%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET617^5 : 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 : n023.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 09:31:56 AM UTC 2026
% Result : Theorem 1.68s 1.42s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 227 ( 79 ~; 37 |; 56 &; 54 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 1 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 33 ^; 4 !; 2 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_9,type,
sK0: a > $o ).
thf(f21,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
sK0 != sK0,
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( sK0
!= ( ^ [Y0: a] : ( sK0 @ Y0 ) ) ),
inference(boolean_simplification,[status(thm)],[f18]) ).
thf(f18,plain,
( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& $true ) ) ),
inference(boolean_simplification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ $false ) )
!= sK0 ),
inference(boolean_simplification,[status(thm)],[f16]) ).
thf(f16,plain,
( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK0 != sK0 )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) )
| ( sK0
!= ( ^ [Y0: a] : ( sK0 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& $true ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) ) ),
inference(boolean_simplification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( ~ ( sK0 @ Y0 )
& $false ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& $true ) ) ) ),
inference(boolean_simplification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ $false ) )
!= sK0 )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( ~ ( sK0 @ Y0 )
& $false ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( ~ ( sK0 @ Y0 )
& $false ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( sK0 @ Y0 ) ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( ~ ( sK0 @ Y0 )
& $false ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( ~ ( sK0 @ Y0 )
& $false ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( sK0 @ Y0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ $false )
| ( ~ ( X0 @ Y0 )
& $false ) ) )
!= X0 )
| ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( X0 @ Y0 ) ) ) )
!= X0 ) )
=> ( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( ~ ( sK0 @ Y0 )
& $false ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( sK0 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ $false )
| ( ~ ( X0 @ Y0 )
& $false ) ) )
!= X0 )
| ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( X0 @ Y0 ) ) ) )
!= X0 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( X0 @ Y0 ) ) ) )
= X0 )
& ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ $false )
| ( ~ ( X0 @ Y0 )
& $false ) ) )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ( X0
= ( ^ [X1: a] :
( ( $false
& ~ ( X0 @ X1 ) )
| ( ~ $false
& ( X0 @ X1 ) ) ) ) )
& ( X0
= ( ^ [X2: a] :
( ( ~ ( X0 @ X2 )
& $false )
| ( ~ $false
& ( X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ( X0
= ( ^ [X1: a] :
( ( $false
& ~ ( X0 @ X1 ) )
| ( ~ $false
& ( X0 @ X1 ) ) ) ) )
& ( X0
= ( ^ [X1: a] :
( ( ~ ( X0 @ X1 )
& $false )
| ( ~ $false
& ( X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o] :
( ( X0
= ( ^ [X1: a] :
( ( $false
& ~ ( X0 @ X1 ) )
| ( ~ $false
& ( X0 @ X1 ) ) ) ) )
& ( X0
= ( ^ [X1: a] :
( ( ~ ( X0 @ X1 )
& $false )
| ( ~ $false
& ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5jw000Avzs/DTF2THF_15610.p',cBOOL_PROP_92_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET617^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n023.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:01:34 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.33/0.48 thf(spec,logic,$$dhol).
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 % File : SET617^5 : TPTP v9.2.1. Released v4.0.0.
% 0.33/0.48 % Domain : Set Theory
% 0.33/0.48 % Problem : TPS problem BOOL-PROP-92
% 0.33/0.48 % Version : Especial.
% 0.33/0.48 % English : Trybulec's 92nd Boolean property of sets
% 0.33/0.48
% 0.33/0.48 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.33/0.48 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.48 % Source : [Bro09]
% 0.33/0.48 % Names : tps_0387 [Bro09]
% 0.33/0.48 % : BOOL-PROP-92 [TPS]
% 0.33/0.48
% 0.33/0.48 % Status : Theorem
% 0.33/0.48 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 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 v4.0.0
% 0.33/0.48 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.33/0.48 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.33/0.48 % Maximal formula atoms : 2 ( 6 avg)
% 0.33/0.48 % Number of connectives : 15 ( 4 ~; 2 |; 5 &; 4 @)
% 0.33/0.48 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.33/0.48 % Maximal formula depth : 3 ( 3 avg)
% 0.33/0.48 % Number of types : 2 ( 1 usr)
% 0.33/0.48 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.33/0.48 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.33/0.48 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.33/0.48 % SPC : TH0_THM_EQU_NAR
% 0.33/0.48
% 0.33/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.33/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.33/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.33/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.33/0.48 % : Polymorphic definitions expanded.
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 thf(a_type,type,
% 0.33/0.48 a: $tType ).
% 0.33/0.48
% 0.33/0.48 thf(cBOOL_PROP_92_pme,conjecture,
% 0.33/0.48 ! [X: a > $o] :
% 0.33/0.48 ( ( ( ^ [Xz: a] :
% 0.33/0.48 ( ( ( X @ Xz )
% 0.33/0.48 & ~ $false )
% 0.33/0.48 | ( $false
% 0.33/0.48 & ~ ( X @ Xz ) ) ) )
% 0.33/0.48 = X )
% 0.33/0.48 & ( ( ^ [Xz: a] :
% 0.33/0.48 ( ( $false
% 0.33/0.48 & ~ ( X @ Xz ) )
% 0.33/0.48 | ( ( X @ Xz )
% 0.33/0.48 & ~ $false ) ) )
% 0.33/0.48 = X ) ) ).
% 0.33/0.48
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 ------------------------
% 1.47/1.39 ---- Embedded in THF ---
% 1.47/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.39 %%% Generated on Tue Feb 24 12:01:35 EST 2026
% 1.47/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.39 %%% Logic specification used:
% 1.47/1.39 %%% thf(spec, logic, $$dhol).
% 1.47/1.39
% 1.47/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5jw000Avzs/DTF2DTF15610.p
% See solution above
% 1.47/1.39 ------------------------
% 1.68/1.40 ---- Cleaned THF ---
% 1.68/1.40 thf(a_type,type,
% 1.68/1.40 a: $tType ).
% 1.68/1.40
% 1.68/1.40 thf(cBOOL_PROP_92_pme,conjecture,
% 1.68/1.40 ! [X: a > $o] :
% 1.68/1.40 ( ( ( ^ [Xz: a] :
% 1.68/1.40 ( ( ( X @ Xz )
% 1.68/1.40 & ~ $false )
% 1.68/1.40 | ( $false
% 1.68/1.40 & ~ ( X @ Xz ) ) ) )
% 1.68/1.40 = X )
% 1.68/1.40 & ( ( ^ [Xz: a] :
% 1.68/1.40 ( ( $false
% 1.68/1.40 & ~ ( X @ Xz ) )
% 1.68/1.40 | ( ( X @ Xz )
% 1.68/1.40 & ~ $false ) ) )
% 1.68/1.40 = X ) ) ).
% 1.68/1.40 ------------------------
% 1.68/1.42 % (15725)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_15610 for (3000ds/2Mi)
% 1.68/1.42 % (15723)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_15610 for (3000ds/27Mi)
% 1.68/1.42 % (15722)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_15610 for (3000ds/4Mi)
% 1.68/1.42 % (15726)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_15610 for (3000ds/275Mi)
% 1.68/1.42 % (15727)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15610 for (3000ds/18Mi)
% 1.68/1.42 % (15724)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15610 for (3000ds/2Mi)
% 1.68/1.42 % (15721)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15610 for (3000ds/183Mi)
% 1.68/1.42 % (15724)Instruction limit reached!
% 1.68/1.42 % (15724)------------------------------
% 1.68/1.42 % (15724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.42 % (15724)Termination reason: Unknown
% 1.68/1.42 % (15726)First to succeed.
% 1.68/1.42 % (15724)Termination phase: Saturation
% 1.68/1.42 % (15725)Instruction limit reached!
% 1.68/1.42 % (15725)------------------------------
% 1.68/1.42 % (15725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.42 % (15725)Termination reason: Unknown
% 1.68/1.42 % (15725)Termination phase: Saturation
% 1.68/1.42
% 1.68/1.42 % (15725)Memory used [KB]: 5373
% 1.68/1.42 % (15725)Time elapsed: 0.003 s
% 1.68/1.42 % (15725)Instructions burned: 2 (million)
% 1.68/1.42 % (15725)------------------------------
% 1.68/1.42 % (15725)------------------------------
% 1.68/1.42
% 1.68/1.42 % (15724)Memory used [KB]: 5373
% 1.68/1.42 % (15724)Time elapsed: 0.003 s
% 1.68/1.42 % (15724)Instructions burned: 2 (million)
% 1.68/1.42 % (15724)------------------------------
% 1.68/1.42 % (15724)------------------------------
% 1.68/1.42 % (15723)Also succeeded, but the first one will report.
% 1.68/1.42 % (15726)Refutation found. Thanks to Tanya!
% 1.68/1.42 % SZS status Theorem for DTF2THF_15610
% 1.68/1.42 % SZS output start Proof for DTF2THF_15610
% 1.68/1.42 thf(type_def_5, type, a: $tType).
% 1.68/1.42 thf(func_def_0, type, a: $tType).
% 1.68/1.42 thf(func_def_9, type, sK0: a > $o).
% 1.68/1.42 thf(f21,plain,(
% 1.68/1.42 $false),
% 1.68/1.42 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.68/1.42 thf(f20,plain,(
% 1.68/1.42 (sK0 != sK0)),
% 1.68/1.42 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.68/1.42 thf(f19,plain,(
% 1.68/1.42 (sK0 != (^[Y0 : a]: (sK0 @ Y0)))),
% 1.68/1.42 inference(boolean_simplification,[status(thm)],[f18])).
% 1.68/1.42 thf(f18,plain,(
% 1.68/1.42 (sK0 != (^[Y0 : a]: ((sK0 @ Y0) & $true)))),
% 1.68/1.42 inference(boolean_simplification,[status(thm)],[f17])).
% 1.68/1.42 thf(f17,plain,(
% 1.68/1.42 ((^[Y0 : a]: ((sK0 @ Y0) & (~ $false))) != sK0)),
% 1.68/1.42 inference(boolean_simplification,[status(thm)],[f16])).
% 1.68/1.42 thf(f16,plain,(
% 1.68/1.42 (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | $false)))),
% 1.68/1.42 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.68/1.42 thf(f15,plain,(
% 1.68/1.42 (sK0 != sK0) | (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | $false)))),
% 1.68/1.42 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.68/1.42 thf(f14,plain,(
% 1.68/1.42 (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | $false))) | (sK0 != (^[Y0 : a]: (sK0 @ Y0)))),
% 1.68/1.42 inference(boolean_simplification,[status(thm)],[f13])).
% 1.68/1.42 thf(f13,plain,(
% 1.68/1.42 (sK0 != (^[Y0 : a]: ((sK0 @ Y0) & $true))) | (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | $false)))),
% 1.68/1.42 inference(boolean_simplification,[status(thm)],[f12])).
% 1.68/1.42 thf(f12,plain,(
% 1.68/1.42 (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | ((~ (sK0 @ Y0)) & $false)))) | (sK0 != (^[Y0 : a]: ((sK0 @ Y0) & $true)))),
% 1.68/1.42 inference(boolean_simplification,[status(thm)],[f11])).
% 1.68/1.42 thf(f11,plain,(
% 1.68/1.42 ((^[Y0 : a]: ((sK0 @ Y0) & (~ $false))) != sK0) | (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | ((~ (sK0 @ Y0)) & $false))))),
% 1.68/1.42 inference(boolean_simplification,[status(thm)],[f10])).
% 1.68/1.42 thf(f10,plain,(
% 1.68/1.42 (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | $false))) | (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | ((~ (sK0 @ Y0)) & $false))))),
% 1.68/1.42 inference(boolean_simplification,[status(thm)],[f9])).
% 1.68/1.42 thf(f9,plain,(
% 1.68/1.42 (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | ($false & (~ (sK0 @ Y0)))))) | (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | ((~ (sK0 @ Y0)) & $false))))),
% 1.68/1.42 inference(cnf_transformation,[status(thm)],[f8])).
% 1.68/1.42 thf(f8,plain,(
% 1.68/1.42 (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | ((~ (sK0 @ Y0)) & $false)))) | (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | ($false & (~ (sK0 @ Y0))))))),
% 1.68/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.68/1.42 thf(f7,plain,(
% 1.68/1.42 ? [X0 : a > $o] : (((^[Y0 : a]: (((X0 @ Y0) & (~ $false)) | ((~ (X0 @ Y0)) & $false))) != X0) | ((^[Y0 : a]: (((X0 @ Y0) & (~ $false)) | ($false & (~ (X0 @ Y0))))) != X0)) => ((sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | ((~ (sK0 @ Y0)) & $false)))) | (sK0 != (^[Y0 : a]: (((sK0 @ Y0) & (~ $false)) | ($false & (~ (sK0 @ Y0)))))))),
% 1.68/1.42 introduced(definition,[],[choice_axiom])).
% 1.68/1.42 thf(f6,plain,(
% 1.68/1.42 ? [X0 : a > $o] : (((^[Y0 : a]: (((X0 @ Y0) & (~ $false)) | ((~ (X0 @ Y0)) & $false))) != X0) | ((^[Y0 : a]: (((X0 @ Y0) & (~ $false)) | ($false & (~ (X0 @ Y0))))) != X0))),
% 1.68/1.42 inference(ennf_transformation,[status(thm)],[f5])).
% 1.68/1.42 thf(f5,plain,(
% 1.68/1.42 ~! [X0 : a > $o] : (((^[Y0 : a]: (((X0 @ Y0) & (~ $false)) | ($false & (~ (X0 @ Y0))))) = X0) & ((^[Y0 : a]: (((X0 @ Y0) & (~ $false)) | ((~ (X0 @ Y0)) & $false))) = X0))),
% 1.68/1.42 inference(fool_elimination,[status(thm)],[f4])).
% 1.68/1.42 thf(f4,plain,(
% 1.68/1.42 ~! [X0 : a > $o] : ((X0 = (^[X1 : a] : (($false & ~(X0 @ X1)) | (~$false & (X0 @ X1))))) & (X0 = (^[X2 : a] : ((~(X0 @ X2) & $false) | (~$false & (X0 @ X2))))))),
% 1.68/1.42 inference(rectify,[status(thm)],[f2])).
% 1.68/1.42 thf(f2,negated_conjecture,(
% 1.68/1.42 ~! [X0 : a > $o] : ((X0 = (^[X1 : a] : (($false & ~(X0 @ X1)) | (~$false & (X0 @ X1))))) & (X0 = (^[X1 : a] : ((~(X0 @ X1) & $false) | (~$false & (X0 @ X1))))))),
% 1.68/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.68/1.42 thf(f1,conjecture,(
% 1.68/1.42 ! [X0 : a > $o] : ((X0 = (^[X1 : a] : (($false & ~(X0 @ X1)) | (~$false & (X0 @ X1))))) & (X0 = (^[X1 : a] : ((~(X0 @ X1) & $false) | (~$false & (X0 @ X1))))))),
% 1.68/1.42 file('/export/starexec/sandbox/tmp/tmp.5jw000Avzs/DTF2THF_15610.p',cBOOL_PROP_92_pme)).
% 1.68/1.42 % SZS output end Proof for DTF2THF_15610
% 1.68/1.42 % (15726)------------------------------
% 1.68/1.42 % (15726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.42 % (15726)Termination reason: Refutation
% 1.68/1.42
% 1.68/1.42 % (15726)Memory used [KB]: 5373
% 1.68/1.42 % (15726)Time elapsed: 0.003 s
% 1.68/1.42 % (15726)Instructions burned: 1 (million)
% 1.68/1.42 % (15726)------------------------------
% 1.68/1.42 % (15726)------------------------------
% 1.68/1.42 % (15720)Success in time 0.018 s
%------------------------------------------------------------------------------