% 1.31/1.12 & ( Xp @ Xy @ Xz ) )
% 1.31/1.12 => ( Xp @ Xx @ Xz ) )
% 1.31/1.12 & ( Xp = Xp ) )
% 1.31/1.12 => ! [Xx: a,Xy: a] :
% 1.31/1.12 ( ( Xp @ Xx @ Xy )
% 1.31/1.12 => ( Xp @ Xx @ Xx ) ) ) ).
% 1.31/1.12 ------------------------
% 1.31/1.13 % (19763)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_19662 for (3000ds/4Mi)
% 1.31/1.13 % (19763)Instruction limit reached!
% 1.31/1.13 % (19763)------------------------------
% 1.31/1.13 % (19763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.13 % (19763)Termination reason: Unknown
% 1.31/1.13 % (19763)Termination phase: Saturation
% 1.31/1.13
% 1.31/1.13 % (19763)Memory used [KB]: 5500
% 1.31/1.13 % (19763)Time elapsed: 0.004 s
% 1.31/1.13 % (19763)Instructions burned: 6 (million)
% 1.31/1.13 % (19763)------------------------------
% 1.31/1.13 % (19763)------------------------------
% 1.31/1.14 % (19762)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19662 for (3000ds/183Mi)
% 1.31/1.14 % (19766)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_19662 for (3000ds/2Mi)
% 1.31/1.14 % (19765)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19662 for (3000ds/2Mi)
% 1.31/1.14 % (19764)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_19662 for (3000ds/27Mi)
% 1.31/1.14 % (19767)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_19662 for (3000ds/275Mi)
% 1.31/1.14 % (19768)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19662 for (3000ds/18Mi)
% 1.31/1.14 % (19766)Instruction limit reached!
% 1.31/1.14 % (19766)------------------------------
% 1.31/1.14 % (19766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (19766)Termination reason: Unknown
% 1.31/1.14 % (19766)Termination phase: Property scanning
% 1.31/1.14
% 1.31/1.14 % (19766)Memory used [KB]: 895
% 1.31/1.14 % (19766)Time elapsed: 0.002 s
% 1.31/1.14 % (19766)Instructions burned: 2 (million)
% 1.31/1.14 % (19766)------------------------------
% 1.31/1.14 % (19766)------------------------------
% 1.31/1.14 % (19765)Instruction limit reached!
% 1.31/1.14 % (19765)------------------------------
% 1.31/1.14 % (19765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (19765)Termination reason: Unknown
% 1.31/1.14 % (19765)Termination phase: Saturation
% 1.31/1.14
% 1.31/1.14 % (19765)Memory used [KB]: 5500
% 1.31/1.14 % (19765)Time elapsed: 0.003 s
% 1.31/1.14 % (19765)Instructions burned: 3 (million)
% 1.31/1.14 % (19765)------------------------------
% 1.31/1.14 % (19765)------------------------------
% 1.31/1.14 % (19762)First to succeed.
% 1.31/1.14 % (19764)Also succeeded, but the first one will report.
% 1.31/1.14 % (19762)Refutation found. Thanks to Tanya!
% 1.31/1.14 % SZS status Theorem for DTF2THF_19662
% 1.31/1.14 % SZS output start Proof for DTF2THF_19662
% 1.31/1.14 thf(type_def_5, type, a: $tType).
% 1.31/1.14 thf(func_def_0, type, a: $tType).
% 1.31/1.14 thf(func_def_4, type, sK0: a > a > $o).
% 1.31/1.14 thf(func_def_5, type, sK1: a).
% 1.31/1.14 thf(func_def_6, type, sK2: a).
% 1.31/1.14 thf(f29,plain,(
% 1.31/1.14 $false),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.31/1.14 thf(f26,plain,(
% 1.31/1.14 ($true != $true)),
% 1.31/1.14 inference(superposition,[status(thm)],[f24,f12])).
% 1.31/1.14 thf(f12,plain,(
% 1.31/1.14 ((sK0 @ sK2 @ sK1) = $true)),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.31/1.14 thf(f11,plain,(
% 1.31/1.14 (sK0 = sK0) & ! [X1 : a,X2 : a,X3 : a] : (($true != (sK0 @ X1 @ X3)) | ((sK0 @ X3 @ X2) != $true) | ($true = (sK0 @ X1 @ X2))) & ! [X4 : a,X5 : a] : (($true != (sK0 @ X4 @ X5)) | ($true = (sK0 @ X5 @ X4))) & (((sK0 @ sK2 @ sK2) != $true) & ((sK0 @ sK2 @ sK1) = $true))),
% 1.31/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9])).
% 1.31/1.14 thf(f9,plain,(
% 1.31/1.14 ? [X0 : a > a > $o] : ((X0 = X0) & ! [X1 : a,X2 : a,X3 : a] : (((X0 @ X1 @ X3) != $true) | ((X0 @ X3 @ X2) != $true) | ((X0 @ X1 @ X2) = $true)) & ! [X4 : a,X5 : a] : (($true != (X0 @ X4 @ X5)) | ($true = (X0 @ X5 @ X4))) & ? [X6 : a,X7 : a] : (($true != (X0 @ X7 @ X7)) & ((X0 @ X7 @ X6) = $true))) => ((sK0 = sK0) & ! [X3 : a,X2 : a,X1 : a] : (($true != (sK0 @ X1 @ X3)) | ((sK0 @ X3 @ X2) != $true) | ($true = (sK0 @ X1 @ X2))) & ! [X5 : a,X4 : a] : (($true != (sK0 @ X4 @ X5)) | ($true = (sK0 @ X5 @ X4))) & ? [X7 : a,X6 : a] : (((sK0 @ X7 @ X7) != $true) & ((sK0 @ X7 @ X6) = $true)))),
% 1.31/1.14 introduced(definition,[],[choice_axiom])).
% 1.31/1.14 thf(f10,plain,(
% 1.31/1.14 ? [X7 : a,X6 : a] : (((sK0 @ X7 @ X7) != $true) & ((sK0 @ X7 @ X6) = $true)) => (((sK0 @ sK2 @ sK2) != $true) & ((sK0 @ sK2 @ sK1) = $true))),
% 1.31/1.14 introduced(definition,[],[choice_axiom])).
% 1.31/1.14 thf(f8,plain,(
% 1.31/1.14 ? [X0 : a > a > $o] : ((X0 = X0) & ! [X1 : a,X2 : a,X3 : a] : (((X0 @ X1 @ X3) != $true) | ((X0 @ X3 @ X2) != $true) | ((X0 @ X1 @ X2) = $true)) & ! [X4 : a,X5 : a] : (($true != (X0 @ X4 @ X5)) | ($true = (X0 @ X5 @ X4))) & ? [X6 : a,X7 : a] : (($true != (X0 @ X7 @ X7)) & ((X0 @ X7 @ X6) = $true)))),
% 1.31/1.14 inference(rectify,[status(thm)],[f7])).
% 1.31/1.14 thf(f7,plain,(
% 1.31/1.14 ? [X0 : a > a > $o] : ((X0 = X0) & ! [X4 : a,X3 : a,X5 : a] : (($true != (X0 @ X4 @ X5)) | ($true != (X0 @ X5 @ X3)) | ($true = (X0 @ X4 @ X3))) & ! [X2 : a,X1 : a] : (((X0 @ X2 @ X1) != $true) | ((X0 @ X1 @ X2) = $true)) & ? [X7 : a,X6 : a] : (($true != (X0 @ X6 @ X6)) & ($true = (X0 @ X6 @ X7))))),
% 1.31/1.14 inference(flattening,[status(thm)],[f6])).
% 1.31/1.14 thf(f6,plain,(
% 1.31/1.14 ? [X0 : a > a > $o] : (? [X7 : a,X6 : a] : (($true != (X0 @ X6 @ X6)) & ($true = (X0 @ X6 @ X7))) & ((X0 = X0) & ! [X3 : a,X5 : a,X4 : a] : (($true = (X0 @ X4 @ X3)) | (($true != (X0 @ X4 @ X5)) | ($true != (X0 @ X5 @ X3)))) & ! [X2 : a,X1 : a] : (((X0 @ X2 @ X1) != $true) | ((X0 @ X1 @ X2) = $true))))),
% 1.31/1.14 inference(ennf_transformation,[status(thm)],[f5])).
% 1.31/1.14 thf(f5,plain,(
% 1.31/1.14 ~! [X0 : a > a > $o] : (((X0 = X0) & ! [X3 : a,X5 : a,X4 : a] : ((($true = (X0 @ X4 @ X5)) & ($true = (X0 @ X5 @ X3))) => ($true = (X0 @ X4 @ X3))) & ! [X1 : a,X2 : a] : (((X0 @ X2 @ X1) = $true) => ((X0 @ X1 @ X2) = $true))) => ! [X6 : a,X7 : a] : (($true = (X0 @ X6 @ X7)) => ($true = (X0 @ X6 @ X6))))),
% 1.31/1.14 inference(fool_elimination,[status(thm)],[f4])).
% 1.31/1.14 thf(f4,plain,(
% 1.31/1.14 ~! [X0 : a > a > $o] : ((! [X1 : a,X2 : a] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)) & (X0 = X0) & ! [X3 : a,X4 : a,X5 : a] : (((X0 @ X5 @ X3) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X3))) => ! [X6 : a,X7 : a] : ((X0 @ X6 @ X7) => (X0 @ X6 @ X6)))),
% 1.31/1.14 inference(rectify,[status(thm)],[f2])).
% 1.31/1.14 thf(f2,negated_conjecture,(
% 1.31/1.14 ~! [X0 : a > a > $o] : ((! [X2 : a,X1 : a] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)) & (X0 = X0) & ! [X3 : a,X1 : a,X2 : a] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3))) => ! [X1 : a,X2 : a] : ((X0 @ X1 @ X2) => (X0 @ X1 @ X1)))),
% 1.31/1.14 inference(negated_conjecture,[status(cth)],[f1])).
% 1.31/1.14 thf(f1,conjecture,(
% 1.31/1.14 ! [X0 : a > a > $o] : ((! [X2 : a,X1 : a] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)) & (X0 = X0) & ! [X3 : a,X1 : a,X2 : a] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3))) => ! [X1 : a,X2 : a] : ((X0 @ X1 @ X2) => (X0 @ X1 @ X1)))),
% 1.31/1.14 file('/export/starexec/sandbox2/tmp/tmp.psLSMevQuT/DTF2THF_19662.p',cTHM520_pme)).
% 1.31/1.14 thf(f24,plain,(
% 1.31/1.14 ( ! [X0 : a] : (((sK0 @ sK2 @ X0) != $true)) )),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.31/1.14 thf(f23,plain,(
% 1.31/1.14 ( ! [X0 : a] : (($true != $true) | ((sK0 @ sK2 @ X0) != $true)) )),
% 1.31/1.14 inference(superposition,[status(thm)],[f21,f14])).
% 1.31/1.14 thf(f14,plain,(
% 1.31/1.14 ( ! [X4 : a,X5 : a] : (($true = (sK0 @ X5 @ X4)) | ($true != (sK0 @ X4 @ X5))) )),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.31/1.14 thf(f21,plain,(
% 1.31/1.14 ( ! [X0 : a] : (($true != (sK0 @ X0 @ sK2))) )),
% 1.31/1.14 inference(subsumption_resolution,[status(thm)],[f20,f14])).
% 1.31/1.14 thf(f20,plain,(
% 1.31/1.14 ( ! [X0 : a] : (((sK0 @ sK2 @ X0) != $true) | ($true != (sK0 @ X0 @ sK2))) )),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.31/1.14 thf(f19,plain,(
% 1.31/1.14 ( ! [X0 : a] : (($true != $true) | ((sK0 @ sK2 @ X0) != $true) | ($true != (sK0 @ X0 @ sK2))) )),
% 1.31/1.14 inference(superposition,[status(thm)],[f13,f15])).
% 1.31/1.14 thf(f15,plain,(
% 1.31/1.14 ( ! [X2 : a,X3 : a,X1 : a] : (($true = (sK0 @ X1 @ X2)) | ((sK0 @ X3 @ X2) != $true) | ($true != (sK0 @ X1 @ X3))) )),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.31/1.14 thf(f13,plain,(
% 1.31/1.14 ((sK0 @ sK2 @ sK2) != $true)),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.31/1.14 % SZS output end Proof for DTF2THF_19662
% 1.31/1.14 % (19762)------------------------------
% 1.31/1.14 % (19762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (19762)Termination reason: Refutation
% 1.31/1.14
% 1.31/1.14 % (19762)Memory used [KB]: 5500
% 1.31/1.14 % (19762)Time elapsed: 0.004 s
% 1.31/1.14 % (19762)Instructions burned: 3 (million)
% 1.31/1.14 % (19762)------------------------------
% 1.31/1.14 % (19762)------------------------------
% 1.31/1.14 % (19761)Success in time 0.017 s
%------------------------------------------------------------------------------