%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV056^5 : 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 : n031.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 09:40:10 AM UTC 2026
% Result : Theorem 1.49s 1.29s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 52 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 234 ( 26 ~; 9 |; 32 &; 156 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 12 ^; 33 !; 38 ?; 83 :)
% 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 > a > $o ) > a ).
thf(func_def_6,type,
sK2: ( a > a > $o ) > a ).
thf(func_def_7,type,
sK3: ( a > a > $o ) > a ).
thf(func_def_8,type,
sK4: ( a > a > $o ) > a ).
thf(func_def_9,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_12,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f34,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
$true != $true,
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $true != $true )
| ( $true != $true ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true
!= ( ^ [Y0: a,Y1: a] : $true
@ ( sK1
@ ^ [Y0: a,Y1: a] : $true )
@ ( sK2
@ ^ [Y0: a,Y1: a] : $true ) ) )
| ( ( ^ [Y0: a,Y1: a] : $true
@ ( sK5
@ ^ [Y0: a,Y1: a] : $true )
@ ( sK4
@ ^ [Y0: a,Y1: a] : $true ) )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: a > a > $o] :
( ( $true
!= ( X1 @ ( sK5 @ X1 ) @ ( sK4 @ X1 ) ) )
| ( $true
!= ( X1 @ ( sK1 @ X1 ) @ ( sK2 @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: a > a > $o] :
( ( ( $true
= ( X1 @ ( sK3 @ X1 ) @ ( sK2 @ X1 ) ) )
& ( $true
= ( X1 @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) ) )
& ( $true
!= ( X1 @ ( sK1 @ X1 ) @ ( sK2 @ X1 ) ) ) )
| ( ( $true
!= ( X1 @ ( sK5 @ X1 ) @ ( sK4 @ X1 ) ) )
& ( $true
= ( sK0 @ ( sK5 @ X1 ) @ ( sK4 @ X1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o] :
! [X1: a > a > $o] :
( ? [X2: a,X3: a,X4: a] :
( ( $true
= ( X1 @ X4 @ X3 ) )
& ( ( X1 @ X2 @ X4 )
= $true )
& ( ( X1 @ X2 @ X3 )
!= $true ) )
| ? [X5: a,X6: a] :
( ( $true
!= ( X1 @ X6 @ X5 ) )
& ( $true
= ( X0 @ X6 @ X5 ) ) ) )
=> ! [X1: a > a > $o] :
( ? [X2: a,X3: a,X4: a] :
( ( $true
= ( X1 @ X4 @ X3 ) )
& ( ( X1 @ X2 @ X4 )
= $true )
& ( ( X1 @ X2 @ X3 )
!= $true ) )
| ? [X6: a,X5: a] :
( ( $true
!= ( X1 @ X6 @ X5 ) )
& ( $true
= ( sK0 @ X6 @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X1: a > a > $o] :
( ? [X2: a,X3: a,X4: a] :
( ( $true
= ( X1 @ X4 @ X3 ) )
& ( ( X1 @ X2 @ X4 )
= $true )
& ( ( X1 @ X2 @ X3 )
!= $true ) )
=> ( ( $true
= ( X1 @ ( sK3 @ X1 ) @ ( sK2 @ X1 ) ) )
& ( $true
= ( X1 @ ( sK1 @ X1 ) @ ( sK3 @ X1 ) ) )
& ( $true
!= ( X1 @ ( sK1 @ X1 ) @ ( sK2 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X1: a > a > $o] :
( ? [X6: a,X5: a] :
( ( $true
!= ( X1 @ X6 @ X5 ) )
& ( $true
= ( sK0 @ X6 @ X5 ) ) )
=> ( ( $true
!= ( X1 @ ( sK5 @ X1 ) @ ( sK4 @ X1 ) ) )
& ( $true
= ( sK0 @ ( sK5 @ X1 ) @ ( sK4 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o] :
! [X1: a > a > $o] :
( ? [X2: a,X3: a,X4: a] :
( ( $true
= ( X1 @ X4 @ X3 ) )
& ( ( X1 @ X2 @ X4 )
= $true )
& ( ( X1 @ X2 @ X3 )
!= $true ) )
| ? [X5: a,X6: a] :
( ( $true
!= ( X1 @ X6 @ X5 ) )
& ( $true
= ( X0 @ X6 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > $o] :
! [X1: a > a > $o] :
( ? [X6: a,X5: a,X4: a] :
( ( $true
= ( X1 @ X4 @ X5 ) )
& ( ( X1 @ X6 @ X4 )
= $true )
& ( $true
!= ( X1 @ X6 @ X5 ) ) )
| ? [X2: a,X3: a] :
( ( $true
!= ( X1 @ X3 @ X2 ) )
& ( $true
= ( X0 @ X3 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > a > $o] :
! [X1: a > a > $o] :
( ? [X5: a,X4: a,X6: a] :
( ( $true
!= ( X1 @ X6 @ X5 ) )
& ( $true
= ( X1 @ X4 @ X5 ) )
& ( ( X1 @ X6 @ X4 )
= $true ) )
| ? [X2: a,X3: a] :
( ( $true
!= ( X1 @ X3 @ X2 ) )
& ( $true
= ( X0 @ X3 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > $o] :
? [X1: a > a > $o] :
( ! [X5: a,X4: a,X6: a] :
( ( ( $true
= ( X1 @ X4 @ X5 ) )
& ( ( X1 @ X6 @ X4 )
= $true ) )
=> ( $true
= ( X1 @ X6 @ X5 ) ) )
& ! [X2: a,X3: a] :
( ( $true
= ( X0 @ X3 @ X2 ) )
=> ( $true
= ( X1 @ X3 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
? [X1: a > a > $o] :
( ! [X2: a,X3: a] :
( ( X0 @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) )
& ! [X4: a,X5: a,X6: a] :
( ( ( X1 @ X6 @ X4 )
& ( X1 @ X4 @ X5 ) )
=> ( X1 @ X6 @ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
? [X1: a > a > $o] :
( ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
& ! [X3: a,X4: a,X2: a] :
( ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
? [X1: a > a > $o] :
( ! [X3: a,X2: a] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
& ! [X3: a,X4: a,X2: a] :
( ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qAdypuk1tO/DTF2THF_23787.p',cTHM275_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV056^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n031.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 12:40:33 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEV056^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.47 % Domain : Set Theory (Relations)
% 0.28/0.47 % Problem : TPS problem THM275
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : tps_0312 [Bro09]
% 0.28/0.47 % : THM275 [TPS]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.28/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.28/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.28/0.47 % Number of connectives : 14 ( 0 ~; 0 |; 2 &; 10 @)
% 0.28/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 11 ( 11 avg)
% 0.28/0.47 % Number of types : 2 ( 1 usr)
% 0.28/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.28/0.47 % Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% 0.28/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.47 % : Polymorphic definitions expanded.
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(a_type,type,
% 0.28/0.47 a: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(cTHM275_pme,conjecture,
% 0.28/0.47 ! [Xr: a > a > $o] :
% 0.28/0.47 ? [Xp: a > a > $o] :
% 0.28/0.47 ( ! [Xx: a,Xy: a] :
% 0.28/0.47 ( ( Xr @ Xx @ Xy )
% 0.28/0.47 => ( Xp @ Xx @ Xy ) )
% 0.28/0.47 & ! [Xx: a,Xy: a,Xz: a] :
% 0.28/0.47 ( ( ( Xp @ Xx @ Xy )
% 0.28/0.47 & ( Xp @ Xy @ Xz ) )
% 0.28/0.47 => ( Xp @ Xx @ Xz ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 12:40:34 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qAdypuk1tO/DTF2DTF23787.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(a_type,type,
% 1.49/1.26 a: $tType ).
% 1.49/1.26
% 1.49/1.26 thf(cTHM275_pme,conjecture,
% 1.49/1.26 ! [Xr: a > a > $o] :
% 1.49/1.26 ? [Xp: a > a > $o] :
% 1.49/1.26 ( ! [Xx: a,Xy: a] :
% 1.49/1.26 ( ( Xr @ Xx @ Xy )
% 1.49/1.26 => ( Xp @ Xx @ Xy ) )
% 1.49/1.26 & ! [Xx: a,Xy: a,Xz: a] :
% 1.49/1.26 ( ( ( Xp @ Xx @ Xy )
% 1.49/1.26 & ( Xp @ Xy @ Xz ) )
% 1.49/1.26 => ( Xp @ Xx @ Xz ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.27 % (23890)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23787 for (3000ds/18Mi)
% 1.49/1.27 % (23885)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_23787 for (3000ds/4Mi)
% 1.49/1.28 % (23885)Instruction limit reached!
% 1.49/1.28 % (23885)------------------------------
% 1.49/1.28 % (23885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (23890)Instruction limit reached!
% 1.49/1.28 % (23890)------------------------------
% 1.49/1.28 % (23890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (23887)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23787 for (3000ds/2Mi)
% 1.49/1.28 % (23890)Termination reason: Unknown
% 1.49/1.28 % (23890)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (23890)Memory used [KB]: 5628
% 1.49/1.28 % (23890)Time elapsed: 0.008 s
% 1.49/1.28 % (23890)Instructions burned: 19 (million)
% 1.49/1.28 % (23890)------------------------------
% 1.49/1.28 % (23890)------------------------------
% 1.49/1.28 % (23885)Termination reason: Unknown
% 1.49/1.28 % (23885)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (23885)Memory used [KB]: 5500
% 1.49/1.28 % (23885)Time elapsed: 0.003 s
% 1.49/1.28 % (23885)Instructions burned: 5 (million)
% 1.49/1.28 % (23885)------------------------------
% 1.49/1.28 % (23885)------------------------------
% 1.49/1.28 % (23887)Instruction limit reached!
% 1.49/1.28 % (23887)------------------------------
% 1.49/1.28 % (23887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (23887)Termination reason: Unknown
% 1.49/1.28 % (23887)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (23887)Memory used [KB]: 5373
% 1.49/1.28 % (23887)Time elapsed: 0.003 s
% 1.49/1.28 % (23884)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23787 for (3000ds/183Mi)
% 1.49/1.28 % (23887)Instructions burned: 2 (million)
% 1.49/1.28 % (23887)------------------------------
% 1.49/1.28 % (23887)------------------------------
% 1.49/1.28 % (23889)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_23787 for (3000ds/275Mi)
% 1.49/1.28 % (23884)First to succeed.
% 1.49/1.29 % (23889)Also succeeded, but the first one will report.
% 1.49/1.29 % (23888)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_23787 for (3000ds/2Mi)
% 1.49/1.29 % (23884)Refutation found. Thanks to Tanya!
% 1.49/1.29 % SZS status Theorem for DTF2THF_23787
% 1.49/1.29 % SZS output start Proof for DTF2THF_23787
% 1.49/1.29 thf(type_def_5, type, a: $tType).
% 1.49/1.29 thf(func_def_0, type, a: $tType).
% 1.49/1.29 thf(func_def_4, type, sK0: a > a > $o).
% 1.49/1.29 thf(func_def_5, type, sK1: (a > a > $o) > a).
% 1.49/1.29 thf(func_def_6, type, sK2: (a > a > $o) > a).
% 1.49/1.29 thf(func_def_7, type, sK3: (a > a > $o) > a).
% 1.49/1.29 thf(func_def_8, type, sK4: (a > a > $o) > a).
% 1.49/1.29 thf(func_def_9, type, sK5: (a > a > $o) > a).
% 1.49/1.29 thf(func_def_12, type, ph7: !>[X0: $tType]:(X0)).
% 1.49/1.29 thf(f34,plain,(
% 1.49/1.29 $false),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.49/1.29 thf(f33,plain,(
% 1.49/1.29 ($true != $true)),
% 1.49/1.29 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.49/1.29 thf(f32,plain,(
% 1.49/1.29 ($true != $true) | ($true != $true)),
% 1.49/1.29 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.49/1.29 thf(f21,plain,(
% 1.49/1.29 ($true != ((^[Y0 : a]: ((^[Y1 : a]: ($true)))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: ($true))))) @ (sK2 @ (^[Y0 : a]: ((^[Y1 : a]: ($true))))))) | (((^[Y0 : a]: ((^[Y1 : a]: ($true)))) @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: ($true))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: ($true)))))) != $true)),
% 1.49/1.29 inference(primitive_instantiation,[status(thm)],[f14])).
% 1.49/1.29 thf(f14,plain,(
% 1.49/1.29 ( ! [X1 : a > a > $o] : (($true != (X1 @ (sK5 @ X1) @ (sK4 @ X1))) | ($true != (X1 @ (sK1 @ X1) @ (sK2 @ X1)))) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.29 thf(f12,plain,(
% 1.49/1.29 ! [X1 : a > a > $o] : ((($true = (X1 @ (sK3 @ X1) @ (sK2 @ X1))) & ($true = (X1 @ (sK1 @ X1) @ (sK3 @ X1))) & ($true != (X1 @ (sK1 @ X1) @ (sK2 @ X1)))) | (($true != (X1 @ (sK5 @ X1) @ (sK4 @ X1))) & ($true = (sK0 @ (sK5 @ X1) @ (sK4 @ X1)))))),
% 1.49/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9])).
% 1.49/1.29 thf(f9,plain,(
% 1.49/1.29 ? [X0 : a > a > $o] : ! [X1 : a > a > $o] : (? [X2 : a,X3 : a,X4 : a] : (($true = (X1 @ X4 @ X3)) & ((X1 @ X2 @ X4) = $true) & ((X1 @ X2 @ X3) != $true)) | ? [X5 : a,X6 : a] : (($true != (X1 @ X6 @ X5)) & ($true = (X0 @ X6 @ X5)))) => ! [X1 : a > a > $o] : (? [X2 : a,X3 : a,X4 : a] : (($true = (X1 @ X4 @ X3)) & ((X1 @ X2 @ X4) = $true) & ((X1 @ X2 @ X3) != $true)) | ? [X6 : a,X5 : a] : (($true != (X1 @ X6 @ X5)) & ($true = (sK0 @ X6 @ X5))))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f10,plain,(
% 1.49/1.29 ! [X1 : a > a > $o] : (? [X2 : a,X3 : a,X4 : a] : (($true = (X1 @ X4 @ X3)) & ((X1 @ X2 @ X4) = $true) & ((X1 @ X2 @ X3) != $true)) => (($true = (X1 @ (sK3 @ X1) @ (sK2 @ X1))) & ($true = (X1 @ (sK1 @ X1) @ (sK3 @ X1))) & ($true != (X1 @ (sK1 @ X1) @ (sK2 @ X1)))))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f11,plain,(
% 1.49/1.29 ! [X1 : a > a > $o] : (? [X6 : a,X5 : a] : (($true != (X1 @ X6 @ X5)) & ($true = (sK0 @ X6 @ X5))) => (($true != (X1 @ (sK5 @ X1) @ (sK4 @ X1))) & ($true = (sK0 @ (sK5 @ X1) @ (sK4 @ X1)))))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f8,plain,(
% 1.49/1.29 ? [X0 : a > a > $o] : ! [X1 : a > a > $o] : (? [X2 : a,X3 : a,X4 : a] : (($true = (X1 @ X4 @ X3)) & ((X1 @ X2 @ X4) = $true) & ((X1 @ X2 @ X3) != $true)) | ? [X5 : a,X6 : a] : (($true != (X1 @ X6 @ X5)) & ($true = (X0 @ X6 @ X5))))),
% 1.49/1.29 inference(rectify,[status(thm)],[f7])).
% 1.49/1.29 thf(f7,plain,(
% 1.49/1.29 ? [X0 : a > a > $o] : ! [X1 : a > a > $o] : (? [X6 : a,X5 : a,X4 : a] : (($true = (X1 @ X4 @ X5)) & ((X1 @ X6 @ X4) = $true) & ($true != (X1 @ X6 @ X5))) | ? [X2 : a,X3 : a] : (($true != (X1 @ X3 @ X2)) & ($true = (X0 @ X3 @ X2))))),
% 1.49/1.29 inference(flattening,[status(thm)],[f6])).
% 1.49/1.29 thf(f6,plain,(
% 1.49/1.29 ? [X0 : a > a > $o] : ! [X1 : a > a > $o] : (? [X5 : a,X4 : a,X6 : a] : (($true != (X1 @ X6 @ X5)) & (($true = (X1 @ X4 @ X5)) & ((X1 @ X6 @ X4) = $true))) | ? [X2 : a,X3 : a] : (($true != (X1 @ X3 @ X2)) & ($true = (X0 @ X3 @ X2))))),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.29 thf(f5,plain,(
% 1.49/1.29 ~! [X0 : a > a > $o] : ? [X1 : a > a > $o] : (! [X5 : a,X4 : a,X6 : a] : ((($true = (X1 @ X4 @ X5)) & ((X1 @ X6 @ X4) = $true)) => ($true = (X1 @ X6 @ X5))) & ! [X2 : a,X3 : a] : (($true = (X0 @ X3 @ X2)) => ($true = (X1 @ X3 @ X2))))),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.29 thf(f4,plain,(
% 1.49/1.29 ~! [X0 : a > a > $o] : ? [X1 : a > a > $o] : (! [X2 : a,X3 : a] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)) & ! [X4 : a,X5 : a,X6 : a] : (((X1 @ X6 @ X4) & (X1 @ X4 @ X5)) => (X1 @ X6 @ X5)))),
% 1.49/1.29 inference(rectify,[status(thm)],[f2])).
% 1.49/1.29 thf(f2,negated_conjecture,(
% 1.49/1.29 ~! [X0 : a > a > $o] : ? [X1 : a > a > $o] : (! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)) & ! [X3 : a,X4 : a,X2 : a] : (((X1 @ X2 @ X3) & (X1 @ X3 @ X4)) => (X1 @ X2 @ X4)))),
% 1.49/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.29 thf(f1,conjecture,(
% 1.49/1.29 ! [X0 : a > a > $o] : ? [X1 : a > a > $o] : (! [X3 : a,X2 : a] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)) & ! [X3 : a,X4 : a,X2 : a] : (((X1 @ X2 @ X3) & (X1 @ X3 @ X4)) => (X1 @ X2 @ X4)))),
% 1.49/1.29 file('/export/starexec/sandbox/tmp/tmp.qAdypuk1tO/DTF2THF_23787.p',cTHM275_pme)).
% 1.49/1.29 % SZS output end Proof for DTF2THF_23787
% 1.49/1.29 % (23884)------------------------------
% 1.49/1.29 % (23884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (23884)Termination reason: Refutation
% 1.49/1.29
% 1.49/1.29 % (23884)Memory used [KB]: 5500
% 1.49/1.29 % (23884)Time elapsed: 0.006 s
% 1.49/1.29 % (23884)Instructions burned: 4 (million)
% 1.49/1.29 % (23884)------------------------------
% 1.49/1.29 % (23884)------------------------------
% 1.49/1.29 % (23883)Success in time 0.021 s
%------------------------------------------------------------------------------