%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET616^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 09:31:55 AM UTC 2026
% Result : Theorem 1.50s 1.27s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 6 unt; 0 typ; 4 def)
% Number of atoms : 236 ( 70 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 247 ( 60 ~; 42 |; 34 &; 102 @)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 20 ^; 21 !; 4 ?; 45 :)
% 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_11,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK4: a ).
thf(f86,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f31,f37,f70,f85]) ).
thf(f85,plain,
( spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
| spl2_3
| ~ spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f80,f25]) ).
thf(f25,plain,
( ( ( sK1 @ sK4 )
!= $false )
| spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl2_3
<=> ( ( sK1 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f80,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true = $false )
| ( ( sK1 @ sK4 )
= $false )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f30,f49]) ).
thf(f49,plain,
! [X1: a] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: a] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: a] :
( ( ( ~ ( sK1 @ X1 ) )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( ( sK0 @ X1 )
& ~ ( sK1 @ X1 ) ) )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ~ ( sK0 @ X1 ) )
= $false )
| ( $true
= ( ( sK0 @ X1 )
& ~ ( sK1 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: a] :
( ( ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= $false )
| ( $true
= ( ( sK0 @ X1 )
& ~ ( sK1 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: a] :
( ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= ( ( sK0 @ X1 )
& ~ ( sK1 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ X1 )
= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( sK0 != sK1 )
& ( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( X0 != X1 )
& ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) )
=> ( ( sK0 != sK1 )
& ( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( X0 != X1 )
& ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) ) )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.6PAx0BJqXm/DTF2THF_20869.p',cBOOL_PROP_90_pme) ).
thf(f30,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl2_4
<=> ( ( sK0 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f70,plain,
( spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f64,f15,f19]) ).
thf(f19,definition,
( spl2_2
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f15,definition,
( spl2_1
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f64,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK4 ) )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f56,f17]) ).
thf(f17,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f15]) ).
thf(f56,plain,
! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( sK1 @ X1 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: a] :
( ( ( sK1 @ X1 )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( ( sK1 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= $true )
| ( ( sK1 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( ~ ( sK1 @ X1 ) )
= $false )
| ( ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: a] :
( ( ( ( sK0 @ X1 )
& ~ ( sK1 @ X1 ) )
= $false )
| ( ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f37,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f21,f26]) ).
thf(f26,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f21,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f31,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f13,f28,f24]) ).
thf(f13,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( ( sK1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( sK0 @ sK4 )
!= ( sK1 @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f10]) ).
thf(f10,plain,
sK0 != sK1,
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f22,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f12,f19,f15]) ).
thf(f12,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET616^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n015.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 12:01:01 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SET616^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : TPS problem BOOL-PROP-90
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : Trybulec's 90th Boolean property of sets
% 0.19/0.45
% 0.19/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0288 [Bro09]
% 0.19/0.45 % : BOOL-PROP-90 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.18 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, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 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
% 0.19/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.19/0.45 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.45 % Number of connectives : 9 ( 2 ~; 0 |; 2 &; 4 @)
% 0.19/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 4 ( 4 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.45 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 % : Polymorphic definitions expanded.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(cBOOL_PROP_90_pme,conjecture,
% 0.19/0.45 ! [X: a > $o,Y: a > $o] :
% 0.19/0.45 ( ( ( ^ [Xx: a] :
% 0.19/0.45 ( ( X @ Xx )
% 0.19/0.45 & ~ ( Y @ Xx ) ) )
% 0.19/0.45 = ( ^ [Xx: a] :
% 0.19/0.45 ( ( Y @ Xx )
% 0.19/0.45 & ~ ( X @ Xx ) ) ) )
% 0.19/0.45 => ( X = Y ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.50/1.23 ---- Embedded in THF ---
% 1.50/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.23 %%% Generated on Tue Feb 24 12:01:02 EST 2026
% 1.50/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.23 %%% Logic specification used:
% 1.50/1.23 %%% thf(spec, logic, $$dhol).
% 1.50/1.23
% 1.50/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6PAx0BJqXm/DTF2DTF20869.p
% See solution above
% 1.50/1.23 ------------------------
% 1.50/1.24 ---- Cleaned THF ---
% 1.50/1.24 thf(a_type,type,
% 1.50/1.24 a: $tType ).
% 1.50/1.24
% 1.50/1.24 thf(cBOOL_PROP_90_pme,conjecture,
% 1.50/1.24 ! [X: a > $o,Y: a > $o] :
% 1.50/1.24 ( ( ( ^ [Xx: a] :
% 1.50/1.24 ( ( X @ Xx )
% 1.50/1.24 & ~ ( Y @ Xx ) ) )
% 1.50/1.24 = ( ^ [Xx: a] :
% 1.50/1.24 ( ( Y @ Xx )
% 1.50/1.24 & ~ ( X @ Xx ) ) ) )
% 1.50/1.24 => ( X = Y ) ) ).
% 1.50/1.24 ------------------------
% 1.50/1.26 % (21089)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_20869 for (3000ds/4Mi)
% 1.50/1.26 % (21089)Instruction limit reached!
% 1.50/1.26 % (21089)------------------------------
% 1.50/1.26 % (21089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (21089)Termination reason: Unknown
% 1.50/1.26 % (21089)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (21089)Memory used [KB]: 5500
% 1.50/1.26 % (21089)Time elapsed: 0.004 s
% 1.50/1.26 % (21089)Instructions burned: 5 (million)
% 1.50/1.26 % (21089)------------------------------
% 1.50/1.26 % (21089)------------------------------
% 1.50/1.26 % (21088)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20869 for (3000ds/183Mi)
% 1.50/1.26 % (21090)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_20869 for (3000ds/27Mi)
% 1.50/1.26 % (21091)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20869 for (3000ds/2Mi)
% 1.50/1.26 % (21094)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20869 for (3000ds/18Mi)
% 1.50/1.26 % (21092)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_20869 for (3000ds/2Mi)
% 1.50/1.26 % (21093)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_20869 for (3000ds/275Mi)
% 1.50/1.26 % (21091)Instruction limit reached!
% 1.50/1.26 % (21091)------------------------------
% 1.50/1.26 % (21091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (21091)Termination reason: Unknown
% 1.50/1.26 % (21091)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (21091)Memory used [KB]: 5500
% 1.50/1.26 % (21091)Time elapsed: 0.004 s
% 1.50/1.26 % (21091)Instructions burned: 2 (million)
% 1.50/1.26 % (21091)------------------------------
% 1.50/1.26 % (21091)------------------------------
% 1.50/1.26 % (21092)Instruction limit reached!
% 1.50/1.26 % (21092)------------------------------
% 1.50/1.26 % (21092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (21092)Termination reason: Unknown
% 1.50/1.26 % (21092)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (21092)Memory used [KB]: 5500
% 1.50/1.26 % (21092)Time elapsed: 0.004 s
% 1.50/1.26 % (21092)Instructions burned: 2 (million)
% 1.50/1.26 % (21092)------------------------------
% 1.50/1.26 % (21092)------------------------------
% 1.50/1.27 % (21088)First to succeed.
% 1.50/1.27 % (21095)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20869 for (2999ds/3Mi)
% 1.50/1.27 % (21093)Also succeeded, but the first one will report.
% 1.50/1.27 % (21090)Also succeeded, but the first one will report.
% 1.50/1.27 % (21088)Refutation found. Thanks to Tanya!
% 1.50/1.27 % SZS status Theorem for DTF2THF_20869
% 1.50/1.27 % SZS output start Proof for DTF2THF_20869
% 1.50/1.27 thf(type_def_5, type, a: $tType).
% 1.50/1.27 thf(func_def_0, type, a: $tType).
% 1.50/1.27 thf(func_def_8, type, sK0: a > $o).
% 1.50/1.27 thf(func_def_9, type, sK1: a > $o).
% 1.50/1.27 thf(func_def_11, type, ph3: !>[X0: $tType]:(X0)).
% 1.50/1.27 thf(func_def_12, type, sK4: a).
% 1.50/1.27 thf(f86,plain,(
% 1.50/1.27 $false),
% 1.50/1.27 inference(avatar_sat_refutation,[status(thm)],[f22,f31,f37,f70,f85])).
% 1.50/1.27 thf(f85,plain,(
% 1.50/1.27 spl2_3 | ~spl2_4),
% 1.50/1.27 inference(avatar_contradiction_clause,[status(thm)],[f84])).
% 1.50/1.27 thf(f84,plain,(
% 1.50/1.27 $false | (spl2_3 | ~spl2_4)),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f80,f25])).
% 1.50/1.27 thf(f25,plain,(
% 1.50/1.27 ((sK1 @ sK4) != $false) | spl2_3),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.50/1.27 thf(f24,definition,(
% 1.50/1.27 spl2_3 <=> ((sK1 @ sK4) = $false)),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.50/1.27 thf(f80,plain,(
% 1.50/1.27 ((sK1 @ sK4) = $false) | ~spl2_4),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.50/1.27 thf(f73,plain,(
% 1.50/1.27 ($true = $false) | ((sK1 @ sK4) = $false) | ~spl2_4),
% 1.50/1.27 inference(superposition,[status(thm)],[f30,f49])).
% 1.50/1.27 thf(f49,plain,(
% 1.50/1.27 ( ! [X1 : a] : (($true = (sK0 @ X1)) | ((sK1 @ X1) = $false)) )),
% 1.50/1.27 inference(duplicate_literal_removal,[status(thm)],[f48])).
% 1.50/1.27 thf(f48,plain,(
% 1.50/1.27 ( ! [X1 : a] : (($true = (sK0 @ X1)) | ((sK1 @ X1) = $false) | ((sK1 @ X1) = $false)) )),
% 1.50/1.27 inference(not_proxy_clausification,[status(thm)],[f45])).
% 1.50/1.27 thf(f45,plain,(
% 1.50/1.27 ( ! [X1 : a] : (((~ (sK1 @ X1)) = $true) | ((sK1 @ X1) = $false) | ($true = (sK0 @ X1))) )),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.50/1.27 thf(f44,plain,(
% 1.50/1.27 ( ! [X1 : a] : (((sK1 @ X1) = $false) | ($true = ((sK0 @ X1) & (~ (sK1 @ X1)))) | ($true = (sK0 @ X1))) )),
% 1.50/1.27 inference(not_proxy_clausification,[status(thm)],[f43])).
% 1.50/1.27 thf(f43,plain,(
% 1.50/1.27 ( ! [X1 : a] : (((sK1 @ X1) = $false) | ((~ (sK0 @ X1)) = $false) | ($true = ((sK0 @ X1) & (~ (sK1 @ X1))))) )),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.50/1.27 thf(f42,plain,(
% 1.50/1.27 ( ! [X1 : a] : ((((~ (sK0 @ X1)) & (sK1 @ X1)) = $false) | ($true = ((sK0 @ X1) & (~ (sK1 @ X1))))) )),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.50/1.27 thf(f40,plain,(
% 1.50/1.27 ( ! [X1 : a] : ((((~ (sK0 @ X1)) & (sK1 @ X1)) = ((sK0 @ X1) & (~ (sK1 @ X1))))) )),
% 1.50/1.27 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.50/1.27 thf(f39,plain,(
% 1.50/1.27 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK0 @ Y0) & (~ (sK1 @ Y0)))) @ X1) = ((^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0))) @ X1))) )),
% 1.50/1.27 inference(argument_congruence,[status(thm)],[f9])).
% 1.50/1.27 thf(f9,plain,(
% 1.50/1.27 ((^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0))) = (^[Y0 : a]: ((sK0 @ Y0) & (~ (sK1 @ Y0)))))),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f8])).
% 1.50/1.27 thf(f8,plain,(
% 1.50/1.27 (sK0 != sK1) & ((^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0))) = (^[Y0 : a]: ((sK0 @ Y0) & (~ (sK1 @ Y0)))))),
% 1.50/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.50/1.27 thf(f7,plain,(
% 1.50/1.27 ? [X0 : a > $o,X1 : a > $o] : ((X0 != X1) & ((^[Y0 : a]: ((X0 @ Y0) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0))))) => ((sK0 != sK1) & ((^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0))) = (^[Y0 : a]: ((sK0 @ Y0) & (~ (sK1 @ Y0))))))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f6,plain,(
% 1.50/1.27 ? [X0 : a > $o,X1 : a > $o] : ((X0 != X1) & ((^[Y0 : a]: ((X0 @ Y0) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0)))))),
% 1.50/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.27 thf(f5,plain,(
% 1.50/1.27 ~! [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ((X0 @ Y0) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0)))) => (X0 = X1))),
% 1.50/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.27 thf(f4,plain,(
% 1.50/1.27 ~! [X0 : a > $o,X1 : a > $o] : (((^[X2 : a] : (~(X1 @ X2) & (X0 @ X2))) = (^[X3 : a] : ((X1 @ X3) & ~(X0 @ X3)))) => (X0 = X1))),
% 1.50/1.27 inference(rectify,[status(thm)],[f2])).
% 1.50/1.27 thf(f2,negated_conjecture,(
% 1.50/1.27 ~! [X1 : a > $o,X0 : a > $o] : (((^[X2 : a] : (~(X0 @ X2) & (X1 @ X2))) = (^[X2 : a] : ((X0 @ X2) & ~(X1 @ X2)))) => (X0 = X1))),
% 1.50/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.27 thf(f1,conjecture,(
% 1.50/1.27 ! [X1 : a > $o,X0 : a > $o] : (((^[X2 : a] : (~(X0 @ X2) & (X1 @ X2))) = (^[X2 : a] : ((X0 @ X2) & ~(X1 @ X2)))) => (X0 = X1))),
% 1.50/1.27 file('/export/starexec/sandbox2/tmp/tmp.6PAx0BJqXm/DTF2THF_20869.p',cBOOL_PROP_90_pme)).
% 1.50/1.27 thf(f30,plain,(
% 1.50/1.27 ((sK0 @ sK4) = $false) | ~spl2_4),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.50/1.27 thf(f28,definition,(
% 1.50/1.27 spl2_4 <=> ((sK0 @ sK4) = $false)),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.50/1.27 thf(f70,plain,(
% 1.50/1.27 spl2_2 | ~spl2_1),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f64,f15,f19])).
% 1.50/1.27 thf(f19,definition,(
% 1.50/1.27 spl2_2 <=> ($true = (sK1 @ sK4))),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.50/1.27 thf(f15,definition,(
% 1.50/1.27 spl2_1 <=> ((sK0 @ sK4) = $true)),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.50/1.27 thf(f64,plain,(
% 1.50/1.27 ($true = (sK1 @ sK4)) | ~spl2_1),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.50/1.27 thf(f57,plain,(
% 1.50/1.27 ($true = $false) | ($true = (sK1 @ sK4)) | ~spl2_1),
% 1.50/1.27 inference(superposition,[status(thm)],[f56,f17])).
% 1.50/1.27 thf(f17,plain,(
% 1.50/1.27 ((sK0 @ sK4) = $true) | ~spl2_1),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f15])).
% 1.50/1.27 thf(f56,plain,(
% 1.50/1.27 ( ! [X1 : a] : (($false = (sK0 @ X1)) | ((sK1 @ X1) = $true)) )),
% 1.50/1.27 inference(duplicate_literal_removal,[status(thm)],[f52])).
% 1.50/1.27 thf(f52,plain,(
% 1.50/1.27 ( ! [X1 : a] : (((sK1 @ X1) = $true) | ($false = (sK0 @ X1)) | ((sK1 @ X1) = $true)) )),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.50/1.27 thf(f51,plain,(
% 1.50/1.27 ( ! [X1 : a] : (($false = (sK0 @ X1)) | (((~ (sK0 @ X1)) & (sK1 @ X1)) = $true) | ((sK1 @ X1) = $true)) )),
% 1.50/1.27 inference(not_proxy_clausification,[status(thm)],[f50])).
% 1.50/1.27 thf(f50,plain,(
% 1.50/1.27 ( ! [X1 : a] : (($false = (sK0 @ X1)) | ((~ (sK1 @ X1)) = $false) | (((~ (sK0 @ X1)) & (sK1 @ X1)) = $true)) )),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.50/1.27 thf(f41,plain,(
% 1.50/1.27 ( ! [X1 : a] : ((((sK0 @ X1) & (~ (sK1 @ X1))) = $false) | (((~ (sK0 @ X1)) & (sK1 @ X1)) = $true)) )),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.50/1.27 thf(f37,plain,(
% 1.50/1.27 ~spl2_2 | ~spl2_3),
% 1.50/1.27 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.50/1.27 thf(f36,plain,(
% 1.50/1.27 $false | (~spl2_2 | ~spl2_3)),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.50/1.27 thf(f33,plain,(
% 1.50/1.27 ($true = $false) | (~spl2_2 | ~spl2_3)),
% 1.50/1.27 inference(superposition,[status(thm)],[f21,f26])).
% 1.50/1.27 thf(f26,plain,(
% 1.50/1.27 ((sK1 @ sK4) = $false) | ~spl2_3),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.50/1.27 thf(f21,plain,(
% 1.50/1.27 ($true = (sK1 @ sK4)) | ~spl2_2),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.50/1.27 thf(f31,plain,(
% 1.50/1.27 spl2_3 | spl2_4),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f13,f28,f24])).
% 1.50/1.27 thf(f13,plain,(
% 1.50/1.27 ((sK0 @ sK4) = $false) | ((sK1 @ sK4) = $false)),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.50/1.27 thf(f11,plain,(
% 1.50/1.27 ((sK0 @ sK4) != (sK1 @ sK4))),
% 1.50/1.27 inference(negative_extensionality,[status(thm)],[f10])).
% 1.50/1.27 thf(f10,plain,(
% 1.50/1.27 (sK0 != sK1)),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f8])).
% 1.50/1.27 thf(f22,plain,(
% 1.50/1.27 spl2_1 | spl2_2),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f12,f19,f15])).
% 1.50/1.27 thf(f12,plain,(
% 1.50/1.27 ($true = (sK1 @ sK4)) | ((sK0 @ sK4) = $true)),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.50/1.27 % SZS output end Proof for DTF2THF_20869
% 1.50/1.27 % (21088)------------------------------
% 1.50/1.27 % (21088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (21088)Termination reason: Refutation
% 1.50/1.27
% 1.50/1.27 % (21088)Memory used [KB]: 5500
% 1.50/1.27 % (21088)Time elapsed: 0.007 s
% 1.50/1.27 % (21088)Instructions burned: 3 (million)
% 1.50/1.27 % (21088)------------------------------
% 1.50/1.27 % (21088)------------------------------
% 1.50/1.27 % (21087)Success in time 0.022 s
%------------------------------------------------------------------------------