%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET587^5 : 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 : n008.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 09:31:49 AM UTC 2026
% Result : Theorem 1.66s 1.42s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 4 unt; 0 typ; 4 def)
% Number of atoms : 278 ( 82 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 317 ( 85 ~; 62 |; 38 &; 115 @)
% ( 9 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 89 ( 48 ^; 28 !; 13 ?; 89 :)
% 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 ).
thf(func_def_12,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK5: a ).
thf(f63,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f28,f33,f46,f62]) ).
thf(f62,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f61]) ).
thf(f61,plain,
( $false
| spl3_1
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true = $false )
| spl3_1
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f56,f32]) ).
thf(f32,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl3_4
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f56,plain,
( ( $false
= ( sK0 @ sK2 ) )
| spl3_1
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $true != $true )
| spl3_1
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f19,f54]) ).
thf(f54,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl3_2 ),
inference(not_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( ~ ( sK1 @ X1 ) )
= $false ) )
| ~ spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ! [X1: a] :
( $false
= ( ~ ( sK1 @ X1 )
& ( sK0 @ X1 ) ) )
| ~ spl3_2 ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) )
| ~ spl3_2 ),
inference(argument_congruence,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl3_2
<=> ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f19,plain,
( ( $true
!= ( sK1 @ sK2 ) )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl3_1
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f46,plain,
( spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| spl3_2
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f41,f36]) ).
thf(f36,plain,
( ( $true
= ( sK0 @ sK5 ) )
| spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $false
!= ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) ) )
| spl3_2 ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK5 )
!= ( ^ [Y0: a] : $false
@ sK5 ) )
| spl3_2 ),
inference(negative_extensionality,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f41,plain,
( ( $true
!= ( sK0 @ sK5 ) )
| spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true
!= ( sK0 @ sK5 ) )
| ( $true = $false )
| spl3_2
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f38,f27]) ).
thf(f27,plain,
( ! [X3: a] :
( ( ( sK1 @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl3_3
<=> ! [X3: a] :
( ( ( sK1 @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f38,plain,
( ( $false
= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(not_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true
= ( ~ ( sK1 @ sK5 ) ) )
| spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f33,plain,
( spl3_4
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f21,f30]) ).
thf(f15,plain,
( ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( $true
= ( sK0 @ sK2 ) )
& ( $true
!= ( sK1 @ sK2 ) ) )
| ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
= $true ) )
| ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) )
& ( ! [X3: a] :
( ( $true
!= ( X0 @ X3 ) )
| ( ( X1 @ X3 )
= $true ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) ) )
=> ( ( ? [X2: a] :
( ( $true
= ( sK0 @ X2 ) )
& ( $true
!= ( sK1 @ X2 ) ) )
| ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
= $true ) )
| ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X2: a] :
( ( $true
= ( sK0 @ X2 ) )
& ( $true
!= ( sK1 @ X2 ) ) )
=> ( ( $true
= ( sK0 @ sK2 ) )
& ( $true
!= ( sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) )
& ( ! [X3: a] :
( ( $true
!= ( X0 @ X3 ) )
| ( ( X1 @ X3 )
= $true ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) )
& ( ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
<~> ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) )
<=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
<=> ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
=> ( $true
= ( X1 @ X4 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) )
= ( ^ [X3: a] : $false ) )
<=> ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) )
= ( ^ [X2: a] : $false ) )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) )
= ( ^ [X2: a] : $false ) )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WrOiXTVRlG/DTF2THF_29854.p',cBOOL_PROP_45_pme) ).
thf(f28,plain,
( spl3_3
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f21,f26]) ).
thf(f13,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
= $true )
| ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f24,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f21,f17]) ).
thf(f14,plain,
( ( ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) )
| ( $true
!= ( sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET587^5 : 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
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:59:39 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SET587^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : TPS problem BOOL-PROP-45
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English : Trybulec's 45th Boolean property of sets
% 0.19/0.47
% 0.19/0.47 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_0345 [Bro09]
% 0.19/0.47 % : BOOL-PROP-45 [TPS]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % 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, 0.14 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
% 0.19/0.47 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.47 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 1 ( 2 avg)
% 0.19/0.47 % Number of connectives : 8 ( 1 ~; 0 |; 1 &; 4 @)
% 0.19/0.47 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.47 % Number of types : 2 ( 1 usr)
% 0.19/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.47 % : Polymorphic definitions expanded.
% 0.19/0.47 % :
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(a_type,type,
% 0.19/0.47 a: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(cBOOL_PROP_45_pme,conjecture,
% 0.19/0.47 ! [X: a > $o,Y: a > $o] :
% 0.19/0.47 ( ( ( ^ [Xx: a] :
% 0.19/0.47 ( ( X @ Xx )
% 0.19/0.47 & ~ ( Y @ Xx ) ) )
% 0.19/0.47 = ( ^ [Xx: a] : $false ) )
% 0.19/0.47 <=> ! [Xx: a] :
% 0.19/0.47 ( ( X @ Xx )
% 0.19/0.47 => ( Y @ Xx ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.46/1.39 ---- Embedded in THF ---
% 1.46/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.39 %%% Generated on Tue Feb 24 11:59:40 EST 2026
% 1.46/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.39 %%% Logic specification used:
% 1.46/1.39 %%% thf(spec, logic, $$dhol).
% 1.46/1.39
% 1.46/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WrOiXTVRlG/DTF2DTF29854.p
% See solution above
% 1.46/1.39 ------------------------
% 1.46/1.39 ---- Cleaned THF ---
% 1.46/1.40 thf(a_type,type,
% 1.46/1.40 a: $tType ).
% 1.46/1.40
% 1.46/1.40 thf(cBOOL_PROP_45_pme,conjecture,
% 1.46/1.40 ! [X: a > $o,Y: a > $o] :
% 1.46/1.40 ( ( ( ^ [Xx: a] :
% 1.46/1.40 ( ( X @ Xx )
% 1.46/1.40 & ~ ( Y @ Xx ) ) )
% 1.46/1.40 = ( ^ [Xx: a] : $false ) )
% 1.46/1.40 <=> ! [Xx: a] :
% 1.46/1.40 ( ( X @ Xx )
% 1.46/1.40 => ( Y @ Xx ) ) ) ).
% 1.46/1.40 ------------------------
% 1.66/1.42 % (29954)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29854 for (3000ds/2Mi)
% 1.66/1.42 % (29955)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_29854 for (3000ds/2Mi)
% 1.66/1.42 % (29956)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_29854 for (3000ds/275Mi)
% 1.66/1.42 % (29952)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_29854 for (3000ds/4Mi)
% 1.66/1.42 % (29953)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_29854 for (3000ds/27Mi)
% 1.66/1.42 % (29951)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29854 for (3000ds/183Mi)
% 1.66/1.42 % (29957)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29854 for (3000ds/18Mi)
% 1.66/1.42 % (29954)Instruction limit reached!
% 1.66/1.42 % (29954)------------------------------
% 1.66/1.42 % (29954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (29954)Termination reason: Unknown
% 1.66/1.42 % (29954)Termination phase: Saturation
% 1.66/1.42 % (29955)Instruction limit reached!
% 1.66/1.42 % (29955)------------------------------
% 1.66/1.42 % (29955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42
% 1.66/1.42 % (29954)Memory used [KB]: 5500
% 1.66/1.42 % (29954)Time elapsed: 0.003 s
% 1.66/1.42 % (29954)Instructions burned: 2 (million)
% 1.66/1.42 % (29954)------------------------------
% 1.66/1.42 % (29954)------------------------------
% 1.66/1.42 % (29955)Termination reason: Unknown
% 1.66/1.42 % (29955)Termination phase: Saturation
% 1.66/1.42
% 1.66/1.42 % (29955)Memory used [KB]: 5500
% 1.66/1.42 % (29955)Time elapsed: 0.003 s
% 1.66/1.42 % (29955)Instructions burned: 2 (million)
% 1.66/1.42 % (29955)------------------------------
% 1.66/1.42 % (29955)------------------------------
% 1.66/1.42 % (29956)First to succeed.
% 1.66/1.42 % (29952)Instruction limit reached!
% 1.66/1.42 % (29952)------------------------------
% 1.66/1.42 % (29952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (29952)Termination reason: Unknown
% 1.66/1.42 % (29952)Termination phase: Saturation
% 1.66/1.42
% 1.66/1.42 % (29952)Memory used [KB]: 5500
% 1.66/1.42 % (29952)Time elapsed: 0.005 s
% 1.66/1.42 % (29952)Instructions burned: 4 (million)
% 1.66/1.42 % (29952)------------------------------
% 1.66/1.42 % (29952)------------------------------
% 1.66/1.42 % (29951)Also succeeded, but the first one will report.
% 1.66/1.42 % (29956)Refutation found. Thanks to Tanya!
% 1.66/1.42 % SZS status Theorem for DTF2THF_29854
% 1.66/1.42 % SZS output start Proof for DTF2THF_29854
% 1.66/1.42 thf(type_def_5, type, a: $tType).
% 1.66/1.42 thf(func_def_0, type, a: $tType).
% 1.66/1.42 thf(func_def_8, type, sK0: a > $o).
% 1.66/1.42 thf(func_def_9, type, sK1: a > $o).
% 1.66/1.42 thf(func_def_10, type, sK2: a).
% 1.66/1.42 thf(func_def_12, type, ph4: !>[X0: $tType]:(X0)).
% 1.66/1.42 thf(func_def_13, type, sK5: a).
% 1.66/1.42 thf(f63,plain,(
% 1.66/1.42 $false),
% 1.66/1.42 inference(avatar_sat_refutation,[status(thm)],[f24,f28,f33,f46,f62])).
% 1.66/1.42 thf(f62,plain,(
% 1.66/1.42 spl3_1 | ~spl3_2 | ~spl3_4),
% 1.66/1.42 inference(avatar_contradiction_clause,[status(thm)],[f61])).
% 1.66/1.42 thf(f61,plain,(
% 1.66/1.42 $false | (spl3_1 | ~spl3_2 | ~spl3_4)),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.66/1.42 thf(f57,plain,(
% 1.66/1.42 ($true = $false) | (spl3_1 | ~spl3_2 | ~spl3_4)),
% 1.66/1.42 inference(superposition,[status(thm)],[f56,f32])).
% 1.66/1.42 thf(f32,plain,(
% 1.66/1.42 ($true = (sK0 @ sK2)) | ~spl3_4),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.66/1.42 thf(f30,definition,(
% 1.66/1.42 spl3_4 <=> ($true = (sK0 @ sK2))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.66/1.42 thf(f56,plain,(
% 1.66/1.42 ($false = (sK0 @ sK2)) | (spl3_1 | ~spl3_2)),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.66/1.42 thf(f55,plain,(
% 1.66/1.42 ($false = (sK0 @ sK2)) | ($true != $true) | (spl3_1 | ~spl3_2)),
% 1.66/1.42 inference(superposition,[status(thm)],[f19,f54])).
% 1.66/1.42 thf(f54,plain,(
% 1.66/1.42 ( ! [X1 : a] : (($true = (sK1 @ X1)) | ($false = (sK0 @ X1))) ) | ~spl3_2),
% 1.66/1.42 inference(not_proxy_clausification,[status(thm)],[f53])).
% 1.66/1.42 thf(f53,plain,(
% 1.66/1.42 ( ! [X1 : a] : (($false = (sK0 @ X1)) | ((~ (sK1 @ X1)) = $false)) ) | ~spl3_2),
% 1.66/1.42 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.66/1.42 thf(f52,plain,(
% 1.66/1.42 ( ! [X1 : a] : (($false = ((~ (sK1 @ X1)) & (sK0 @ X1)))) ) | ~spl3_2),
% 1.66/1.42 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.66/1.42 thf(f51,plain,(
% 1.66/1.42 ( ! [X1 : a] : ((((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) @ X1) = ((^[Y0 : a]: ($false)) @ X1))) ) | ~spl3_2),
% 1.66/1.42 inference(argument_congruence,[status(thm)],[f22])).
% 1.66/1.42 thf(f22,plain,(
% 1.66/1.42 ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) = (^[Y0 : a]: ($false))) | ~spl3_2),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.66/1.42 thf(f21,definition,(
% 1.66/1.42 spl3_2 <=> ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) = (^[Y0 : a]: ($false)))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.66/1.42 thf(f19,plain,(
% 1.66/1.42 ($true != (sK1 @ sK2)) | spl3_1),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.66/1.42 thf(f17,definition,(
% 1.66/1.42 spl3_1 <=> ($true = (sK1 @ sK2))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.66/1.42 thf(f46,plain,(
% 1.66/1.42 spl3_2 | ~spl3_3),
% 1.66/1.42 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.66/1.42 thf(f45,plain,(
% 1.66/1.42 $false | (spl3_2 | ~spl3_3)),
% 1.66/1.42 inference(subsumption_resolution,[status(thm)],[f41,f36])).
% 1.66/1.42 thf(f36,plain,(
% 1.66/1.42 ($true = (sK0 @ sK5)) | spl3_2),
% 1.66/1.42 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.66/1.42 thf(f35,plain,(
% 1.66/1.42 ($false != ((~ (sK1 @ sK5)) & (sK0 @ sK5))) | spl3_2),
% 1.66/1.42 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.66/1.42 thf(f34,plain,(
% 1.66/1.42 (((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) @ sK5) != ((^[Y0 : a]: ($false)) @ sK5)) | spl3_2),
% 1.66/1.42 inference(negative_extensionality,[status(thm)],[f23])).
% 1.66/1.42 thf(f23,plain,(
% 1.66/1.42 ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) != (^[Y0 : a]: ($false))) | spl3_2),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.66/1.42 thf(f41,plain,(
% 1.66/1.42 ($true != (sK0 @ sK5)) | (spl3_2 | ~spl3_3)),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.66/1.42 thf(f39,plain,(
% 1.66/1.42 ($true != (sK0 @ sK5)) | ($true = $false) | (spl3_2 | ~spl3_3)),
% 1.66/1.42 inference(superposition,[status(thm)],[f38,f27])).
% 1.66/1.42 thf(f27,plain,(
% 1.66/1.42 ( ! [X3 : a] : (((sK1 @ X3) = $true) | ($true != (sK0 @ X3))) ) | ~spl3_3),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.66/1.42 thf(f26,definition,(
% 1.66/1.42 spl3_3 <=> ! [X3 : a] : (((sK1 @ X3) = $true) | ($true != (sK0 @ X3)))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.66/1.42 thf(f38,plain,(
% 1.66/1.42 ($false = (sK1 @ sK5)) | spl3_2),
% 1.66/1.42 inference(not_proxy_clausification,[status(thm)],[f37])).
% 1.66/1.42 thf(f37,plain,(
% 1.66/1.42 ($true = (~ (sK1 @ sK5))) | spl3_2),
% 1.66/1.42 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.66/1.42 thf(f33,plain,(
% 1.66/1.42 spl3_4 | ~spl3_2),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f15,f21,f30])).
% 1.66/1.42 thf(f15,plain,(
% 1.66/1.42 ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) != (^[Y0 : a]: ($false))) | ($true = (sK0 @ sK2))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.66/1.42 thf(f12,plain,(
% 1.66/1.42 ((($true = (sK0 @ sK2)) & ($true != (sK1 @ sK2))) | ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) != (^[Y0 : a]: ($false)))) & (! [X3 : a] : (($true != (sK0 @ X3)) | ((sK1 @ X3) = $true)) | ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) = (^[Y0 : a]: ($false))))),
% 1.66/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10])).
% 1.66/1.42 thf(f10,plain,(
% 1.66/1.42 ? [X0 : a > $o,X1 : a > $o] : ((? [X2 : a] : (((X0 @ X2) = $true) & ((X1 @ X2) != $true)) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0))))) & (! [X3 : a] : (($true != (X0 @ X3)) | ((X1 @ X3) = $true)) | ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0)))))) => ((? [X2 : a] : (($true = (sK0 @ X2)) & ($true != (sK1 @ X2))) | ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) != (^[Y0 : a]: ($false)))) & (! [X3 : a] : (($true != (sK0 @ X3)) | ((sK1 @ X3) = $true)) | ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) = (^[Y0 : a]: ($false)))))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f11,plain,(
% 1.66/1.42 ? [X2 : a] : (($true = (sK0 @ X2)) & ($true != (sK1 @ X2))) => (($true = (sK0 @ sK2)) & ($true != (sK1 @ sK2)))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f9,plain,(
% 1.66/1.42 ? [X0 : a > $o,X1 : a > $o] : ((? [X2 : a] : (((X0 @ X2) = $true) & ((X1 @ X2) != $true)) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0))))) & (! [X3 : a] : (($true != (X0 @ X3)) | ((X1 @ X3) = $true)) | ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0))))))),
% 1.66/1.42 inference(rectify,[status(thm)],[f8])).
% 1.66/1.42 thf(f8,plain,(
% 1.66/1.42 ? [X0 : a > $o,X1 : a > $o] : ((? [X2 : a] : (((X0 @ X2) = $true) & ((X1 @ X2) != $true)) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0))))) & (! [X2 : a] : (((X0 @ X2) != $true) | ((X1 @ X2) = $true)) | ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0))))))),
% 1.66/1.42 inference(nnf_transformation,[status(thm)],[f7])).
% 1.66/1.42 thf(f7,plain,(
% 1.66/1.42 ? [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0)))) <~> ! [X2 : a] : (((X0 @ X2) != $true) | ((X1 @ X2) = $true)))),
% 1.66/1.42 inference(ennf_transformation,[status(thm)],[f6])).
% 1.66/1.42 thf(f6,plain,(
% 1.66/1.42 ~! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X0 @ X2) = $true) => ((X1 @ X2) = $true)) <=> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0)))))),
% 1.66/1.42 inference(rectify,[status(thm)],[f5])).
% 1.66/1.42 thf(f5,plain,(
% 1.66/1.42 ~! [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0)))) <=> ! [X4 : a] : (($true = (X0 @ X4)) => ($true = (X1 @ X4))))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.42 thf(f4,plain,(
% 1.66/1.42 ~! [X0 : a > $o,X1 : a > $o] : (((^[X2 : a] : ((X0 @ X2) & ~(X1 @ X2))) = (^[X3 : a] : ($false))) <=> ! [X4 : a] : ((X0 @ X4) => (X1 @ X4)))),
% 1.66/1.42 inference(rectify,[status(thm)],[f2])).
% 1.66/1.42 thf(f2,negated_conjecture,(
% 1.66/1.42 ~! [X0 : a > $o,X1 : a > $o] : (((^[X2 : a] : ((X0 @ X2) & ~(X1 @ X2))) = (^[X2 : a] : ($false))) <=> ! [X2 : a] : ((X0 @ X2) => (X1 @ X2)))),
% 1.66/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.42 thf(f1,conjecture,(
% 1.66/1.42 ! [X0 : a > $o,X1 : a > $o] : (((^[X2 : a] : ((X0 @ X2) & ~(X1 @ X2))) = (^[X2 : a] : ($false))) <=> ! [X2 : a] : ((X0 @ X2) => (X1 @ X2)))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.WrOiXTVRlG/DTF2THF_29854.p',cBOOL_PROP_45_pme)).
% 1.66/1.42 thf(f28,plain,(
% 1.66/1.42 spl3_3 | spl3_2),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f13,f21,f26])).
% 1.66/1.42 thf(f13,plain,(
% 1.66/1.42 ( ! [X3 : a] : (((sK1 @ X3) = $true) | ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) = (^[Y0 : a]: ($false))) | ($true != (sK0 @ X3))) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.66/1.42 thf(f24,plain,(
% 1.66/1.42 ~spl3_1 | ~spl3_2),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f14,f21,f17])).
% 1.66/1.42 thf(f14,plain,(
% 1.66/1.42 ((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) != (^[Y0 : a]: ($false))) | ($true != (sK1 @ sK2))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.66/1.42 % SZS output end Proof for DTF2THF_29854
% 1.66/1.42 % (29956)------------------------------
% 1.66/1.42 % (29956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (29956)Termination reason: Refutation
% 1.66/1.42
% 1.66/1.42 % (29956)Memory used [KB]: 5500
% 1.66/1.42 % (29956)Time elapsed: 0.005 s
% 1.66/1.42 % (29956)Instructions burned: 3 (million)
% 1.66/1.42 % (29956)------------------------------
% 1.66/1.42 % (29956)------------------------------
% 1.66/1.42 % (29950)Success in time 0.019 s
%------------------------------------------------------------------------------