%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET594^5 : 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 : n001.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 09:31:50 AM UTC 2026
% Result : Theorem 1.49s 1.24s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 174 ( 61 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 228 ( 21 ~; 29 |; 50 &; 116 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 52 ( 12 ^; 26 !; 14 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_10,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(func_def_13,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f66,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
$false = $true,
inference(superposition,[status(thm)],[f59,f12]) ).
thf(f12,plain,
( ( sK1 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
= sK1 )
& ( $true
!= ( sK0 @ sK3 ) )
& ( ( sK2 @ sK3 )
!= $true )
& ( ( sK1 @ sK3 )
= $true ) ),
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] :
( ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= X1 )
& ? [X3: a] :
( ( ( X0 @ X3 )
!= $true )
& ( ( X2 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) ) )
=> ( ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
= sK1 )
& ? [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
& ( ( sK2 @ X3 )
!= $true )
& ( $true
= ( sK1 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
& ( ( sK2 @ X3 )
!= $true )
& ( $true
= ( sK1 @ X3 ) ) )
=> ( ( $true
!= ( sK0 @ sK3 ) )
& ( ( sK2 @ sK3 )
!= $true )
& ( ( sK1 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= X1 )
& ? [X3: a] :
( ( ( X0 @ X3 )
!= $true )
& ( ( X2 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( X0 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= X1 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= X1 )
=> ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= X1 )
=> ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
=> ( ( ( X0 @ X4 )
= $true )
| ( ( X2 @ X4 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( X1
= ( ^ [X3: a] :
( ( ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ( X2 @ X3 )
& ( X1 @ X3 ) ) ) ) )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( ( X0 @ X4 )
| ( X2 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( X0
= ( ^ [X3: a] :
( ( ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X2 @ X3 )
& ( X0 @ X3 ) ) ) ) )
=> ! [X4: a] :
( ( X0 @ X4 )
=> ( ( X1 @ X4 )
| ( X2 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( X0
= ( ^ [X3: a] :
( ( ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X2 @ X3 )
& ( X0 @ X3 ) ) ) ) )
=> ! [X4: a] :
( ( X0 @ X4 )
=> ( ( X1 @ X4 )
| ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9kLk2pTm67/DTF2THF_28065.p',cBOOL_PROP_53_pme) ).
thf(f59,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(subsumption_resolution,[status(thm)],[f56,f14]) ).
thf(f14,plain,
( $true
!= ( sK0 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f56,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f13,f26]) ).
thf(f26,plain,
! [X1: a] :
( ( ( sK2 @ X1 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: a] :
( ( ( sK0 @ X1 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ X1 )
& ( sK2 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ X1 )
& ( sK0 @ X1 ) )
= $true )
| ( ( ( sK1 @ X1 )
& ( sK2 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ( ( sK1 @ X1 )
& ( sK2 @ X1 ) )
| ( ( sK1 @ X1 )
& ( sK0 @ X1 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: a] :
( ( sK1 @ X1 )
= ( ( ( sK1 @ X1 )
& ( sK2 @ X1 ) )
| ( ( sK1 @ X1 )
& ( sK0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: a] :
( ( sK1 @ X1 )
= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
= sK1 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f13,plain,
( ( sK2 @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET594^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n001.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:00:35 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : SET594^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.44 % Domain : Set Theory
% 0.19/0.44 % Problem : TPS problem BOOL-PROP-53
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English : Trybulec's 53rd Boolean property of sets
% 0.19/0.44
% 0.19/0.44 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.44 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Bro09]
% 0.19/0.44 % Names : tps_0247 [Bro09]
% 0.19/0.44 % : BOOL-PROP-53 [TPS]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % 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 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.19/0.44 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.44 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.44 % Number of connectives : 13 ( 0 ~; 2 |; 2 &; 7 @)
% 0.19/0.44 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 9 ( 9 avg)
% 0.19/0.44 % Number of types : 2 ( 1 usr)
% 0.19/0.44 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.44 % Number of variables : 5 ( 1 ^; 4 !; 0 ?; 5 :)
% 0.19/0.44 % SPC : TH0_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.44 % : Polymorphic definitions expanded.
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(a_type,type,
% 0.19/0.44 a: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(cBOOL_PROP_53_pme,conjecture,
% 0.19/0.44 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.19/0.44 ( ( ( ^ [Xz: a] :
% 0.19/0.44 ( ( ( X @ Xz )
% 0.19/0.44 & ( Y @ Xz ) )
% 0.19/0.44 | ( ( X @ Xz )
% 0.19/0.44 & ( Z @ Xz ) ) ) )
% 0.19/0.44 = X )
% 0.19/0.44 => ! [Xx: a] :
% 0.19/0.44 ( ( X @ Xx )
% 0.19/0.44 => ( ( Y @ Xx )
% 0.19/0.44 | ( Z @ Xx ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 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 12:00:36 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.9kLk2pTm67/DTF2DTF28065.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_53_pme,conjecture,
% 1.49/1.22 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.49/1.22 ( ( ( ^ [Xz: a] :
% 1.49/1.22 ( ( ( X @ Xz )
% 1.49/1.22 & ( Y @ Xz ) )
% 1.49/1.22 | ( ( X @ Xz )
% 1.49/1.22 & ( Z @ Xz ) ) ) )
% 1.49/1.22 = X )
% 1.49/1.22 => ! [Xx: a] :
% 1.49/1.22 ( ( X @ Xx )
% 1.49/1.22 => ( ( Y @ Xx )
% 1.49/1.22 | ( Z @ Xx ) ) ) ) ).
% 1.49/1.22 ------------------------
% 1.49/1.24 % (28361)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_28065 for (2999ds/275Mi)
% 1.49/1.24 % (28359)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28065 for (2999ds/2Mi)
% 1.49/1.24 % (28359)Instruction limit reached!
% 1.49/1.24 % (28359)------------------------------
% 1.49/1.24 % (28359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.24 % (28359)Termination reason: Unknown
% 1.49/1.24 % (28359)Termination phase: Saturation
% 1.49/1.24
% 1.49/1.24 % (28359)Memory used [KB]: 5500
% 1.49/1.24 % (28359)Time elapsed: 0.002 s
% 1.49/1.24 % (28359)Instructions burned: 2 (million)
% 1.49/1.24 % (28359)------------------------------
% 1.49/1.24 % (28359)------------------------------
% 1.49/1.24 % (28361)First to succeed.
% 1.49/1.24 % (28361)Refutation found. Thanks to Tanya!
% 1.49/1.24 % SZS status Theorem for DTF2THF_28065
% 1.49/1.24 % SZS output start Proof for DTF2THF_28065
% 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_8, type, sK0: a > $o).
% 1.49/1.24 thf(func_def_9, type, sK1: a > $o).
% 1.49/1.24 thf(func_def_10, type, sK2: a > $o).
% 1.49/1.24 thf(func_def_11, type, sK3: a).
% 1.49/1.24 thf(func_def_13, type, ph5: !>[X0: $tType]:(X0)).
% 1.49/1.24 thf(f66,plain,(
% 1.49/1.24 $false),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.49/1.24 thf(f60,plain,(
% 1.49/1.24 ($false = $true)),
% 1.49/1.24 inference(superposition,[status(thm)],[f59,f12])).
% 1.49/1.24 thf(f12,plain,(
% 1.49/1.24 ((sK1 @ sK3) = $true)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.24 thf(f11,plain,(
% 1.49/1.24 ((^[Y0 : a]: (((sK1 @ Y0) & (sK2 @ Y0)) | ((sK1 @ Y0) & (sK0 @ Y0)))) = sK1) & (($true != (sK0 @ sK3)) & ((sK2 @ sK3) != $true) & ((sK1 @ sK3) = $true))),
% 1.49/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.49/1.24 thf(f9,plain,(
% 1.49/1.24 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((^[Y0 : a]: (((X1 @ Y0) & (X2 @ Y0)) | ((X1 @ Y0) & (X0 @ Y0)))) = X1) & ? [X3 : a] : (((X0 @ X3) != $true) & ((X2 @ X3) != $true) & ((X1 @ X3) = $true))) => (((^[Y0 : a]: (((sK1 @ Y0) & (sK2 @ Y0)) | ((sK1 @ Y0) & (sK0 @ Y0)))) = sK1) & ? [X3 : a] : (($true != (sK0 @ X3)) & ((sK2 @ X3) != $true) & ($true = (sK1 @ X3))))),
% 1.49/1.24 introduced(definition,[],[choice_axiom])).
% 1.49/1.24 thf(f10,plain,(
% 1.49/1.24 ? [X3 : a] : (($true != (sK0 @ X3)) & ((sK2 @ X3) != $true) & ($true = (sK1 @ X3))) => (($true != (sK0 @ sK3)) & ((sK2 @ sK3) != $true) & ((sK1 @ sK3) = $true))),
% 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] : (((^[Y0 : a]: (((X1 @ Y0) & (X2 @ Y0)) | ((X1 @ Y0) & (X0 @ Y0)))) = X1) & ? [X3 : a] : (((X0 @ X3) != $true) & ((X2 @ X3) != $true) & ((X1 @ X3) = $true)))),
% 1.49/1.24 inference(flattening,[status(thm)],[f7])).
% 1.49/1.24 thf(f7,plain,(
% 1.49/1.24 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (? [X3 : a] : ((((X2 @ X3) != $true) & ((X0 @ X3) != $true)) & ((X1 @ X3) = $true)) & ((^[Y0 : a]: (((X1 @ Y0) & (X2 @ Y0)) | ((X1 @ Y0) & (X0 @ Y0)))) = X1))),
% 1.49/1.24 inference(ennf_transformation,[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]: (((X1 @ Y0) & (X2 @ Y0)) | ((X1 @ Y0) & (X0 @ Y0)))) = X1) => ! [X3 : a] : (((X1 @ X3) = $true) => (((X2 @ X3) = $true) | ((X0 @ X3) = $true))))),
% 1.49/1.24 inference(rectify,[status(thm)],[f5])).
% 1.49/1.24 thf(f5,plain,(
% 1.49/1.24 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((^[Y0 : a]: (((X1 @ Y0) & (X2 @ Y0)) | ((X1 @ Y0) & (X0 @ Y0)))) = X1) => ! [X4 : a] : (((X1 @ X4) = $true) => (((X0 @ X4) = $true) | ((X2 @ X4) = $true))))),
% 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] : ((X1 = (^[X3 : a] : (((X0 @ X3) & (X1 @ X3)) | ((X2 @ X3) & (X1 @ X3))))) => ! [X4 : a] : ((X1 @ X4) => ((X0 @ X4) | (X2 @ X4))))),
% 1.49/1.24 inference(rectify,[status(thm)],[f2])).
% 1.49/1.24 thf(f2,negated_conjecture,(
% 1.49/1.24 ~! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((X0 = (^[X3 : a] : (((X1 @ X3) & (X0 @ X3)) | ((X2 @ X3) & (X0 @ X3))))) => ! [X4 : a] : ((X0 @ X4) => ((X1 @ X4) | (X2 @ X4))))),
% 1.49/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.24 thf(f1,conjecture,(
% 1.49/1.24 ! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((X0 = (^[X3 : a] : (((X1 @ X3) & (X0 @ X3)) | ((X2 @ X3) & (X0 @ X3))))) => ! [X4 : a] : ((X0 @ X4) => ((X1 @ X4) | (X2 @ X4))))),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.9kLk2pTm67/DTF2THF_28065.p',cBOOL_PROP_53_pme)).
% 1.49/1.24 thf(f59,plain,(
% 1.49/1.24 ($false = (sK1 @ sK3))),
% 1.49/1.24 inference(subsumption_resolution,[status(thm)],[f56,f14])).
% 1.49/1.24 thf(f14,plain,(
% 1.49/1.24 ($true != (sK0 @ sK3))),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.24 thf(f56,plain,(
% 1.49/1.24 ($false = (sK1 @ sK3)) | ($true = (sK0 @ sK3))),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.49/1.24 thf(f52,plain,(
% 1.49/1.24 ($true = (sK0 @ sK3)) | ($false = (sK1 @ sK3)) | ($true != $true)),
% 1.49/1.24 inference(superposition,[status(thm)],[f13,f26])).
% 1.49/1.24 thf(f26,plain,(
% 1.49/1.24 ( ! [X1 : a] : (((sK2 @ X1) = $true) | ((sK1 @ X1) = $false) | ((sK0 @ X1) = $true)) )),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.49/1.24 thf(f21,plain,(
% 1.49/1.24 ( ! [X1 : a] : (((sK0 @ X1) = $true) | ((sK1 @ X1) = $false) | (((sK1 @ X1) & (sK2 @ X1)) = $true)) )),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.49/1.24 thf(f20,plain,(
% 1.49/1.24 ( ! [X1 : a] : (((sK1 @ X1) = $false) | (((sK1 @ X1) & (sK0 @ X1)) = $true) | (((sK1 @ X1) & (sK2 @ X1)) = $true)) )),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.49/1.24 thf(f19,plain,(
% 1.49/1.24 ( ! [X1 : a] : (((sK1 @ X1) = $false) | ((((sK1 @ X1) & (sK2 @ X1)) | ((sK1 @ X1) & (sK0 @ X1))) = $true)) )),
% 1.49/1.24 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.49/1.24 thf(f17,plain,(
% 1.49/1.24 ( ! [X1 : a] : (((sK1 @ X1) = (((sK1 @ X1) & (sK2 @ X1)) | ((sK1 @ X1) & (sK0 @ X1))))) )),
% 1.49/1.24 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.49/1.24 thf(f16,plain,(
% 1.49/1.24 ( ! [X1 : a] : (((sK1 @ X1) = ((^[Y0 : a]: (((sK1 @ Y0) & (sK2 @ Y0)) | ((sK1 @ Y0) & (sK0 @ Y0)))) @ X1))) )),
% 1.49/1.24 inference(argument_congruence,[status(thm)],[f15])).
% 1.49/1.24 thf(f15,plain,(
% 1.49/1.24 ((^[Y0 : a]: (((sK1 @ Y0) & (sK2 @ Y0)) | ((sK1 @ Y0) & (sK0 @ Y0)))) = sK1)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.24 thf(f13,plain,(
% 1.49/1.24 ((sK2 @ sK3) != $true)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.24 % SZS output end Proof for DTF2THF_28065
% 1.49/1.24 % (28361)------------------------------
% 1.49/1.24 % (28361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.24 % (28361)Termination reason: Refutation
% 1.49/1.24
% 1.49/1.24 % (28361)Memory used [KB]: 5500
% 1.49/1.24 % (28361)Time elapsed: 0.003 s
% 1.49/1.24 % (28361)Instructions burned: 4 (million)
% 1.49/1.24 % (28361)------------------------------
% 1.49/1.24 % (28361)------------------------------
% 1.49/1.24 % (28355)Success in time 0.013 s
%------------------------------------------------------------------------------