%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET633^5 : 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 : n026.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 09:31:59 AM UTC 2026
% Result : Theorem 1.63s 1.30s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 3 unt; 0 typ; 3 def)
% Number of atoms : 337 ( 126 equ; 0 cnn)
% Maximal formula atoms : 22 ( 9 avg)
% Number of connectives : 388 ( 82 ~; 64 |; 61 &; 156 @)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 44 !; 18 ?; 62 :)
% 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_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_7,type,
sK2: a > $o ).
thf(func_def_8,type,
sK3: a ).
thf(f43,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f29,f36,f39,f42]) ).
thf(f42,plain,
( spl4_3
| spl4_2
| ~ spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f41,f21,f25,f33]) ).
thf(f33,definition,
( spl4_3
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f25,definition,
( spl4_2
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f21,definition,
( spl4_1
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f41,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( $true != $true )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f19,f22]) ).
thf(f22,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f19,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
= $true )
| ( ( sK2 @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
= $true )
| ( ( sK2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( ( sK2 @ X4 )
!= $true )
| ( ( sK0 @ X4 )
= $true ) )
& ( ( sK0 @ sK3 )
!= $true )
& ( ( ( ( sK2 @ sK3 )
!= $true )
& ( ( sK1 @ sK3 )
= $true ) )
| ( ( ( sK2 @ sK3 )
= $true )
& ( ( sK1 @ sK3 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
| ( ( X2 @ X4 )
!= $true )
| ( ( X0 @ X4 )
= $true ) )
& ? [X5: a] :
( ( ( X0 @ X5 )
!= $true )
& ( ( ( $true
!= ( X2 @ X5 ) )
& ( ( X1 @ X5 )
= $true ) )
| ( ( $true
= ( X2 @ X5 ) )
& ( ( X1 @ X5 )
!= $true ) ) ) ) )
=> ( ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
= $true )
| ( ( sK2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( ( sK2 @ X4 )
!= $true )
| ( ( sK0 @ X4 )
= $true ) )
& ? [X5: a] :
( ( ( sK0 @ X5 )
!= $true )
& ( ( ( $true
!= ( sK2 @ X5 ) )
& ( ( sK1 @ X5 )
= $true ) )
| ( ( $true
= ( sK2 @ X5 ) )
& ( ( sK1 @ X5 )
!= $true ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: a] :
( ( ( sK0 @ X5 )
!= $true )
& ( ( ( $true
!= ( sK2 @ X5 ) )
& ( ( sK1 @ X5 )
= $true ) )
| ( ( $true
= ( sK2 @ X5 ) )
& ( ( sK1 @ X5 )
!= $true ) ) ) )
=> ( ( ( sK0 @ sK3 )
!= $true )
& ( ( ( ( sK2 @ sK3 )
!= $true )
& ( ( sK1 @ sK3 )
= $true ) )
| ( ( ( sK2 @ sK3 )
= $true )
& ( ( sK1 @ sK3 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
| ( ( X2 @ X4 )
!= $true )
| ( ( X0 @ X4 )
= $true ) )
& ? [X5: a] :
( ( ( X0 @ X5 )
!= $true )
& ( ( ( $true
!= ( X2 @ X5 ) )
& ( ( X1 @ X5 )
= $true ) )
| ( ( $true
= ( X2 @ X5 ) )
& ( ( X1 @ X5 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ! [X4: a] :
( ( ( X2 @ X4 )
!= $true )
| ( ( X0 @ X4 )
= $true )
| ( ( X1 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ? [X5: a] :
( ( ( X0 @ X5 )
!= $true )
& ( ( ( ( X1 @ X5 )
!= $true )
& ( $true
= ( X2 @ X5 ) ) )
| ( ( ( X1 @ X5 )
= $true )
& ( $true
!= ( X2 @ X5 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ? [X5: a] :
( ( ( X0 @ X5 )
!= $true )
& ( ( ( ( X1 @ X5 )
!= $true )
& ( $true
= ( X2 @ X5 ) ) )
| ( ( ( X1 @ X5 )
= $true )
& ( $true
!= ( X2 @ X5 ) ) ) ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
| ( ( X2 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ! [X4: a] :
( ( ( ( X2 @ X4 )
= $true )
& ( ( X1 @ X4 )
!= $true ) )
=> ( ( X0 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( ( X1 @ X3 )
= $true )
& ( ( X2 @ X3 )
!= $true ) )
=> ( ( X0 @ X3 )
= $true ) ) )
=> ! [X5: a] :
( ( ( ( ( X1 @ X5 )
!= $true )
& ( $true
= ( X2 @ X5 ) ) )
| ( ( ( X1 @ X5 )
= $true )
& ( $true
!= ( X2 @ X5 ) ) ) )
=> ( ( X0 @ X5 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( ( X2 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
=> ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( ( X2 @ X4 )
= $true )
& ( ( X1 @ X4 )
!= $true ) )
=> ( ( X0 @ X4 )
= $true ) ) )
=> ! [X5: a] :
( ( ( ( ( X1 @ X5 )
!= $true )
& ( $true
= ( X2 @ X5 ) ) )
| ( ( ( X1 @ X5 )
= $true )
& ( $true
!= ( X2 @ X5 ) ) ) )
=> ( ( X0 @ X5 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) )
=> ( X0 @ X3 ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
& ~ ( X1 @ X4 ) )
=> ( X0 @ X4 ) ) )
=> ! [X5: a] :
( ( ( ~ ( X1 @ X5 )
& ( X2 @ X5 ) )
| ( ( X1 @ X5 )
& ~ ( X2 @ X5 ) ) )
=> ( X0 @ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] :
( ( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
=> ( X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] :
( ( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ~ ( X0 @ X3 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7cg0CmW1X9/DTF2THF_12360.p',cBOOL_PROP_115_pme) ).
thf(f39,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true != $true )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f17,f35]) ).
thf(f35,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f17,plain,
( ( sK0 @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f36,plain,
( spl4_3
| spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f31,f25,f21,f33]) ).
thf(f31,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true != $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f18,f26]) ).
thf(f26,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f18,plain,
! [X4: a] :
( ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( sK1 @ X4 ) )
| ( ( sK0 @ X4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f29,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f14,f21,f25]) ).
thf(f14,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f28,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f25,f21]) ).
thf(f15,plain,
( ( ( sK2 @ sK3 )
!= $true )
| ( ( sK1 @ sK3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET633^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n026.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 12:01:25 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SET633^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : TPS problem BOOL-PROP-115
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : Trybulec's 115th Boolean property of sets
% 0.20/0.46
% 0.20/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_0363 [Bro09]
% 0.20/0.46 % : BOOL-PROP-115 [TPS]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.46 % Number of connectives : 25 ( 4 ~; 1 |; 5 &; 11 @)
% 0.20/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 11 ( 11 avg)
% 0.20/0.46 % Number of types : 2 ( 1 usr)
% 0.20/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.46 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.20/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 % : Polymorphic definitions expanded.
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(a_type,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(cBOOL_PROP_115_pme,conjecture,
% 0.20/0.46 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.20/0.46 ( ( ! [Xx: a] :
% 0.20/0.46 ( ( ( X @ Xx )
% 0.20/0.46 & ~ ( Y @ Xx ) )
% 0.20/0.46 => ( Z @ Xx ) )
% 0.20/0.46 & ! [Xx: a] :
% 0.20/0.46 ( ( ( Y @ Xx )
% 0.20/0.46 & ~ ( X @ Xx ) )
% 0.20/0.46 => ( Z @ Xx ) ) )
% 0.20/0.46 => ! [Xx: a] :
% 0.20/0.46 ( ( ( ( X @ Xx )
% 0.20/0.46 & ~ ( Y @ Xx ) )
% 0.20/0.46 | ( ( Y @ Xx )
% 0.20/0.46 & ~ ( X @ Xx ) ) )
% 0.20/0.46 => ( Z @ Xx ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 12:01:26 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7cg0CmW1X9/DTF2DTF12360.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.28 thf(a_type,type,
% 1.46/1.28 a: $tType ).
% 1.46/1.28
% 1.46/1.28 thf(cBOOL_PROP_115_pme,conjecture,
% 1.46/1.28 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.46/1.28 ( ( ! [Xx: a] :
% 1.46/1.28 ( ( ( X @ Xx )
% 1.46/1.28 & ~ ( Y @ Xx ) )
% 1.46/1.28 => ( Z @ Xx ) )
% 1.46/1.28 & ! [Xx: a] :
% 1.46/1.28 ( ( ( Y @ Xx )
% 1.46/1.28 & ~ ( X @ Xx ) )
% 1.46/1.28 => ( Z @ Xx ) ) )
% 1.46/1.28 => ! [Xx: a] :
% 1.46/1.28 ( ( ( ( X @ Xx )
% 1.46/1.28 & ~ ( Y @ Xx ) )
% 1.46/1.28 | ( ( Y @ Xx )
% 1.46/1.28 & ~ ( X @ Xx ) ) )
% 1.46/1.28 => ( Z @ Xx ) ) ) ).
% 1.46/1.28 ------------------------
% 1.63/1.30 % (12515)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_12360 for (3000ds/27Mi)
% 1.63/1.30 % (12515)First to succeed.
% 1.63/1.30 % (12516)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12360 for (3000ds/2Mi)
% 1.63/1.30 % (12516)Instruction limit reached!
% 1.63/1.30 % (12516)------------------------------
% 1.63/1.30 % (12516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (12516)Termination reason: Unknown
% 1.63/1.30 % (12516)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (12516)Memory used [KB]: 5500
% 1.63/1.30 % (12516)Time elapsed: 0.003 s
% 1.63/1.30 % (12516)Instructions burned: 2 (million)
% 1.63/1.30 % (12516)------------------------------
% 1.63/1.30 % (12516)------------------------------
% 1.63/1.30 % (12515)Refutation found. Thanks to Tanya!
% 1.63/1.30 % SZS status Theorem for DTF2THF_12360
% 1.63/1.30 % SZS output start Proof for DTF2THF_12360
% 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_5, type, sK0: a > $o).
% 1.63/1.30 thf(func_def_6, type, sK1: a > $o).
% 1.63/1.30 thf(func_def_7, type, sK2: a > $o).
% 1.63/1.30 thf(func_def_8, type, sK3: a).
% 1.63/1.30 thf(f43,plain,(
% 1.63/1.30 $false),
% 1.63/1.30 inference(avatar_sat_refutation,[status(thm)],[f28,f29,f36,f39,f42])).
% 1.63/1.30 thf(f42,plain,(
% 1.63/1.30 spl4_3 | spl4_2 | ~spl4_1),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f41,f21,f25,f33])).
% 1.63/1.30 thf(f33,definition,(
% 1.63/1.30 spl4_3 <=> ((sK0 @ sK3) = $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.63/1.30 thf(f25,definition,(
% 1.63/1.30 spl4_2 <=> ((sK2 @ sK3) = $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.63/1.30 thf(f21,definition,(
% 1.63/1.30 spl4_1 <=> ((sK1 @ sK3) = $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.63/1.30 thf(f41,plain,(
% 1.63/1.30 ((sK0 @ sK3) = $true) | ((sK2 @ sK3) = $true) | ~spl4_1),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.63/1.30 thf(f40,plain,(
% 1.63/1.30 ((sK2 @ sK3) = $true) | ((sK0 @ sK3) = $true) | ($true != $true) | ~spl4_1),
% 1.63/1.30 inference(superposition,[status(thm)],[f19,f22])).
% 1.63/1.30 thf(f22,plain,(
% 1.63/1.30 ((sK1 @ sK3) = $true) | ~spl4_1),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.63/1.30 thf(f19,plain,(
% 1.63/1.30 ( ! [X3 : a] : (((sK1 @ X3) != $true) | ((sK0 @ X3) = $true) | ((sK2 @ X3) = $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.30 thf(f12,plain,(
% 1.63/1.30 ! [X3 : a] : (((sK1 @ X3) != $true) | ((sK0 @ X3) = $true) | ((sK2 @ X3) = $true)) & ! [X4 : a] : (($true = (sK1 @ X4)) | ((sK2 @ X4) != $true) | ((sK0 @ X4) = $true)) & (((sK0 @ sK3) != $true) & ((((sK2 @ sK3) != $true) & ((sK1 @ sK3) = $true)) | (((sK2 @ sK3) = $true) & ((sK1 @ sK3) != $true))))),
% 1.63/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10])).
% 1.63/1.30 thf(f10,plain,(
% 1.63/1.30 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X1 @ X3) != $true) | ((X0 @ X3) = $true) | ((X2 @ X3) = $true)) & ! [X4 : a] : (((X1 @ X4) = $true) | ((X2 @ X4) != $true) | ((X0 @ X4) = $true)) & ? [X5 : a] : (((X0 @ X5) != $true) & ((($true != (X2 @ X5)) & ((X1 @ X5) = $true)) | (($true = (X2 @ X5)) & ((X1 @ X5) != $true))))) => (! [X3 : a] : (((sK1 @ X3) != $true) | ((sK0 @ X3) = $true) | ((sK2 @ X3) = $true)) & ! [X4 : a] : (($true = (sK1 @ X4)) | ((sK2 @ X4) != $true) | ((sK0 @ X4) = $true)) & ? [X5 : a] : (((sK0 @ X5) != $true) & ((($true != (sK2 @ X5)) & ((sK1 @ X5) = $true)) | (($true = (sK2 @ X5)) & ((sK1 @ X5) != $true)))))),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f11,plain,(
% 1.63/1.30 ? [X5 : a] : (((sK0 @ X5) != $true) & ((($true != (sK2 @ X5)) & ((sK1 @ X5) = $true)) | (($true = (sK2 @ X5)) & ((sK1 @ X5) != $true)))) => (((sK0 @ sK3) != $true) & ((((sK2 @ sK3) != $true) & ((sK1 @ sK3) = $true)) | (((sK2 @ sK3) = $true) & ((sK1 @ sK3) != $true))))),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f9,plain,(
% 1.63/1.30 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X1 @ X3) != $true) | ((X0 @ X3) = $true) | ((X2 @ X3) = $true)) & ! [X4 : a] : (((X1 @ X4) = $true) | ((X2 @ X4) != $true) | ((X0 @ X4) = $true)) & ? [X5 : a] : (((X0 @ X5) != $true) & ((($true != (X2 @ X5)) & ((X1 @ X5) = $true)) | (($true = (X2 @ X5)) & ((X1 @ X5) != $true)))))),
% 1.63/1.30 inference(rectify,[status(thm)],[f8])).
% 1.63/1.30 thf(f8,plain,(
% 1.63/1.30 ? [X0 : a > $o,X2 : a > $o,X1 : a > $o] : (! [X4 : a] : (((X2 @ X4) != $true) | ((X0 @ X4) = $true) | ((X1 @ X4) = $true)) & ! [X3 : a] : (((X2 @ X3) = $true) | ((X1 @ X3) != $true) | ((X0 @ X3) = $true)) & ? [X5 : a] : (((X0 @ X5) != $true) & ((((X1 @ X5) != $true) & ($true = (X2 @ X5))) | (((X1 @ X5) = $true) & ($true != (X2 @ X5))))))),
% 1.63/1.30 inference(flattening,[status(thm)],[f7])).
% 1.63/1.30 thf(f7,plain,(
% 1.63/1.30 ? [X0 : a > $o,X2 : a > $o,X1 : a > $o] : (? [X5 : a] : (((X0 @ X5) != $true) & ((((X1 @ X5) != $true) & ($true = (X2 @ X5))) | (((X1 @ X5) = $true) & ($true != (X2 @ X5))))) & (! [X4 : a] : (((X0 @ X4) = $true) | (((X2 @ X4) != $true) | ((X1 @ X4) = $true))) & ! [X3 : a] : (((X0 @ X3) = $true) | (((X1 @ X3) != $true) | ((X2 @ X3) = $true)))))),
% 1.63/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.63/1.30 thf(f6,plain,(
% 1.63/1.30 ~! [X0 : a > $o,X2 : a > $o,X1 : a > $o] : ((! [X4 : a] : ((((X2 @ X4) = $true) & ((X1 @ X4) != $true)) => ((X0 @ X4) = $true)) & ! [X3 : a] : ((((X1 @ X3) = $true) & ((X2 @ X3) != $true)) => ((X0 @ X3) = $true))) => ! [X5 : a] : (((((X1 @ X5) != $true) & ($true = (X2 @ X5))) | (((X1 @ X5) = $true) & ($true != (X2 @ X5)))) => ((X0 @ X5) = $true)))),
% 1.63/1.30 inference(flattening,[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] : ((~((X2 @ X3) = $true) & ((X1 @ X3) = $true)) => ((X0 @ X3) = $true)) & ! [X4 : a] : ((((X2 @ X4) = $true) & ~((X1 @ X4) = $true)) => ((X0 @ X4) = $true))) => ! [X5 : a] : (((~((X1 @ X5) = $true) & ($true = (X2 @ X5))) | (((X1 @ X5) = $true) & ~($true = (X2 @ X5)))) => ((X0 @ X5) = $true)))),
% 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] : ((~(X2 @ X3) & (X1 @ X3)) => (X0 @ X3)) & ! [X4 : a] : (((X2 @ X4) & ~(X1 @ X4)) => (X0 @ X4))) => ! [X5 : a] : (((~(X1 @ X5) & (X2 @ X5)) | ((X1 @ X5) & ~(X2 @ 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,X1 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((~(X0 @ X3) & (X1 @ X3)) => (X2 @ X3)) & ! [X3 : a] : (((X0 @ X3) & ~(X1 @ X3)) => (X2 @ X3))) => ! [X3 : a] : (((~(X1 @ X3) & (X0 @ X3)) | ((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,X1 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((~(X0 @ X3) & (X1 @ X3)) => (X2 @ X3)) & ! [X3 : a] : (((X0 @ X3) & ~(X1 @ X3)) => (X2 @ X3))) => ! [X3 : a] : (((~(X1 @ X3) & (X0 @ X3)) | ((X1 @ X3) & ~(X0 @ X3))) => (X2 @ X3)))),
% 1.63/1.30 file('/export/starexec/sandbox2/tmp/tmp.7cg0CmW1X9/DTF2THF_12360.p',cBOOL_PROP_115_pme)).
% 1.63/1.30 thf(f39,plain,(
% 1.63/1.30 ~spl4_3),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.63/1.30 thf(f38,plain,(
% 1.63/1.30 $false | ~spl4_3),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.63/1.30 thf(f37,plain,(
% 1.63/1.30 ($true != $true) | ~spl4_3),
% 1.63/1.30 inference(superposition,[status(thm)],[f17,f35])).
% 1.63/1.30 thf(f35,plain,(
% 1.63/1.30 ((sK0 @ sK3) = $true) | ~spl4_3),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.63/1.30 thf(f17,plain,(
% 1.63/1.30 ((sK0 @ sK3) != $true)),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.30 thf(f36,plain,(
% 1.63/1.30 spl4_3 | spl4_1 | ~spl4_2),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f31,f25,f21,f33])).
% 1.63/1.30 thf(f31,plain,(
% 1.63/1.30 ((sK1 @ sK3) = $true) | ((sK0 @ sK3) = $true) | ~spl4_2),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.63/1.30 thf(f30,plain,(
% 1.63/1.30 ($true != $true) | ((sK1 @ sK3) = $true) | ((sK0 @ sK3) = $true) | ~spl4_2),
% 1.63/1.30 inference(superposition,[status(thm)],[f18,f26])).
% 1.63/1.30 thf(f26,plain,(
% 1.63/1.30 ((sK2 @ sK3) = $true) | ~spl4_2),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.63/1.30 thf(f18,plain,(
% 1.63/1.30 ( ! [X4 : a] : (((sK2 @ X4) != $true) | ($true = (sK1 @ X4)) | ((sK0 @ X4) = $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.30 thf(f29,plain,(
% 1.63/1.30 spl4_2 | spl4_1),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f14,f21,f25])).
% 1.63/1.30 thf(f14,plain,(
% 1.63/1.30 ((sK2 @ sK3) = $true) | ((sK1 @ sK3) = $true)),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.30 thf(f28,plain,(
% 1.63/1.30 ~spl4_1 | ~spl4_2),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f15,f25,f21])).
% 1.63/1.30 thf(f15,plain,(
% 1.63/1.30 ((sK2 @ sK3) != $true) | ((sK1 @ sK3) != $true)),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.63/1.30 % SZS output end Proof for DTF2THF_12360
% 1.63/1.30 % (12515)------------------------------
% 1.63/1.30 % (12515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (12515)Termination reason: Refutation
% 1.63/1.30
% 1.63/1.30 % (12515)Memory used [KB]: 5500
% 1.63/1.30 % (12515)Time elapsed: 0.005 s
% 1.63/1.30 % (12515)Instructions burned: 2 (million)
% 1.63/1.30 % (12515)------------------------------
% 1.63/1.30 % (12515)------------------------------
% 1.63/1.30 % (12512)Success in time 0.016 s
%------------------------------------------------------------------------------