%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET638^5 : 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 09:32:00 AM UTC 2026
% Result : Theorem 1.51s 1.39s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 180 ( 69 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 191 ( 21 ~; 22 |; 35 &; 96 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 24 ^; 34 !; 14 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a > $o ).
thf(func_def_10,type,
sK3: a ).
thf(func_def_12,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f28,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
$true = $false,
inference(superposition,[status(thm)],[f18,f25]) ).
thf(f25,plain,
( ( sK0 @ sK3 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true = $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(superposition,[status(thm)],[f21,f13]) ).
thf(f13,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
& ! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK2 @ X3 ) )
| ( $true
= ( sK0 @ X3 ) ) )
& ( $true
= ( sK2 @ sK3 ) )
& ( $true
!= ( sK1 @ sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( $true
!= ( X1 @ X4 ) ) ) )
=> ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
& ! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK2 @ X3 ) )
| ( $true
= ( sK0 @ X3 ) ) )
& ? [X4: a] :
( ( $true
= ( sK2 @ X4 ) )
& ( $true
!= ( sK1 @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X4: a] :
( ( $true
= ( sK2 @ X4 ) )
& ( $true
!= ( sK1 @ X4 ) ) )
=> ( ( $true
= ( sK2 @ sK3 ) )
& ( $true
!= ( sK1 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( $true
!= ( X1 @ X4 ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X4: a] :
( ( $true
= ( X2 @ X4 ) )
& ( $true
!= ( X1 @ X4 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) ) )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) ) )
=> ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
=> ( $true
= ( X1 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
& ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
=> ( ( $true
= ( X1 @ X5 ) )
| ( $true
= ( X0 @ X5 ) ) ) ) )
=> ! [X6: a] :
( ( $true
= ( X2 @ X6 ) )
=> ( $true
= ( X1 @ X6 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [X3: a] : $false )
= ( ^ [X4: a] :
( ( X0 @ X4 )
& ( X2 @ X4 ) ) ) )
& ! [X5: a] :
( ( X2 @ X5 )
=> ( ( X1 @ X5 )
| ( X0 @ X5 ) ) ) )
=> ! [X6: a] :
( ( X2 @ X6 )
=> ( X1 @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ( ( ^ [X3: a] : $false )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X0 @ X3 ) ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ( ( ^ [X3: a] : $false )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X0 @ X3 ) ) ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.acqLDq9ALQ/DTF2THF_25895.p',cBOOL_PROP_120_pme) ).
thf(f21,plain,
! [X1: a] :
( ( ( sK2 @ X1 )
= $false )
| ( ( sK0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: a] :
( ( ( sK2 @ X1 )
& ( sK0 @ X1 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
@ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f18,plain,
( ( sK0 @ sK3 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f17,f13]) ).
thf(f17,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
!= ( sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f14]) ).
thf(f14,plain,
! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
= ( sK0 @ X3 ) )
| ( $true
!= ( sK2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f12,plain,
( $true
!= ( sK1 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET638^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n031.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:02:18 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SET638^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : TPS problem BOOL-PROP-120
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : Trybulec's 120th Boolean property of sets
% 0.16/0.39
% 0.16/0.39 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.16/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0391 [Bro09]
% 0.16/0.39 % : BOOL-PROP-120 [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 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, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.16/0.39 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 1 ( 2 avg)
% 0.16/0.39 % Number of connectives : 13 ( 0 ~; 1 |; 2 &; 7 @)
% 0.16/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 10 ( 10 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 7 ( 2 ^; 5 !; 0 ?; 7 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 % : Polymorphic definitions expanded.
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(a_type,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(cBOOL_PROP_120_pme,conjecture,
% 0.16/0.39 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.16/0.39 ( ( ! [Xx: a] :
% 0.16/0.39 ( ( X @ Xx )
% 0.16/0.39 => ( ( Y @ Xx )
% 0.16/0.39 | ( Z @ Xx ) ) )
% 0.16/0.39 & ( ( ^ [Xx: a] :
% 0.16/0.39 ( ( X @ Xx )
% 0.16/0.39 & ( Z @ Xx ) ) )
% 0.16/0.39 = ( ^ [Xx: a] : $false ) ) )
% 0.16/0.39 => ! [Xx: a] :
% 0.16/0.39 ( ( X @ Xx )
% 0.16/0.39 => ( Y @ Xx ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.51/1.36 ---- Embedded in THF ---
% 1.51/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.36 %%% Generated on Tue Feb 24 12:02:19 EST 2026
% 1.51/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.36 %%% Logic specification used:
% 1.51/1.36 %%% thf(spec, logic, $$dhol).
% 1.51/1.36
% 1.51/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.acqLDq9ALQ/DTF2DTF25895.p
% See solution above
% 1.51/1.36 ------------------------
% 1.51/1.37 ---- Cleaned THF ---
% 1.51/1.37 thf(a_type,type,
% 1.51/1.37 a: $tType ).
% 1.51/1.37
% 1.51/1.37 thf(cBOOL_PROP_120_pme,conjecture,
% 1.51/1.37 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.51/1.37 ( ( ! [Xx: a] :
% 1.51/1.37 ( ( X @ Xx )
% 1.51/1.37 => ( ( Y @ Xx )
% 1.51/1.37 | ( Z @ Xx ) ) )
% 1.51/1.37 & ( ( ^ [Xx: a] :
% 1.51/1.37 ( ( X @ Xx )
% 1.51/1.37 & ( Z @ Xx ) ) )
% 1.51/1.37 = ( ^ [Xx: a] : $false ) ) )
% 1.51/1.37 => ! [Xx: a] :
% 1.51/1.37 ( ( X @ Xx )
% 1.51/1.37 => ( Y @ Xx ) ) ) ).
% 1.51/1.37 ------------------------
% 1.51/1.39 % (25997)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_25895 for (3000ds/275Mi)
% 1.51/1.39 % (25996)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_25895 for (3000ds/2Mi)
% 1.51/1.39 % (25993)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_25895 for (3000ds/4Mi)
% 1.51/1.39 % (25992)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25895 for (3000ds/183Mi)
% 1.51/1.39 % (25995)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25895 for (3000ds/2Mi)
% 1.51/1.39 % (25994)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_25895 for (3000ds/27Mi)
% 1.51/1.39 % (25998)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25895 for (3000ds/18Mi)
% 1.51/1.39 % (25996)Instruction limit reached!
% 1.51/1.39 % (25996)------------------------------
% 1.51/1.39 % (25996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.39 % (25996)Termination reason: Unknown
% 1.51/1.39 % (25996)Termination phase: shuffling
% 1.51/1.39
% 1.51/1.39 % (25996)Memory used [KB]: 895
% 1.51/1.39 % (25996)Time elapsed: 0.003 s
% 1.51/1.39 % (25996)Instructions burned: 2 (million)
% 1.51/1.39 % (25996)------------------------------
% 1.51/1.39 % (25996)------------------------------
% 1.51/1.39 % (25995)Instruction limit reached!
% 1.51/1.39 % (25995)------------------------------
% 1.51/1.39 % (25995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.39 % (25995)Termination reason: Unknown
% 1.51/1.39 % (25995)Termination phase: Saturation
% 1.51/1.39
% 1.51/1.39 % (25995)Memory used [KB]: 5500
% 1.51/1.39 % (25995)Time elapsed: 0.004 s
% 1.51/1.39 % (25995)Instructions burned: 2 (million)
% 1.51/1.39 % (25995)------------------------------
% 1.51/1.39 % (25995)------------------------------
% 1.51/1.39 % (25997)First to succeed.
% 1.51/1.39 % (25992)Also succeeded, but the first one will report.
% 1.51/1.39 % (25998)Also succeeded, but the first one will report.
% 1.51/1.39 % (25997)Refutation found. Thanks to Tanya!
% 1.51/1.39 % SZS status Theorem for DTF2THF_25895
% 1.51/1.39 % SZS output start Proof for DTF2THF_25895
% 1.51/1.39 thf(type_def_5, type, a: $tType).
% 1.51/1.39 thf(func_def_0, type, a: $tType).
% 1.51/1.39 thf(func_def_7, type, sK0: a > $o).
% 1.51/1.39 thf(func_def_8, type, sK1: a > $o).
% 1.51/1.39 thf(func_def_9, type, sK2: a > $o).
% 1.51/1.39 thf(func_def_10, type, sK3: a).
% 1.51/1.39 thf(func_def_12, type, ph5: !>[X0: $tType]:(X0)).
% 1.51/1.39 thf(f28,plain,(
% 1.51/1.39 $false),
% 1.51/1.39 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.51/1.39 thf(f27,plain,(
% 1.51/1.39 ($true = $false)),
% 1.51/1.39 inference(superposition,[status(thm)],[f18,f25])).
% 1.51/1.39 thf(f25,plain,(
% 1.51/1.39 ((sK0 @ sK3) = $false)),
% 1.51/1.39 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.51/1.39 thf(f22,plain,(
% 1.51/1.39 ($true = $false) | ((sK0 @ sK3) = $false)),
% 1.51/1.39 inference(superposition,[status(thm)],[f21,f13])).
% 1.51/1.39 thf(f13,plain,(
% 1.51/1.39 ($true = (sK2 @ sK3))),
% 1.51/1.39 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.39 thf(f11,plain,(
% 1.51/1.39 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK2 @ Y0) & (sK0 @ Y0)))) & ! [X3 : a] : (($true = (sK1 @ X3)) | ($true != (sK2 @ X3)) | ($true = (sK0 @ X3))) & (($true = (sK2 @ sK3)) & ($true != (sK1 @ sK3)))),
% 1.51/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.51/1.39 thf(f9,plain,(
% 1.51/1.39 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X2 @ Y0) & (X0 @ Y0)))) & ! [X3 : a] : (((X1 @ X3) = $true) | ((X2 @ X3) != $true) | ((X0 @ X3) = $true)) & ? [X4 : a] : (($true = (X2 @ X4)) & ($true != (X1 @ X4)))) => (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK2 @ Y0) & (sK0 @ Y0)))) & ! [X3 : a] : (($true = (sK1 @ X3)) | ($true != (sK2 @ X3)) | ($true = (sK0 @ X3))) & ? [X4 : a] : (($true = (sK2 @ X4)) & ($true != (sK1 @ X4))))),
% 1.51/1.39 introduced(definition,[],[choice_axiom])).
% 1.51/1.39 thf(f10,plain,(
% 1.51/1.39 ? [X4 : a] : (($true = (sK2 @ X4)) & ($true != (sK1 @ X4))) => (($true = (sK2 @ sK3)) & ($true != (sK1 @ sK3)))),
% 1.51/1.39 introduced(definition,[],[choice_axiom])).
% 1.51/1.39 thf(f8,plain,(
% 1.51/1.39 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X2 @ Y0) & (X0 @ Y0)))) & ! [X3 : a] : (((X1 @ X3) = $true) | ((X2 @ X3) != $true) | ((X0 @ X3) = $true)) & ? [X4 : a] : (($true = (X2 @ X4)) & ($true != (X1 @ X4))))),
% 1.51/1.39 inference(flattening,[status(thm)],[f7])).
% 1.51/1.39 thf(f7,plain,(
% 1.51/1.39 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (? [X4 : a] : (($true = (X2 @ X4)) & ($true != (X1 @ X4))) & (! [X3 : a] : ((((X1 @ X3) = $true) | ((X0 @ X3) = $true)) | ((X2 @ X3) != $true)) & ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X2 @ Y0) & (X0 @ Y0))))))),
% 1.51/1.39 inference(ennf_transformation,[status(thm)],[f6])).
% 1.51/1.39 thf(f6,plain,(
% 1.51/1.39 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : (((X2 @ X3) = $true) => (((X1 @ X3) = $true) | ((X0 @ X3) = $true))) & ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X2 @ Y0) & (X0 @ Y0))))) => ! [X4 : a] : (($true = (X2 @ X4)) => ($true = (X1 @ X4))))),
% 1.51/1.39 inference(rectify,[status(thm)],[f5])).
% 1.51/1.39 thf(f5,plain,(
% 1.51/1.39 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X2 @ Y0) & (X0 @ Y0)))) & ! [X5 : a] : (($true = (X2 @ X5)) => (($true = (X1 @ X5)) | ($true = (X0 @ X5))))) => ! [X6 : a] : (($true = (X2 @ X6)) => ($true = (X1 @ X6))))),
% 1.51/1.39 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.39 thf(f4,plain,(
% 1.51/1.39 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((((^[X3 : a] : ($false)) = (^[X4 : a] : ((X0 @ X4) & (X2 @ X4)))) & ! [X5 : a] : ((X2 @ X5) => ((X1 @ X5) | (X0 @ X5)))) => ! [X6 : a] : ((X2 @ X6) => (X1 @ X6)))),
% 1.51/1.39 inference(rectify,[status(thm)],[f2])).
% 1.51/1.39 thf(f2,negated_conjecture,(
% 1.51/1.39 ~! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((((^[X3 : a] : ($false)) = (^[X3 : a] : ((X2 @ X3) & (X0 @ X3)))) & ! [X3 : a] : ((X0 @ X3) => ((X1 @ X3) | (X2 @ X3)))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)))),
% 1.51/1.39 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.39 thf(f1,conjecture,(
% 1.51/1.39 ! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((((^[X3 : a] : ($false)) = (^[X3 : a] : ((X2 @ X3) & (X0 @ X3)))) & ! [X3 : a] : ((X0 @ X3) => ((X1 @ X3) | (X2 @ X3)))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)))),
% 1.51/1.39 file('/export/starexec/sandbox/tmp/tmp.acqLDq9ALQ/DTF2THF_25895.p',cBOOL_PROP_120_pme)).
% 1.51/1.39 thf(f21,plain,(
% 1.51/1.39 ( ! [X1 : a] : (((sK2 @ X1) = $false) | ((sK0 @ X1) = $false)) )),
% 1.51/1.40 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.51/1.40 thf(f20,plain,(
% 1.51/1.40 ( ! [X1 : a] : ((((sK2 @ X1) & (sK0 @ X1)) = $false)) )),
% 1.51/1.40 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.51/1.40 thf(f19,plain,(
% 1.51/1.40 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK2 @ Y0) & (sK0 @ Y0))) @ X1) = ((^[Y0 : a]: ($false)) @ X1))) )),
% 1.51/1.40 inference(argument_congruence,[status(thm)],[f15])).
% 1.51/1.40 thf(f15,plain,(
% 1.51/1.40 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK2 @ Y0) & (sK0 @ Y0))))),
% 1.51/1.40 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.40 thf(f18,plain,(
% 1.51/1.40 ((sK0 @ sK3) = $true)),
% 1.51/1.40 inference(subsumption_resolution,[status(thm)],[f17,f13])).
% 1.51/1.40 thf(f17,plain,(
% 1.51/1.40 ((sK0 @ sK3) = $true) | ($true != (sK2 @ sK3))),
% 1.51/1.40 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.51/1.40 thf(f16,plain,(
% 1.51/1.40 ($true != (sK2 @ sK3)) | ((sK0 @ sK3) = $true) | ($true != $true)),
% 1.51/1.40 inference(superposition,[status(thm)],[f12,f14])).
% 1.51/1.40 thf(f14,plain,(
% 1.51/1.40 ( ! [X3 : a] : (($true = (sK1 @ X3)) | ($true = (sK0 @ X3)) | ($true != (sK2 @ X3))) )),
% 1.51/1.40 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.40 thf(f12,plain,(
% 1.51/1.40 ($true != (sK1 @ sK3))),
% 1.51/1.40 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.40 % SZS output end Proof for DTF2THF_25895
% 1.51/1.40 % (25997)------------------------------
% 1.51/1.40 % (25997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.40 % (25997)Termination reason: Refutation
% 1.51/1.40
% 1.51/1.40 % (25997)Memory used [KB]: 5500
% 1.51/1.40 % (25997)Time elapsed: 0.005 s
% 1.51/1.40 % (25997)Instructions burned: 2 (million)
% 1.51/1.40 % (25997)------------------------------
% 1.51/1.40 % (25997)------------------------------
% 1.51/1.40 % (25991)Success in time 0.019 s
%------------------------------------------------------------------------------