%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET159^5 : 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 : n010.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 09:31:20 AM UTC 2026
% Result : Theorem 1.53s 1.37s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 16 unt; 0 typ; 6 def)
% Number of atoms : 299 ( 75 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 318 ( 34 ~; 122 |; 0 &; 155 @)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 38 ( 20 ^; 12 !; 6 ?; 38 :)
% 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_11,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK5: a ).
thf(f84,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f51,f61,f69,f70,f75,f79,f83]) ).
thf(f83,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f82]) ).
thf(f82,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f42,f55]) ).
thf(f55,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl3_4
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f42,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl3_1
<=> ( $true
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f79,plain,
( ~ spl3_3
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| ~ spl3_3
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $false = $true )
| ~ spl3_3
| ~ spl3_6 ),
inference(forward_demodulation,[status(thm)],[f50,f65]) ).
thf(f65,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl3_6
<=> ( ( sK1 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f50,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl3_3
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f75,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f74]) ).
thf(f74,plain,
( $false
| ~ spl3_2
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f46,f59]) ).
thf(f59,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f57,definition,
( spl3_5
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f46,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl3_2
<=> ( $true
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f70,plain,
spl3_5,
inference(avatar_split_clause,[status(thm)],[f22,f57]) ).
thf(f22,plain,
( $false
= ( sK0 @ sK5 ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ( sK1 @ sK5 )
| ( sK2 @ sK5 )
| ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $false )
| ( $false
= ( ( sK1 @ sK5 )
| ( sK2 @ sK5 )
| ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( ( sK0 @ sK5 )
| ( sK1 @ sK5 )
| ( sK2 @ sK5 ) ) )
| ( $false
= ( ( sK1 @ sK5 )
| ( sK2 @ sK5 )
| ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 )
| ( sK2 @ sK5 ) )
!= ( ( sK1 @ sK5 )
| ( sK2 @ sK5 )
| ( sK0 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK5 )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 )
| ( sK0 @ Y0 ) )
@ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 )
| ( sK0 @ 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] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 )
| ( X2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 @ Y0 )
| ( X0 @ Y0 ) ) ) )
=> ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 )
| ( X2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 @ Y0 )
| ( X0 @ Y0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 )
| ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 @ Y0 )
| ( X0 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
| ( X2 @ X3 )
| ( X1 @ X3 ) ) )
= ( ^ [X4: a] :
( ( X2 @ X4 )
| ( X1 @ X4 )
| ( X0 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( X2 @ X3 )
| ( X0 @ X3 )
| ( X1 @ X3 ) ) )
= ( ^ [X3: a] :
( ( X0 @ X3 )
| ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( X2 @ X3 )
| ( X0 @ X3 )
| ( X1 @ X3 ) ) )
= ( ^ [X3: a] :
( ( X0 @ X3 )
| ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yg4ejwmncd/DTF2THF_10812.p',cBOOL_PROP_64_pme) ).
thf(f69,plain,
spl3_6,
inference(avatar_split_clause,[status(thm)],[f27,f63]) ).
thf(f27,plain,
( ( sK1 @ sK5 )
= $false ),
inference(duplicate_literal_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( sK1 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) )
= $false )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( ( sK1 @ sK5 )
| ( sK2 @ sK5 )
| ( sK0 @ sK5 ) ) )
| ( ( sK1 @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f61,plain,
spl3_4,
inference(avatar_split_clause,[status(thm)],[f32,f53]) ).
thf(f32,plain,
( $false
= ( sK2 @ sK5 ) ),
inference(duplicate_literal_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) )
= $false )
| ( $false
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( sK1 @ sK5 )
| ( sK2 @ sK5 )
| ( sK0 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f51,plain,
( spl3_1
| spl3_2
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f38,f48,f44,f40]) ).
thf(f38,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK0 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( ( sK1 @ sK5 )
= $true )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $true )
| ( $true
= ( sK2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true
= ( sK2 @ sK5 ) )
| ( ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) )
= $true )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 )
| ( sK2 @ sK5 ) )
= $true )
| ( ( ( sK1 @ sK5 )
| ( sK2 @ sK5 ) )
= $true )
| ( $true
= ( sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( sK1 @ sK5 )
| ( sK2 @ sK5 )
| ( sK0 @ sK5 ) )
= $true )
| ( ( ( sK0 @ sK5 )
| ( sK1 @ sK5 )
| ( sK2 @ sK5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET159^5 : 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
% 0.12/0.30 % Computer : n010.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 11:53:33 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
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SET159^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.39 % Domain : Set Theory
% 0.17/0.39 % Problem : TPS problem BOOL-PROP-64
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English : Trybulec's 64th Boolean property of sets
% 0.17/0.39
% 0.17/0.39 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.17/0.39 % : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.17/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Bro09]
% 0.17/0.39 % Names : tps_0232 [Bro09]
% 0.17/0.39 % : 28 [Bar92]
% 0.17/0.39 % : GAZING-THM28 [TPS]
% 0.17/0.39 % : BOOL-PROP-64 [TPS]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.00 v6.0.0, 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
% 0.17/0.39 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.17/0.39 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 1 ( 1 avg)
% 0.17/0.39 % Number of connectives : 10 ( 0 ~; 4 |; 0 &; 6 @)
% 0.17/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 4 ( 4 avg)
% 0.17/0.39 % Number of types : 2 ( 1 usr)
% 0.17/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.17/0.39 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.39 % : Polymorphic definitions expanded.
% 0.17/0.39 % :
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(a_type,type,
% 0.17/0.39 a: $tType ).
% 0.17/0.39
% 0.17/0.39 thf(cBOOL_PROP_64_pme,conjecture,
% 0.17/0.39 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.17/0.39 ( ( ^ [Xz: a] :
% 0.17/0.39 ( ( X @ Xz )
% 0.17/0.39 | ( Y @ Xz )
% 0.17/0.39 | ( Z @ Xz ) ) )
% 0.17/0.39 = ( ^ [Xz: a] :
% 0.17/0.39 ( ( X @ Xz )
% 0.17/0.39 | ( Y @ Xz )
% 0.17/0.39 | ( Z @ Xz ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.53/1.34 ---- Embedded in THF ---
% 1.53/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.34 %%% Generated on Tue Feb 24 11:53:34 EST 2026
% 1.53/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.34 %%% Logic specification used:
% 1.53/1.34 %%% thf(spec, logic, $$dhol).
% 1.53/1.34
% 1.53/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.yg4ejwmncd/DTF2DTF10812.p
% See solution above
% 1.53/1.34 ------------------------
% 1.53/1.35 ---- Cleaned THF ---
% 1.53/1.35 thf(a_type,type,
% 1.53/1.35 a: $tType ).
% 1.53/1.35
% 1.53/1.35 thf(cBOOL_PROP_64_pme,conjecture,
% 1.53/1.35 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.53/1.35 ( ( ^ [Xz: a] :
% 1.53/1.35 ( ( X @ Xz )
% 1.53/1.35 | ( Y @ Xz )
% 1.53/1.35 | ( Z @ Xz ) ) )
% 1.53/1.35 = ( ^ [Xz: a] :
% 1.53/1.35 ( ( X @ Xz )
% 1.53/1.35 | ( Y @ Xz )
% 1.53/1.35 | ( Z @ Xz ) ) ) ) ).
% 1.53/1.35 ------------------------
% 1.53/1.37 % (10913)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_10812 for (3000ds/2Mi)
% 1.53/1.37 % (10909)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10812 for (3000ds/183Mi)
% 1.53/1.37 % (10910)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_10812 for (3000ds/4Mi)
% 1.53/1.37 % (10914)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_10812 for (3000ds/275Mi)
% 1.53/1.37 % (10915)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10812 for (3000ds/18Mi)
% 1.53/1.37 % (10912)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10812 for (3000ds/2Mi)
% 1.53/1.37 % (10911)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_10812 for (3000ds/27Mi)
% 1.53/1.37 % (10912)Instruction limit reached!
% 1.53/1.37 % (10912)------------------------------
% 1.53/1.37 % (10912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (10912)Termination reason: Unknown
% 1.53/1.37 % (10912)Termination phase: Saturation
% 1.53/1.37
% 1.53/1.37 % (10913)Instruction limit reached!
% 1.53/1.37 % (10913)------------------------------
% 1.53/1.37 % (10913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (10913)Termination reason: Unknown
% 1.53/1.37 % (10913)Termination phase: Saturation
% 1.53/1.37
% 1.53/1.37 % (10913)Memory used [KB]: 5373
% 1.53/1.37 % (10913)Time elapsed: 0.003 s
% 1.53/1.37 % (10913)Instructions burned: 2 (million)
% 1.53/1.37 % (10913)------------------------------
% 1.53/1.37 % (10913)------------------------------
% 1.53/1.37 % (10912)Memory used [KB]: 5373
% 1.53/1.37 % (10912)Time elapsed: 0.003 s
% 1.53/1.37 % (10912)Instructions burned: 2 (million)
% 1.53/1.37 % (10912)------------------------------
% 1.53/1.37 % (10912)------------------------------
% 1.53/1.37 % (10914)First to succeed.
% 1.53/1.37 % (10909)Also succeeded, but the first one will report.
% 1.53/1.37 % (10915)Also succeeded, but the first one will report.
% 1.53/1.37 % (10914)Refutation found. Thanks to Tanya!
% 1.53/1.37 % SZS status Theorem for DTF2THF_10812
% 1.53/1.37 % SZS output start Proof for DTF2THF_10812
% 1.53/1.37 thf(type_def_5, type, a: $tType).
% 1.53/1.37 thf(func_def_0, type, a: $tType).
% 1.53/1.37 thf(func_def_7, type, sK0: a > $o).
% 1.53/1.37 thf(func_def_8, type, sK1: a > $o).
% 1.53/1.37 thf(func_def_9, type, sK2: a > $o).
% 1.53/1.37 thf(func_def_11, type, ph4: !>[X0: $tType]:(X0)).
% 1.53/1.37 thf(func_def_12, type, sK5: a).
% 1.53/1.37 thf(f84,plain,(
% 1.53/1.37 $false),
% 1.53/1.37 inference(avatar_sat_refutation,[status(thm)],[f51,f61,f69,f70,f75,f79,f83])).
% 1.53/1.37 thf(f83,plain,(
% 1.53/1.37 ~spl3_1 | ~spl3_4),
% 1.53/1.37 inference(avatar_contradiction_clause,[status(thm)],[f82])).
% 1.53/1.37 thf(f82,plain,(
% 1.53/1.37 $false | (~spl3_1 | ~spl3_4)),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.53/1.37 thf(f81,plain,(
% 1.53/1.37 ($false = $true) | (~spl3_1 | ~spl3_4)),
% 1.53/1.37 inference(forward_demodulation,[status(thm)],[f42,f55])).
% 1.53/1.37 thf(f55,plain,(
% 1.53/1.37 ($false = (sK2 @ sK5)) | ~spl3_4),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.53/1.37 thf(f53,definition,(
% 1.53/1.37 spl3_4 <=> ($false = (sK2 @ sK5))),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.53/1.37 thf(f42,plain,(
% 1.53/1.37 ($true = (sK2 @ sK5)) | ~spl3_1),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.53/1.37 thf(f40,definition,(
% 1.53/1.37 spl3_1 <=> ($true = (sK2 @ sK5))),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.53/1.37 thf(f79,plain,(
% 1.53/1.37 ~spl3_3 | ~spl3_6),
% 1.53/1.37 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.53/1.37 thf(f78,plain,(
% 1.53/1.37 $false | (~spl3_3 | ~spl3_6)),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.53/1.37 thf(f77,plain,(
% 1.53/1.37 ($false = $true) | (~spl3_3 | ~spl3_6)),
% 1.53/1.37 inference(forward_demodulation,[status(thm)],[f50,f65])).
% 1.53/1.37 thf(f65,plain,(
% 1.53/1.37 ((sK1 @ sK5) = $false) | ~spl3_6),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.53/1.37 thf(f63,definition,(
% 1.53/1.37 spl3_6 <=> ((sK1 @ sK5) = $false)),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.53/1.37 thf(f50,plain,(
% 1.53/1.37 ((sK1 @ sK5) = $true) | ~spl3_3),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.53/1.37 thf(f48,definition,(
% 1.53/1.37 spl3_3 <=> ((sK1 @ sK5) = $true)),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.53/1.37 thf(f75,plain,(
% 1.53/1.37 ~spl3_2 | ~spl3_5),
% 1.53/1.37 inference(avatar_contradiction_clause,[status(thm)],[f74])).
% 1.53/1.37 thf(f74,plain,(
% 1.53/1.37 $false | (~spl3_2 | ~spl3_5)),
% 1.53/1.37 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.53/1.37 thf(f73,plain,(
% 1.53/1.37 ($false = $true) | (~spl3_2 | ~spl3_5)),
% 1.53/1.37 inference(forward_demodulation,[status(thm)],[f46,f59])).
% 1.53/1.37 thf(f59,plain,(
% 1.53/1.37 ($false = (sK0 @ sK5)) | ~spl3_5),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.53/1.37 thf(f57,definition,(
% 1.53/1.37 spl3_5 <=> ($false = (sK0 @ sK5))),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.53/1.37 thf(f46,plain,(
% 1.53/1.37 ($true = (sK0 @ sK5)) | ~spl3_2),
% 1.53/1.37 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.53/1.37 thf(f44,definition,(
% 1.53/1.37 spl3_2 <=> ($true = (sK0 @ sK5))),
% 1.53/1.37 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.53/1.37 thf(f70,plain,(
% 1.53/1.37 spl3_5),
% 1.53/1.37 inference(avatar_split_clause,[status(thm)],[f22,f57])).
% 1.53/1.37 thf(f22,plain,(
% 1.53/1.37 ($false = (sK0 @ sK5))),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 1.53/1.37 thf(f18,plain,(
% 1.53/1.37 ($false = (sK0 @ sK5)) | ($false = (sK0 @ sK5))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.53/1.37 thf(f17,plain,(
% 1.53/1.37 ($false = (sK0 @ sK5)) | ($false = (((sK1 @ sK5) | (sK2 @ sK5)) | (sK0 @ sK5)))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.53/1.37 thf(f15,plain,(
% 1.53/1.37 (((sK0 @ sK5) | (sK1 @ sK5)) = $false) | ($false = (((sK1 @ sK5) | (sK2 @ sK5)) | (sK0 @ sK5)))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.53/1.37 thf(f13,plain,(
% 1.53/1.37 ($false = (((sK0 @ sK5) | (sK1 @ sK5)) | (sK2 @ sK5))) | ($false = (((sK1 @ sK5) | (sK2 @ sK5)) | (sK0 @ sK5)))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.53/1.37 thf(f11,plain,(
% 1.53/1.37 ((((sK0 @ sK5) | (sK1 @ sK5)) | (sK2 @ sK5)) != (((sK1 @ sK5) | (sK2 @ sK5)) | (sK0 @ sK5)))),
% 1.53/1.37 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.53/1.37 thf(f10,plain,(
% 1.53/1.37 (((^[Y0 : a]: (((sK0 @ Y0) | (sK1 @ Y0)) | (sK2 @ Y0))) @ sK5) != ((^[Y0 : a]: (((sK1 @ Y0) | (sK2 @ Y0)) | (sK0 @ Y0))) @ sK5))),
% 1.53/1.37 inference(negative_extensionality,[status(thm)],[f9])).
% 1.53/1.37 thf(f9,plain,(
% 1.53/1.37 ((^[Y0 : a]: (((sK0 @ Y0) | (sK1 @ Y0)) | (sK2 @ Y0))) != (^[Y0 : a]: (((sK1 @ Y0) | (sK2 @ Y0)) | (sK0 @ Y0))))),
% 1.53/1.37 inference(cnf_transformation,[status(thm)],[f8])).
% 1.53/1.37 thf(f8,plain,(
% 1.53/1.37 ((^[Y0 : a]: (((sK0 @ Y0) | (sK1 @ Y0)) | (sK2 @ Y0))) != (^[Y0 : a]: (((sK1 @ Y0) | (sK2 @ Y0)) | (sK0 @ Y0))))),
% 1.53/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7])).
% 1.53/1.37 thf(f7,plain,(
% 1.53/1.37 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((X0 @ Y0) | (X1 @ Y0)) | (X2 @ Y0))) != (^[Y0 : a]: (((X1 @ Y0) | (X2 @ Y0)) | (X0 @ Y0)))) => ((^[Y0 : a]: (((sK0 @ Y0) | (sK1 @ Y0)) | (sK2 @ Y0))) != (^[Y0 : a]: (((sK1 @ Y0) | (sK2 @ Y0)) | (sK0 @ Y0))))),
% 1.53/1.37 introduced(definition,[],[choice_axiom])).
% 1.53/1.37 thf(f6,plain,(
% 1.53/1.37 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((X0 @ Y0) | (X1 @ Y0)) | (X2 @ Y0))) != (^[Y0 : a]: (((X1 @ Y0) | (X2 @ Y0)) | (X0 @ Y0))))),
% 1.53/1.37 inference(ennf_transformation,[status(thm)],[f5])).
% 1.53/1.37 thf(f5,plain,(
% 1.53/1.37 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[Y0 : a]: (((X0 @ Y0) | (X1 @ Y0)) | (X2 @ Y0))) = (^[Y0 : a]: (((X1 @ Y0) | (X2 @ Y0)) | (X0 @ Y0))))),
% 1.53/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.37 thf(f4,plain,(
% 1.53/1.37 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((^[X3 : a] : ((X0 @ X3) | (X2 @ X3) | (X1 @ X3))) = (^[X4 : a] : ((X2 @ X4) | (X1 @ X4) | (X0 @ X4))))),
% 1.53/1.37 inference(rectify,[status(thm)],[f2])).
% 1.53/1.37 thf(f2,negated_conjecture,(
% 1.53/1.37 ~! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((^[X3 : a] : ((X2 @ X3) | (X0 @ X3) | (X1 @ X3))) = (^[X3 : a] : ((X0 @ X3) | (X1 @ X3) | (X2 @ X3))))),
% 1.53/1.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.37 thf(f1,conjecture,(
% 1.53/1.37 ! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((^[X3 : a] : ((X2 @ X3) | (X0 @ X3) | (X1 @ X3))) = (^[X3 : a] : ((X0 @ X3) | (X1 @ X3) | (X2 @ X3))))),
% 1.53/1.37 file('/export/starexec/sandbox/tmp/tmp.yg4ejwmncd/DTF2THF_10812.p',cBOOL_PROP_64_pme)).
% 1.53/1.37 thf(f69,plain,(
% 1.53/1.37 spl3_6),
% 1.53/1.37 inference(avatar_split_clause,[status(thm)],[f27,f63])).
% 1.53/1.37 thf(f27,plain,(
% 1.53/1.37 ((sK1 @ sK5) = $false)),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f26])).
% 1.53/1.37 thf(f26,plain,(
% 1.53/1.37 ((sK1 @ sK5) = $false) | ((sK1 @ sK5) = $false)),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.53/1.37 thf(f24,plain,(
% 1.53/1.37 (((sK1 @ sK5) | (sK2 @ sK5)) = $false) | ((sK1 @ sK5) = $false)),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.53/1.37 thf(f16,plain,(
% 1.53/1.37 ($false = (((sK1 @ sK5) | (sK2 @ sK5)) | (sK0 @ sK5))) | ((sK1 @ sK5) = $false)),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.53/1.37 thf(f61,plain,(
% 1.53/1.37 spl3_4),
% 1.53/1.37 inference(avatar_split_clause,[status(thm)],[f32,f53])).
% 1.53/1.37 thf(f32,plain,(
% 1.53/1.37 ($false = (sK2 @ sK5))),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f30])).
% 1.53/1.37 thf(f30,plain,(
% 1.53/1.37 ($false = (sK2 @ sK5)) | ($false = (sK2 @ sK5))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.53/1.37 thf(f29,plain,(
% 1.53/1.37 (((sK1 @ sK5) | (sK2 @ sK5)) = $false) | ($false = (sK2 @ sK5))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.53/1.37 thf(f14,plain,(
% 1.53/1.37 ($false = (sK2 @ sK5)) | ($false = (((sK1 @ sK5) | (sK2 @ sK5)) | (sK0 @ sK5)))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.53/1.37 thf(f51,plain,(
% 1.53/1.37 spl3_1 | spl3_2 | spl3_3),
% 1.53/1.37 inference(avatar_split_clause,[status(thm)],[f38,f48,f44,f40])).
% 1.53/1.37 thf(f38,plain,(
% 1.53/1.37 ($true = (sK0 @ sK5)) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $true)),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f37])).
% 1.53/1.37 thf(f37,plain,(
% 1.53/1.37 ($true = (sK0 @ sK5)) | ($true = (sK0 @ sK5)) | ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $true)),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.53/1.37 thf(f36,plain,(
% 1.53/1.37 ($true = (sK2 @ sK5)) | ((sK1 @ sK5) = $true) | ($true = (sK0 @ sK5)) | (((sK0 @ sK5) | (sK1 @ sK5)) = $true)),
% 1.53/1.37 inference(duplicate_literal_removal,[status(thm)],[f35])).
% 1.53/1.37 thf(f35,plain,(
% 1.53/1.37 ($true = (sK0 @ sK5)) | ((sK1 @ sK5) = $true) | ($true = (sK2 @ sK5)) | (((sK0 @ sK5) | (sK1 @ sK5)) = $true) | ($true = (sK2 @ sK5))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.53/1.37 thf(f34,plain,(
% 1.53/1.37 ($true = (sK0 @ sK5)) | ($true = (sK2 @ sK5)) | (((sK1 @ sK5) | (sK2 @ sK5)) = $true) | (((sK0 @ sK5) | (sK1 @ sK5)) = $true)),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.53/1.37 thf(f33,plain,(
% 1.53/1.37 ((((sK0 @ sK5) | (sK1 @ sK5)) | (sK2 @ sK5)) = $true) | (((sK1 @ sK5) | (sK2 @ sK5)) = $true) | ($true = (sK0 @ sK5))),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.53/1.37 thf(f12,plain,(
% 1.53/1.37 ((((sK1 @ sK5) | (sK2 @ sK5)) | (sK0 @ sK5)) = $true) | ((((sK0 @ sK5) | (sK1 @ sK5)) | (sK2 @ sK5)) = $true)),
% 1.53/1.37 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.53/1.37 % SZS output end Proof for DTF2THF_10812
% 1.53/1.37 % (10914)------------------------------
% 1.53/1.37 % (10914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.37 % (10914)Termination reason: Refutation
% 1.53/1.37
% 1.53/1.37 % (10914)Memory used [KB]: 5500
% 1.53/1.37 % (10914)Time elapsed: 0.005 s
% 1.53/1.37 % (10914)Instructions burned: 2 (million)
% 1.53/1.37 % (10914)------------------------------
% 1.53/1.37 % (10914)------------------------------
% 1.53/1.37 % (10908)Success in time 0.019 s
%------------------------------------------------------------------------------