%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET144^5 : 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 : n017.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 09:31:18 AM UTC 2026
% Result : Theorem 1.63s 1.30s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 353 ( 92 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 379 ( 48 ~; 104 |; 38 &; 174 @)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 20 ^; 21 !; 6 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
sK0: a > $o ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: a > $o ).
thf(func_def_13,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK5: a ).
thf(f89,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f47,f54,f68,f69,f73,f79,f84,f88]) ).
thf(f88,plain,
( ~ spl3_1
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl3_1
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f42,f62]) ).
thf(f62,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f60,definition,
( spl3_5
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f42,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl3_1
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f84,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
| ~ spl3_2
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_6 ),
inference(backward_demodulation,[status(thm)],[f46,f66]) ).
thf(f66,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl3_6
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f46,plain,
( ( ( sK2 @ sK5 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl3_2
<=> ( ( sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f79,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f76,f58]) ).
thf(f58,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl3_4
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f76,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true != $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f10,f42]) ).
thf(f10,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X3: a] :
( ( ( sK0 @ X3 )
= $true )
| ( ( sK1 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( sK1 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ) )
=> ( ! [X3: a] :
( ( ( sK0 @ X3 )
= $true )
| ( ( sK1 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( sK1 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) )
=> ( ( ^ [X4: a] :
( ( X1 @ X4 )
| ( ( X2 @ X4 )
& ( X0 @ X4 ) ) ) )
= ( ^ [X5: a] :
( ( ( X2 @ X5 )
| ( X1 @ X5 ) )
& ( X0 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
=> ( ( ^ [X4: a] :
( ( X0 @ X4 )
| ( ( X1 @ X4 )
& ( X2 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( ( X1 @ X3 )
| ( X0 @ X3 ) )
& ( X2 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
=> ( ( ^ [X4: a] :
( ( X0 @ X4 )
| ( ( X1 @ X4 )
& ( X2 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( ( X1 @ X3 )
| ( X0 @ X3 ) )
& ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jSP4zdwkhn/DTF2THF_27498.p',cBOOL_PROP_44_pme) ).
thf(f73,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| ~ spl3_3
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $false = $true )
| ~ spl3_3
| ~ spl3_4 ),
inference(backward_demodulation,[status(thm)],[f51,f58]) ).
thf(f51,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl3_3
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f69,plain,
( spl3_4
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f22,f60,f56]) ).
thf(f22,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( sK1 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $false
= ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( sK1 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ( sK0 @ sK5 )
& ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( sK1 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( sK0 @ sK5 )
& ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) ) )
!= ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( sK1 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( sK1 @ Y0 ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) )
| ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f68,plain,
( spl3_4
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f26,f64,f56]) ).
thf(f26,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( sK1 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f54,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f32,f49,f40]) ).
thf(f32,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true
= ( ( sK0 @ sK5 )
& ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( ( sK0 @ sK5 )
& ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( ( ( sK0 @ sK5 )
& ( sK2 @ sK5 ) )
| ( sK1 @ sK5 ) ) )
| ( $true
= ( ( sK0 @ sK5 )
& ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f47,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f44,f40]) ).
thf(f38,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( sK2 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| ( ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true
= ( ( sK0 @ sK5 )
& ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) ) ) )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET144^5 : 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
% 0.15/0.33 % Computer : n017.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 11:51:56 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SET144^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.45 % Domain : Set Theory
% 0.31/0.45 % Problem : TPS problem BOOL-PROP-44
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English : Trybulec's 44th Boolean property of sets
% 0.31/0.45
% 0.31/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.31/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Bro09]
% 0.31/0.45 % Names : tps_0253 [Bro09]
% 0.31/0.45 % : BOOL-PROP-44 [TPS]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % 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
% 0.31/0.45 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.31/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.31/0.45 % Number of connectives : 14 ( 0 ~; 2 |; 2 &; 8 @)
% 0.31/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 8 ( 8 avg)
% 0.31/0.45 % Number of types : 2 ( 1 usr)
% 0.31/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.31/0.45 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.31/0.45 % SPC : TH0_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.45 % : Polymorphic definitions expanded.
% 0.31/0.45 % :
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf(a_type,type,
% 0.31/0.45 a: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(cBOOL_PROP_44_pme,conjecture,
% 0.31/0.45 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.31/0.45 ( ! [Xx: a] :
% 0.31/0.45 ( ( X @ Xx )
% 0.31/0.45 => ( Z @ Xx ) )
% 0.31/0.45 => ( ( ^ [Xz: a] :
% 0.31/0.45 ( ( X @ Xz )
% 0.31/0.45 | ( ( Y @ Xz )
% 0.31/0.45 & ( Z @ Xz ) ) ) )
% 0.31/0.45 = ( ^ [Xx: a] :
% 0.31/0.45 ( ( ( X @ Xx )
% 0.31/0.45 | ( Y @ Xx ) )
% 0.31/0.45 & ( Z @ Xx ) ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.48/1.27 ---- Embedded in THF ---
% 1.48/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.27 %%% Generated on Tue Feb 24 11:51:56 EST 2026
% 1.48/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.27 %%% Logic specification used:
% 1.48/1.27 %%% thf(spec, logic, $$dhol).
% 1.48/1.27
% 1.48/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jSP4zdwkhn/DTF2DTF27498.p
% See solution above
% 1.48/1.27 ------------------------
% 1.48/1.28 ---- Cleaned THF ---
% 1.48/1.28 thf(a_type,type,
% 1.48/1.28 a: $tType ).
% 1.48/1.28
% 1.48/1.28 thf(cBOOL_PROP_44_pme,conjecture,
% 1.48/1.28 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.48/1.28 ( ! [Xx: a] :
% 1.48/1.28 ( ( X @ Xx )
% 1.48/1.28 => ( Z @ Xx ) )
% 1.48/1.28 => ( ( ^ [Xz: a] :
% 1.48/1.28 ( ( X @ Xz )
% 1.48/1.28 | ( ( Y @ Xz )
% 1.48/1.28 & ( Z @ Xz ) ) ) )
% 1.48/1.28 = ( ^ [Xx: a] :
% 1.48/1.28 ( ( ( X @ Xx )
% 1.48/1.28 | ( Y @ Xx ) )
% 1.48/1.28 & ( Z @ Xx ) ) ) ) ) ).
% 1.48/1.28 ------------------------
% 1.48/1.29 % (27608)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27498 for (2999ds/2Mi)
% 1.48/1.30 % (27608)Instruction limit reached!
% 1.48/1.30 % (27608)------------------------------
% 1.48/1.30 % (27608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.30 % (27608)Termination reason: Unknown
% 1.48/1.30 % (27608)Termination phase: Saturation
% 1.48/1.30
% 1.48/1.30 % (27608)Memory used [KB]: 5500
% 1.48/1.30 % (27608)Time elapsed: 0.002 s
% 1.48/1.30 % (27608)Instructions burned: 2 (million)
% 1.48/1.30 % (27608)------------------------------
% 1.48/1.30 % (27608)------------------------------
% 1.48/1.30 % (27607)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_27498 for (2999ds/27Mi)
% 1.63/1.30 % (27607)First to succeed.
% 1.63/1.30 % (27607)Refutation found. Thanks to Tanya!
% 1.63/1.30 % SZS status Theorem for DTF2THF_27498
% 1.63/1.30 % SZS output start Proof for DTF2THF_27498
% 1.63/1.30 thf(type_def_5, type, a: $tType).
% 1.63/1.30 thf(func_def_0, type, a: $tType).
% 1.63/1.30 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.30 thf(func_def_9, type, sK0: a > $o).
% 1.63/1.30 thf(func_def_10, type, sK1: a > $o).
% 1.63/1.30 thf(func_def_11, type, sK2: a > $o).
% 1.63/1.30 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.63/1.30 thf(func_def_14, type, sK5: a).
% 1.63/1.30 thf(f89,plain,(
% 1.63/1.30 $false),
% 1.63/1.30 inference(avatar_sat_refutation,[status(thm)],[f47,f54,f68,f69,f73,f79,f84,f88])).
% 1.63/1.30 thf(f88,plain,(
% 1.63/1.30 ~spl3_1 | ~spl3_5),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.63/1.30 thf(f87,plain,(
% 1.63/1.30 $false | (~spl3_1 | ~spl3_5)),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.63/1.30 thf(f86,plain,(
% 1.63/1.30 ($false = $true) | (~spl3_1 | ~spl3_5)),
% 1.63/1.30 inference(forward_demodulation,[status(thm)],[f42,f62])).
% 1.63/1.30 thf(f62,plain,(
% 1.63/1.30 ($false = (sK1 @ sK5)) | ~spl3_5),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.63/1.30 thf(f60,definition,(
% 1.63/1.30 spl3_5 <=> ($false = (sK1 @ sK5))),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.63/1.30 thf(f42,plain,(
% 1.63/1.30 ((sK1 @ sK5) = $true) | ~spl3_1),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.63/1.30 thf(f40,definition,(
% 1.63/1.30 spl3_1 <=> ((sK1 @ sK5) = $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.63/1.30 thf(f84,plain,(
% 1.63/1.30 ~spl3_2 | ~spl3_6),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f83])).
% 1.63/1.30 thf(f83,plain,(
% 1.63/1.30 $false | (~spl3_2 | ~spl3_6)),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.63/1.30 thf(f82,plain,(
% 1.63/1.30 ($false = $true) | (~spl3_2 | ~spl3_6)),
% 1.63/1.30 inference(backward_demodulation,[status(thm)],[f46,f66])).
% 1.63/1.30 thf(f66,plain,(
% 1.63/1.30 ($false = (sK2 @ sK5)) | ~spl3_6),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.63/1.30 thf(f64,definition,(
% 1.63/1.30 spl3_6 <=> ($false = (sK2 @ sK5))),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.63/1.30 thf(f46,plain,(
% 1.63/1.30 ((sK2 @ sK5) = $true) | ~spl3_2),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.63/1.30 thf(f44,definition,(
% 1.63/1.30 spl3_2 <=> ((sK2 @ sK5) = $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.63/1.30 thf(f79,plain,(
% 1.63/1.30 ~spl3_1 | ~spl3_4),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.63/1.30 thf(f78,plain,(
% 1.63/1.30 $false | (~spl3_1 | ~spl3_4)),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.63/1.30 thf(f77,plain,(
% 1.63/1.30 ($false = $true) | (~spl3_1 | ~spl3_4)),
% 1.63/1.30 inference(forward_demodulation,[status(thm)],[f76,f58])).
% 1.63/1.30 thf(f58,plain,(
% 1.63/1.30 ($false = (sK0 @ sK5)) | ~spl3_4),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.63/1.30 thf(f56,definition,(
% 1.63/1.30 spl3_4 <=> ($false = (sK0 @ sK5))),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.63/1.30 thf(f76,plain,(
% 1.63/1.30 ((sK0 @ sK5) = $true) | ~spl3_1),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.63/1.30 thf(f75,plain,(
% 1.63/1.30 ((sK0 @ sK5) = $true) | ($true != $true) | ~spl3_1),
% 1.63/1.30 inference(superposition,[status(thm)],[f10,f42])).
% 1.63/1.30 thf(f10,plain,(
% 1.63/1.30 ( ! [X3 : a] : (((sK1 @ X3) != $true) | ((sK0 @ X3) = $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.30 thf(f8,plain,(
% 1.63/1.30 ! [X3 : a] : (((sK0 @ X3) = $true) | ((sK1 @ X3) != $true)) & ((^[Y0 : a]: ((sK0 @ Y0) & ((sK1 @ Y0) | (sK2 @ Y0)))) != (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) | (sK1 @ Y0))))),
% 1.63/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.63/1.30 thf(f7,plain,(
% 1.63/1.30 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) = $true) | ((X1 @ X3) != $true)) & ((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) | (X1 @ Y0))) != (^[Y0 : a]: ((X0 @ Y0) & ((X1 @ Y0) | (X2 @ Y0)))))) => (! [X3 : a] : (((sK0 @ X3) = $true) | ((sK1 @ X3) != $true)) & ((^[Y0 : a]: ((sK0 @ Y0) & ((sK1 @ Y0) | (sK2 @ Y0)))) != (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) | (sK1 @ Y0)))))),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f6,plain,(
% 1.63/1.30 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) = $true) | ((X1 @ X3) != $true)) & ((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) | (X1 @ Y0))) != (^[Y0 : a]: ((X0 @ Y0) & ((X1 @ Y0) | (X2 @ Y0))))))),
% 1.63/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.30 thf(f5,plain,(
% 1.63/1.30 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X1 @ X3) = $true) => ((X0 @ X3) = $true)) => ((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) | (X1 @ Y0))) = (^[Y0 : a]: ((X0 @ Y0) & ((X1 @ Y0) | (X2 @ Y0))))))),
% 1.63/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.30 thf(f4,plain,(
% 1.63/1.30 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : ((X1 @ X3) => (X0 @ X3)) => ((^[X4 : a] : ((X1 @ X4) | ((X2 @ X4) & (X0 @ X4)))) = (^[X5 : a] : (((X2 @ X5) | (X1 @ X5)) & (X0 @ X5)))))),
% 1.63/1.30 inference(rectify,[status(thm)],[f2])).
% 1.63/1.30 thf(f2,negated_conjecture,(
% 1.63/1.30 ~! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : (! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) => ((^[X4 : a] : ((X0 @ X4) | ((X1 @ X4) & (X2 @ X4)))) = (^[X3 : a] : (((X1 @ X3) | (X0 @ X3)) & (X2 @ X3)))))),
% 1.63/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.30 thf(f1,conjecture,(
% 1.63/1.30 ! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : (! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) => ((^[X4 : a] : ((X0 @ X4) | ((X1 @ X4) & (X2 @ X4)))) = (^[X3 : a] : (((X1 @ X3) | (X0 @ X3)) & (X2 @ X3)))))),
% 1.63/1.30 file('/export/starexec/sandbox/tmp/tmp.jSP4zdwkhn/DTF2THF_27498.p',cBOOL_PROP_44_pme)).
% 1.63/1.30 thf(f73,plain,(
% 1.63/1.30 ~spl3_3 | ~spl3_4),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.63/1.30 thf(f72,plain,(
% 1.63/1.30 $false | (~spl3_3 | ~spl3_4)),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.63/1.30 thf(f71,plain,(
% 1.63/1.30 ($false = $true) | (~spl3_3 | ~spl3_4)),
% 1.63/1.30 inference(backward_demodulation,[status(thm)],[f51,f58])).
% 1.63/1.30 thf(f51,plain,(
% 1.63/1.30 ((sK0 @ sK5) = $true) | ~spl3_3),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.63/1.30 thf(f49,definition,(
% 1.63/1.30 spl3_3 <=> ((sK0 @ sK5) = $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.63/1.30 thf(f69,plain,(
% 1.63/1.30 spl3_4 | spl3_5),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f22,f60,f56])).
% 1.63/1.30 thf(f22,plain,(
% 1.63/1.30 ($false = (sK1 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.63/1.30 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 1.63/1.30 thf(f18,plain,(
% 1.63/1.30 ($false = (sK1 @ sK5)) | ($false = (sK0 @ sK5)) | ($false = (sK1 @ sK5))),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.63/1.30 thf(f17,plain,(
% 1.63/1.30 ($false = (((sK0 @ sK5) & (sK2 @ sK5)) | (sK1 @ sK5))) | ($false = (sK1 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.63/1.30 thf(f15,plain,(
% 1.63/1.30 ($false = ((sK1 @ sK5) | (sK2 @ sK5))) | ($false = (((sK0 @ sK5) & (sK2 @ sK5)) | (sK1 @ sK5))) | ($false = (sK0 @ sK5))),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.63/1.30 thf(f14,plain,(
% 1.63/1.30 ($false = ((sK0 @ sK5) & ((sK1 @ sK5) | (sK2 @ sK5)))) | ($false = (((sK0 @ sK5) & (sK2 @ sK5)) | (sK1 @ sK5)))),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.63/1.30 thf(f12,plain,(
% 1.63/1.30 (((sK0 @ sK5) & ((sK1 @ sK5) | (sK2 @ sK5))) != (((sK0 @ sK5) & (sK2 @ sK5)) | (sK1 @ sK5)))),
% 1.63/1.30 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.63/1.30 thf(f11,plain,(
% 1.63/1.30 (((^[Y0 : a]: ((sK0 @ Y0) & ((sK1 @ Y0) | (sK2 @ Y0)))) @ sK5) != ((^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) | (sK1 @ Y0))) @ sK5))),
% 1.63/1.30 inference(negative_extensionality,[status(thm)],[f9])).
% 1.63/1.30 thf(f9,plain,(
% 1.63/1.30 ((^[Y0 : a]: ((sK0 @ Y0) & ((sK1 @ Y0) | (sK2 @ Y0)))) != (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) | (sK1 @ Y0))))),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.30 thf(f68,plain,(
% 1.63/1.30 spl3_4 | spl3_6),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f26,f64,f56])).
% 1.63/1.30 thf(f26,plain,(
% 1.63/1.30 ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.63/1.30 inference(duplicate_literal_removal,[status(thm)],[f25])).
% 1.63/1.30 thf(f25,plain,(
% 1.63/1.30 ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.63/1.30 thf(f24,plain,(
% 1.63/1.30 ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5)) | ($false = ((sK0 @ sK5) & (sK2 @ sK5)))),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.63/1.30 thf(f16,plain,(
% 1.63/1.30 ($false = (((sK0 @ sK5) & (sK2 @ sK5)) | (sK1 @ sK5))) | ($false = (sK0 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.63/1.30 thf(f54,plain,(
% 1.63/1.30 spl3_1 | spl3_3),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f32,f49,f40])).
% 1.63/1.30 thf(f32,plain,(
% 1.63/1.30 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.63/1.30 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 1.63/1.30 thf(f31,plain,(
% 1.63/1.30 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.63/1.30 thf(f29,plain,(
% 1.63/1.30 ($true = ((sK0 @ sK5) & ((sK1 @ sK5) | (sK2 @ sK5)))) | ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true)),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.63/1.30 thf(f27,plain,(
% 1.63/1.30 (((sK0 @ sK5) & (sK2 @ sK5)) = $true) | ((sK1 @ sK5) = $true) | ($true = ((sK0 @ sK5) & ((sK1 @ sK5) | (sK2 @ sK5))))),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.63/1.30 thf(f13,plain,(
% 1.63/1.30 ($true = (((sK0 @ sK5) & (sK2 @ sK5)) | (sK1 @ sK5))) | ($true = ((sK0 @ sK5) & ((sK1 @ sK5) | (sK2 @ sK5))))),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.63/1.30 thf(f47,plain,(
% 1.63/1.30 spl3_1 | spl3_2),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f38,f44,f40])).
% 1.63/1.30 thf(f38,plain,(
% 1.63/1.30 ((sK2 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.63/1.30 inference(duplicate_literal_removal,[status(thm)],[f37])).
% 1.63/1.30 thf(f37,plain,(
% 1.63/1.30 ((sK1 @ sK5) = $true) | ((sK2 @ sK5) = $true) | ((sK1 @ sK5) = $true) | ((sK2 @ sK5) = $true)),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.63/1.30 thf(f35,plain,(
% 1.63/1.30 ((sK2 @ sK5) = $true) | ((sK1 @ sK5) = $true) | (((sK1 @ sK5) | (sK2 @ sK5)) = $true)),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.63/1.30 thf(f28,plain,(
% 1.63/1.30 ($true = ((sK0 @ sK5) & ((sK1 @ sK5) | (sK2 @ sK5)))) | ((sK2 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.63/1.30 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.63/1.30 % SZS output end Proof for DTF2THF_27498
% 1.63/1.30 % (27607)------------------------------
% 1.63/1.30 % (27607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (27607)Termination reason: Refutation
% 1.63/1.30
% 1.63/1.30 % (27607)Memory used [KB]: 5500
% 1.63/1.30 % (27607)Time elapsed: 0.004 s
% 1.63/1.30 % (27607)Instructions burned: 4 (million)
% 1.63/1.30 % (27607)------------------------------
% 1.63/1.30 % (27607)------------------------------
% 1.63/1.30 % (27604)Success in time 0.007 s
%------------------------------------------------------------------------------