%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET632^5 : 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 : n014.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 09:31:59 AM UTC 2026
% Result : Theorem 1.49s 1.24s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 203 ( 80 equ; 0 cnn)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 207 ( 51 ~; 30 |; 30 &; 83 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 73 ( 12 ^; 45 !; 16 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_7,type,
sK2: a > $o ).
thf(func_def_9,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
sK5: a ).
thf(f43,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f41,f35]) ).
thf(f35,plain,
( $true
!= ( sK0 @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f11,f31]) ).
thf(f31,plain,
( $true
= ( sK2 @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( $false != $false ) ),
inference(superposition,[status(thm)],[f16,f21]) ).
thf(f21,plain,
! [X4: a] :
( ( ( sK1 @ X4 )
= $false )
| ( $true
= ( sK2 @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
! [X4: a] :
( ( $true
= ( sK2 @ X4 ) )
| ( ( sK1 @ X4 )
= $false )
| ( $true != $true ) ),
inference(fool_paramodulation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X4: a] :
( ( $true
!= ( sK1 @ X4 ) )
| ( $true
= ( sK2 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X3: a] :
( ( $true
= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
!= $true ) )
& ( sK1
!= ( ^ [Y0: a] : $false ) )
& ! [X4: a] :
( ( $true
!= ( sK1 @ X4 ) )
| ( $true
= ( sK2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] : $false )
!= X1 )
& ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( $true
= ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
!= ( X0 @ X5 ) ) ) )
=> ( ! [X3: a] :
( ( $true
= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
!= $true ) )
& ( sK1
!= ( ^ [Y0: a] : $false ) )
& ! [X4: a] :
( ( $true
!= ( sK1 @ X4 ) )
| ( $true
= ( sK2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] : $false )
!= X1 )
& ! [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
| ( $true
= ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( $true
!= ( X0 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
| ( $true
!= ( X2 @ X5 ) ) )
& ( ( ^ [Y0: a] : $false )
!= X2 )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true
!= ( X1 @ X4 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X2 )
& ! [X3: a] :
( ( ( X2 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true
!= ( X1 @ X4 ) ) )
& ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
| ( $true
!= ( X2 @ X5 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
& ~ ? [X4: a] :
( ( $true
= ( X1 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) )
& ! [X5: a] :
( ( $true
= ( X2 @ X5 ) )
=> ( $true
= ( X1 @ X5 ) ) ) )
=> ( ( ^ [Y0: a] : $false )
= X2 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X0 @ X3 ) )
& ~ ? [X4: a] :
( ( X1 @ X4 )
& ( X0 @ X4 ) )
& ! [X5: a] :
( ( X2 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( ^ [X6: a] : $false )
= X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ~ ? [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ( ^ [X3: a] : $false )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ~ ? [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ( ^ [X3: a] : $false )
= X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.nzpcao46vB/DTF2THF_4095.p',cBOOL_PROP_114_pme) ).
thf(f16,plain,
( ( sK1 @ sK5 )
!= $false ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK1 @ sK5 )
!= ( ^ [Y0: a] : $false
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f13]) ).
thf(f13,plain,
( sK1
!= ( ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f11,plain,
! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f41,plain,
( $true
= ( sK0 @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false != $false )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f16,f23]) ).
thf(f23,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
= $false )
| ( $true
= ( sK0 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
! [X3: a] :
( ( $true != $true )
| ( $true
= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( $true
= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET632^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:01:12 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SET632^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : TPS problem BOOL-PROP-114
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : Trybulec's 114th Boolean property of sets
% 0.18/0.45
% 0.18/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.18/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0315 [Bro09]
% 0.18/0.45 % : BOOL-PROP-114 [TPS]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 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, 0.00 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
% 0.18/0.45 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.18/0.45 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 1 ( 2 avg)
% 0.18/0.45 % Number of connectives : 13 ( 1 ~; 0 |; 3 &; 6 @)
% 0.18/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.18/0.45 % Number of types : 2 ( 1 usr)
% 0.18/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 7 ( 1 ^; 5 !; 1 ?; 7 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 % : Polymorphic definitions expanded.
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(a_type,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(cBOOL_PROP_114_pme,conjecture,
% 0.18/0.45 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.18/0.45 ( ( ! [Xx: a] :
% 0.18/0.45 ( ( X @ Xx )
% 0.18/0.45 => ( Y @ Xx ) )
% 0.18/0.45 & ! [Xx: a] :
% 0.18/0.45 ( ( X @ Xx )
% 0.18/0.45 => ( Z @ Xx ) )
% 0.18/0.45 & ~ ? [Xx: a] :
% 0.18/0.45 ( ( Y @ Xx )
% 0.18/0.45 & ( Z @ Xx ) ) )
% 0.18/0.45 => ( X
% 0.18/0.45 = ( ^ [Xx: a] : $false ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.49/1.21 ---- Embedded in THF ---
% 1.49/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.21 %%% Generated on Tue Feb 24 12:01:13 EST 2026
% 1.49/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.21 %%% Logic specification used:
% 1.49/1.21 %%% thf(spec, logic, $$dhol).
% 1.49/1.21
% 1.49/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.nzpcao46vB/DTF2DTF4095.p
% See solution above
% 1.49/1.21 ------------------------
% 1.49/1.22 ---- Cleaned THF ---
% 1.49/1.22 thf(a_type,type,
% 1.49/1.22 a: $tType ).
% 1.49/1.22
% 1.49/1.22 thf(cBOOL_PROP_114_pme,conjecture,
% 1.49/1.22 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.49/1.22 ( ( ! [Xx: a] :
% 1.49/1.22 ( ( X @ Xx )
% 1.49/1.22 => ( Y @ Xx ) )
% 1.49/1.22 & ! [Xx: a] :
% 1.49/1.22 ( ( X @ Xx )
% 1.49/1.22 => ( Z @ Xx ) )
% 1.49/1.22 & ~ ? [Xx: a] :
% 1.49/1.22 ( ( Y @ Xx )
% 1.49/1.22 & ( Z @ Xx ) ) )
% 1.49/1.22 => ( X
% 1.49/1.22 = ( ^ [Xx: a] : $false ) ) ) ).
% 1.49/1.22 ------------------------
% 1.49/1.23 % (4212)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_4095 for (2999ds/4Mi)
% 1.49/1.23 % (4211)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4095 for (2999ds/183Mi)
% 1.49/1.23 % (4212)First to succeed.
% 1.49/1.23 % (4211)Refutation not found, incomplete strategy
% 1.49/1.23 % (4211)------------------------------
% 1.49/1.23 % (4211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.23 % (4211)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.23
% 1.49/1.23
% 1.49/1.23 % (4211)Memory used [KB]: 5500
% 1.49/1.23 % (4211)Time elapsed: 0.002 s
% 1.49/1.23 % (4211)Instructions burned: 2 (million)
% 1.49/1.23 % (4211)------------------------------
% 1.49/1.23 % (4211)------------------------------
% 1.49/1.24 % (4212)Refutation found. Thanks to Tanya!
% 1.49/1.24 % SZS status Theorem for DTF2THF_4095
% 1.49/1.24 % SZS output start Proof for DTF2THF_4095
% 1.49/1.24 thf(type_def_5, type, a: $tType).
% 1.49/1.24 thf(func_def_0, type, a: $tType).
% 1.49/1.24 thf(func_def_5, type, sK0: a > $o).
% 1.49/1.24 thf(func_def_6, type, sK1: a > $o).
% 1.49/1.24 thf(func_def_7, type, sK2: a > $o).
% 1.49/1.24 thf(func_def_9, type, ph4: !>[X0: $tType]:(X0)).
% 1.49/1.24 thf(func_def_10, type, sK5: a).
% 1.49/1.24 thf(f43,plain,(
% 1.49/1.24 $false),
% 1.49/1.24 inference(subsumption_resolution,[status(thm)],[f41,f35])).
% 1.49/1.24 thf(f35,plain,(
% 1.49/1.24 ($true != (sK0 @ sK5))),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.49/1.24 thf(f34,plain,(
% 1.49/1.24 ($true != $true) | ($true != (sK0 @ sK5))),
% 1.49/1.24 inference(superposition,[status(thm)],[f11,f31])).
% 1.49/1.24 thf(f31,plain,(
% 1.49/1.24 ($true = (sK2 @ sK5))),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.49/1.24 thf(f27,plain,(
% 1.49/1.24 ($true = (sK2 @ sK5)) | ($false != $false)),
% 1.49/1.24 inference(superposition,[status(thm)],[f16,f21])).
% 1.49/1.24 thf(f21,plain,(
% 1.49/1.24 ( ! [X4 : a] : (((sK1 @ X4) = $false) | ($true = (sK2 @ X4))) )),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.49/1.24 thf(f20,plain,(
% 1.49/1.24 ( ! [X4 : a] : (($true = (sK2 @ X4)) | ((sK1 @ X4) = $false) | ($true != $true)) )),
% 1.49/1.24 inference(fool_paramodulation,[status(thm)],[f12])).
% 1.49/1.24 thf(f12,plain,(
% 1.49/1.24 ( ! [X4 : a] : (($true != (sK1 @ X4)) | ($true = (sK2 @ X4))) )),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f10])).
% 1.49/1.24 thf(f10,plain,(
% 1.49/1.24 ! [X3 : a] : (($true = (sK0 @ X3)) | ((sK1 @ X3) != $true)) & (sK1 != (^[Y0 : a]: ($false))) & ! [X4 : a] : (($true != (sK1 @ X4)) | ($true = (sK2 @ X4))) & ! [X5 : a] : (($true != (sK2 @ X5)) | ($true != (sK0 @ X5)))),
% 1.49/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.49/1.24 thf(f9,plain,(
% 1.49/1.24 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) = $true) | ((X1 @ X3) != $true)) & ((^[Y0 : a]: ($false)) != X1) & ! [X4 : a] : (($true != (X1 @ X4)) | ($true = (X2 @ X4))) & ! [X5 : a] : (($true != (X2 @ X5)) | ($true != (X0 @ X5)))) => (! [X3 : a] : (($true = (sK0 @ X3)) | ((sK1 @ X3) != $true)) & (sK1 != (^[Y0 : a]: ($false))) & ! [X4 : a] : (($true != (sK1 @ X4)) | ($true = (sK2 @ X4))) & ! [X5 : a] : (($true != (sK2 @ X5)) | ($true != (sK0 @ X5))))),
% 1.49/1.24 introduced(definition,[],[choice_axiom])).
% 1.49/1.24 thf(f8,plain,(
% 1.49/1.24 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) = $true) | ((X1 @ X3) != $true)) & ((^[Y0 : a]: ($false)) != X1) & ! [X4 : a] : (($true != (X1 @ X4)) | ($true = (X2 @ X4))) & ! [X5 : a] : (($true != (X2 @ X5)) | ($true != (X0 @ X5))))),
% 1.49/1.24 inference(rectify,[status(thm)],[f7])).
% 1.49/1.24 thf(f7,plain,(
% 1.49/1.24 ? [X1 : a > $o,X2 : a > $o,X0 : a > $o] : (! [X5 : a] : (($true = (X1 @ X5)) | ($true != (X2 @ X5))) & ((^[Y0 : a]: ($false)) != X2) & ! [X3 : a] : (((X2 @ X3) != $true) | ((X0 @ X3) = $true)) & ! [X4 : a] : (($true != (X0 @ X4)) | ($true != (X1 @ X4))))),
% 1.49/1.24 inference(flattening,[status(thm)],[f6])).
% 1.49/1.24 thf(f6,plain,(
% 1.49/1.24 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((^[Y0 : a]: ($false)) != X2) & (! [X3 : a] : (((X2 @ X3) != $true) | ((X0 @ X3) = $true)) & ! [X4 : a] : (($true != (X0 @ X4)) | ($true != (X1 @ X4))) & ! [X5 : a] : (($true = (X1 @ X5)) | ($true != (X2 @ X5)))))),
% 1.49/1.24 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.24 thf(f5,plain,(
% 1.49/1.24 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : (((X2 @ X3) = $true) => ((X0 @ X3) = $true)) & ~? [X4 : a] : (($true = (X1 @ X4)) & ($true = (X0 @ X4))) & ! [X5 : a] : (($true = (X2 @ X5)) => ($true = (X1 @ X5)))) => ((^[Y0 : a]: ($false)) = X2))),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.24 thf(f4,plain,(
% 1.49/1.24 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X2 @ X3) => (X0 @ X3)) & ~? [X4 : a] : ((X1 @ X4) & (X0 @ X4)) & ! [X5 : a] : ((X2 @ X5) => (X1 @ X5))) => ((^[X6 : a] : ($false)) = X2))),
% 1.49/1.24 inference(rectify,[status(thm)],[f2])).
% 1.49/1.24 thf(f2,negated_conjecture,(
% 1.49/1.24 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) & ~? [X3 : a] : ((X2 @ X3) & (X1 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => ((^[X3 : a] : ($false)) = X0))),
% 1.49/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.24 thf(f1,conjecture,(
% 1.49/1.24 ! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) & ~? [X3 : a] : ((X2 @ X3) & (X1 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => ((^[X3 : a] : ($false)) = X0))),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.nzpcao46vB/DTF2THF_4095.p',cBOOL_PROP_114_pme)).
% 1.49/1.24 thf(f16,plain,(
% 1.49/1.24 ((sK1 @ sK5) != $false)),
% 1.49/1.24 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.49/1.24 thf(f15,plain,(
% 1.49/1.24 ((sK1 @ sK5) != ((^[Y0 : a]: ($false)) @ sK5))),
% 1.49/1.24 inference(negative_extensionality,[status(thm)],[f13])).
% 1.49/1.24 thf(f13,plain,(
% 1.49/1.24 (sK1 != (^[Y0 : a]: ($false)))),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f10])).
% 1.49/1.24 thf(f11,plain,(
% 1.49/1.24 ( ! [X5 : a] : (($true != (sK2 @ X5)) | ($true != (sK0 @ X5))) )),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f10])).
% 1.49/1.24 thf(f41,plain,(
% 1.49/1.24 ($true = (sK0 @ sK5))),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.49/1.24 thf(f37,plain,(
% 1.49/1.24 ($false != $false) | ($true = (sK0 @ sK5))),
% 1.49/1.24 inference(superposition,[status(thm)],[f16,f23])).
% 1.49/1.24 thf(f23,plain,(
% 1.49/1.24 ( ! [X3 : a] : (((sK1 @ X3) = $false) | ($true = (sK0 @ X3))) )),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.49/1.24 thf(f22,plain,(
% 1.49/1.24 ( ! [X3 : a] : (($true != $true) | ($true = (sK0 @ X3)) | ((sK1 @ X3) = $false)) )),
% 1.49/1.24 inference(fool_paramodulation,[status(thm)],[f14])).
% 1.49/1.24 thf(f14,plain,(
% 1.49/1.24 ( ! [X3 : a] : (((sK1 @ X3) != $true) | ($true = (sK0 @ X3))) )),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f10])).
% 1.49/1.24 % SZS output end Proof for DTF2THF_4095
% 1.49/1.24 % (4212)------------------------------
% 1.49/1.24 % (4212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.24 % (4212)Termination reason: Refutation
% 1.49/1.24
% 1.49/1.24 % (4212)Memory used [KB]: 5500
% 1.49/1.24 % (4212)Time elapsed: 0.003 s
% 1.49/1.24 % (4212)Instructions burned: 3 (million)
% 1.49/1.24 % (4212)------------------------------
% 1.49/1.24 % (4212)------------------------------
% 1.49/1.24 % (4210)Success in time 0.003 s
%------------------------------------------------------------------------------