%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET611^5 : 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 : n005.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 09:31:54 AM UTC 2026
% Result : Theorem 1.63s 1.35s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 59 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 320 ( 82 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 355 ( 79 ~; 81 |; 51 &; 134 @)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 82 ( 60 ^; 16 !; 6 ?; 82 :)
% 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(func_def_13,type,
sK5: a ).
thf(func_def_14,type,
sK6: a ).
thf(f128,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f20,f21,f44,f53,f92,f127]) ).
thf(f127,plain,
( ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f126]) ).
thf(f126,plain,
( $false
| ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( $false = $true )
| ~ spl2_2
| spl2_3
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f117,f43]) ).
thf(f43,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl2_4
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f117,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl2_2
| spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $false != $false )
| ( ( sK0 @ sK4 )
= $false )
| ~ spl2_2
| spl2_3 ),
inference(superposition,[status(thm)],[f38,f95]) ).
thf(f95,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ! [X1: a] :
( ( ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= $false )
| ~ spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f93]) ).
thf(f93,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl2_2
<=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f38,plain,
( ( ( sK1 @ sK4 )
!= $false )
| spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl2_3
<=> ( ( sK1 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f92,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f91]) ).
thf(f91,plain,
( $false
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( $false = $true )
| ~ spl2_1
| spl2_2 ),
inference(superposition,[status(thm)],[f86,f58]) ).
thf(f58,plain,
( ( ( sK0 @ sK5 )
= $true )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $false
!= ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
| spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK5 )
!= ( ^ [Y0: a] : $false
@ sK5 ) )
| spl2_2 ),
inference(negative_extensionality,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f86,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false = $true )
| ~ spl2_1
| spl2_2 ),
inference(superposition,[status(thm)],[f57,f67]) ).
thf(f67,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ~ ( sK0 @ X1 ) )
= $true ) )
| ~ spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= $true ) )
| ~ spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ! [X1: a] :
( ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= ( sK1 @ X1 ) )
| ~ spl2_1 ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( ! [X1: a] :
( ( sK1 @ X1 )
= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ~ spl2_1 ),
inference(argument_congruence,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK1
= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f13]) ).
thf(f13,definition,
( spl2_1
<=> ( sK1
= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f57,plain,
( ( ( sK1 @ sK5 )
= $true )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f53,plain,
( spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
| spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $false = $true )
| spl2_1
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f39,f35]) ).
thf(f35,plain,
( ( ( sK1 @ sK4 )
= $true )
| spl2_1 ),
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( ( sK1 @ sK4 )
= $true )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( ( ~ ( sK0 @ sK4 )
& ( sK1 @ sK4 ) )
= $true )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ~ ( sK0 @ sK4 )
& ( sK1 @ sK4 ) )
!= ( sK1 @ sK4 ) )
| spl2_1 ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK4 )
!= ( sK1 @ sK4 ) )
| spl2_1 ),
inference(negative_extensionality,[status(thm)],[f14]) ).
thf(f14,plain,
( ( sK1
!= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f13]) ).
thf(f39,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f44,plain,
( spl2_3
| spl2_4
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f31,f13,f41,f37]) ).
thf(f31,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK1 @ sK4 )
= $false )
| spl2_1 ),
inference(not_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ~ ( sK0 @ sK4 ) )
= $false )
| ( ( sK1 @ sK4 )
= $false )
| spl2_1 ),
inference(duplicate_literal_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( ~ ( sK0 @ sK4 ) )
= $false )
| ( ( sK1 @ sK4 )
= $false )
| ( ( sK1 @ sK4 )
= $false )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( ~ ( sK0 @ sK4 )
& ( sK1 @ sK4 ) )
= $false )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f21,plain,
( ~ spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f11,f13,f17]) ).
thf(f11,plain,
( ( sK1
!= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( sK1
!= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) )
& ( ( sK1
= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= X1 )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) )
& ( ( ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ) )
=> ( ( ( sK1
!= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) )
& ( ( sK1
= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= X1 )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) )
& ( ( ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
<~> ( ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 )
<=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] : $false )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) )
<=> ( X1
= ( ^ [X4: a] :
( ( X1 @ X4 )
& ~ ( X0 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ( ( ^ [X2: a] : $false )
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
<=> ( X0
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ( ( ^ [X2: a] : $false )
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
<=> ( X0
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8nHIETYvzf/DTF2THF_9787.p',cBOOL_PROP_84_pme) ).
thf(f20,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f10,f17,f13]) ).
thf(f10,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( sK1
= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET611^5 : 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
% 0.17/0.34 % Computer : n005.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 12:00:14 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SET611^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : TPS problem BOOL-PROP-84
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : Trybulec's 84th Boolean property of sets
% 0.31/0.46
% 0.31/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.31/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0429 [Bro09]
% 0.31/0.46 % : BOOL-PROP-84 [TPS]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % 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 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.46 % Number of atoms : 3 ( 2 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 3 avg)
% 0.31/0.46 % Number of connectives : 8 ( 1 ~; 0 |; 2 &; 4 @)
% 0.31/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 4 ( 4 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 5 ( 3 ^; 2 !; 0 ?; 5 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % : Polymorphic definitions expanded.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(cBOOL_PROP_84_pme,conjecture,
% 0.31/0.46 ! [X: a > $o,Y: a > $o] :
% 0.31/0.46 ( ( ( ^ [Xx: a] :
% 0.31/0.46 ( ( X @ Xx )
% 0.31/0.46 & ( Y @ Xx ) ) )
% 0.31/0.46 = ( ^ [Xx: a] : $false ) )
% 0.31/0.46 <=> ( ( ^ [Xx: a] :
% 0.31/0.46 ( ( X @ Xx )
% 0.31/0.46 & ~ ( Y @ Xx ) ) )
% 0.31/0.46 = X ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.63/1.32 ---- Embedded in THF ---
% 1.63/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.32 %%% Generated on Tue Feb 24 12:00:15 EST 2026
% 1.63/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.32 %%% Logic specification used:
% 1.63/1.32 %%% thf(spec, logic, $$dhol).
% 1.63/1.32
% 1.63/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.8nHIETYvzf/DTF2DTF9787.p
% See solution above
% 1.63/1.32 ------------------------
% 1.63/1.33 ---- Cleaned THF ---
% 1.63/1.33 thf(a_type,type,
% 1.63/1.33 a: $tType ).
% 1.63/1.33
% 1.63/1.33 thf(cBOOL_PROP_84_pme,conjecture,
% 1.63/1.33 ! [X: a > $o,Y: a > $o] :
% 1.63/1.33 ( ( ( ^ [Xx: a] :
% 1.63/1.33 ( ( X @ Xx )
% 1.63/1.33 & ( Y @ Xx ) ) )
% 1.63/1.33 = ( ^ [Xx: a] : $false ) )
% 1.63/1.33 <=> ( ( ^ [Xx: a] :
% 1.63/1.33 ( ( X @ Xx )
% 1.63/1.33 & ~ ( Y @ Xx ) ) )
% 1.63/1.33 = X ) ) ).
% 1.63/1.33 ------------------------
% 1.63/1.35 % (10066)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_9787 for (2999ds/275Mi)
% 1.63/1.35 % (10066)First to succeed.
% 1.63/1.35 % (10066)Refutation found. Thanks to Tanya!
% 1.63/1.35 % SZS status Theorem for DTF2THF_9787
% 1.63/1.35 % SZS output start Proof for DTF2THF_9787
% 1.63/1.35 thf(type_def_5, type, a: $tType).
% 1.63/1.35 thf(func_def_0, type, a: $tType).
% 1.63/1.35 thf(func_def_8, type, sK0: a > $o).
% 1.63/1.35 thf(func_def_9, type, sK1: a > $o).
% 1.63/1.35 thf(func_def_11, type, ph3: !>[X0: $tType]:(X0)).
% 1.63/1.35 thf(func_def_12, type, sK4: a).
% 1.63/1.35 thf(func_def_13, type, sK5: a).
% 1.63/1.35 thf(func_def_14, type, sK6: a).
% 1.63/1.35 thf(f128,plain,(
% 1.63/1.35 $false),
% 1.63/1.35 inference(avatar_sat_refutation,[status(thm)],[f20,f21,f44,f53,f92,f127])).
% 1.63/1.35 thf(f127,plain,(
% 1.63/1.35 ~spl2_2 | spl2_3 | ~spl2_4),
% 1.63/1.35 inference(avatar_contradiction_clause,[status(thm)],[f126])).
% 1.63/1.35 thf(f126,plain,(
% 1.63/1.35 $false | (~spl2_2 | spl2_3 | ~spl2_4)),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.63/1.35 thf(f122,plain,(
% 1.63/1.35 ($false = $true) | (~spl2_2 | spl2_3 | ~spl2_4)),
% 1.63/1.35 inference(superposition,[status(thm)],[f117,f43])).
% 1.63/1.35 thf(f43,plain,(
% 1.63/1.35 ((sK0 @ sK4) = $true) | ~spl2_4),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.63/1.35 thf(f41,definition,(
% 1.63/1.35 spl2_4 <=> ((sK0 @ sK4) = $true)),
% 1.63/1.35 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.63/1.35 thf(f117,plain,(
% 1.63/1.35 ((sK0 @ sK4) = $false) | (~spl2_2 | spl2_3)),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.63/1.35 thf(f116,plain,(
% 1.63/1.35 ($false != $false) | ((sK0 @ sK4) = $false) | (~spl2_2 | spl2_3)),
% 1.63/1.35 inference(superposition,[status(thm)],[f38,f95])).
% 1.63/1.35 thf(f95,plain,(
% 1.63/1.35 ( ! [X1 : a] : (((sK1 @ X1) = $false) | ((sK0 @ X1) = $false)) ) | ~spl2_2),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.63/1.35 thf(f94,plain,(
% 1.63/1.35 ( ! [X1 : a] : ((((sK0 @ X1) & (sK1 @ X1)) = $false)) ) | ~spl2_2),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f93])).
% 1.63/1.35 thf(f93,plain,(
% 1.63/1.35 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) @ X1) = ((^[Y0 : a]: ($false)) @ X1))) ) | ~spl2_2),
% 1.63/1.35 inference(argument_congruence,[status(thm)],[f19])).
% 1.63/1.35 thf(f19,plain,(
% 1.63/1.35 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | ~spl2_2),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.63/1.35 thf(f17,definition,(
% 1.63/1.35 spl2_2 <=> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))))),
% 1.63/1.35 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.63/1.35 thf(f38,plain,(
% 1.63/1.35 ((sK1 @ sK4) != $false) | spl2_3),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.63/1.35 thf(f37,definition,(
% 1.63/1.35 spl2_3 <=> ((sK1 @ sK4) = $false)),
% 1.63/1.35 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.63/1.35 thf(f92,plain,(
% 1.63/1.35 ~spl2_1 | spl2_2),
% 1.63/1.35 inference(avatar_contradiction_clause,[status(thm)],[f91])).
% 1.63/1.35 thf(f91,plain,(
% 1.63/1.35 $false | (~spl2_1 | spl2_2)),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.63/1.35 thf(f87,plain,(
% 1.63/1.35 ($false = $true) | (~spl2_1 | spl2_2)),
% 1.63/1.35 inference(superposition,[status(thm)],[f86,f58])).
% 1.63/1.35 thf(f58,plain,(
% 1.63/1.35 ((sK0 @ sK5) = $true) | spl2_2),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.63/1.35 thf(f56,plain,(
% 1.63/1.35 ($false != ((sK0 @ sK5) & (sK1 @ sK5))) | spl2_2),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.63/1.35 thf(f55,plain,(
% 1.63/1.35 (((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) @ sK5) != ((^[Y0 : a]: ($false)) @ sK5)) | spl2_2),
% 1.63/1.35 inference(negative_extensionality,[status(thm)],[f18])).
% 1.63/1.35 thf(f18,plain,(
% 1.63/1.35 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | spl2_2),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.63/1.35 thf(f86,plain,(
% 1.63/1.35 ((sK0 @ sK5) = $false) | (~spl2_1 | spl2_2)),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.63/1.35 thf(f82,plain,(
% 1.63/1.35 ((sK0 @ sK5) = $false) | ($false = $true) | (~spl2_1 | spl2_2)),
% 1.63/1.35 inference(superposition,[status(thm)],[f57,f67])).
% 1.63/1.35 thf(f67,plain,(
% 1.63/1.35 ( ! [X1 : a] : (((sK1 @ X1) = $false) | ((sK0 @ X1) = $false)) ) | ~spl2_1),
% 1.63/1.35 inference(not_proxy_clausification,[status(thm)],[f66])).
% 1.63/1.35 thf(f66,plain,(
% 1.63/1.35 ( ! [X1 : a] : (((sK1 @ X1) = $false) | ((~ (sK0 @ X1)) = $true)) ) | ~spl2_1),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.63/1.35 thf(f61,plain,(
% 1.63/1.35 ( ! [X1 : a] : (((sK1 @ X1) = $false) | (((~ (sK0 @ X1)) & (sK1 @ X1)) = $true)) ) | ~spl2_1),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.63/1.35 thf(f60,plain,(
% 1.63/1.35 ( ! [X1 : a] : ((((~ (sK0 @ X1)) & (sK1 @ X1)) = (sK1 @ X1))) ) | ~spl2_1),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.63/1.35 thf(f59,plain,(
% 1.63/1.35 ( ! [X1 : a] : (((sK1 @ X1) = ((^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0))) @ X1))) ) | ~spl2_1),
% 1.63/1.35 inference(argument_congruence,[status(thm)],[f15])).
% 1.63/1.35 thf(f15,plain,(
% 1.63/1.35 (sK1 = (^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) | ~spl2_1),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f13])).
% 1.63/1.35 thf(f13,definition,(
% 1.63/1.35 spl2_1 <=> (sK1 = (^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0))))),
% 1.63/1.35 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.63/1.35 thf(f57,plain,(
% 1.63/1.35 ((sK1 @ sK5) = $true) | spl2_2),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.63/1.35 thf(f53,plain,(
% 1.63/1.35 spl2_1 | ~spl2_3),
% 1.63/1.35 inference(avatar_contradiction_clause,[status(thm)],[f52])).
% 1.63/1.35 thf(f52,plain,(
% 1.63/1.35 $false | (spl2_1 | ~spl2_3)),
% 1.63/1.35 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.63/1.35 thf(f47,plain,(
% 1.63/1.35 ($false = $true) | (spl2_1 | ~spl2_3)),
% 1.63/1.35 inference(superposition,[status(thm)],[f39,f35])).
% 1.63/1.35 thf(f35,plain,(
% 1.63/1.35 ((sK1 @ sK4) = $true) | spl2_1),
% 1.63/1.35 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.63/1.35 thf(f32,plain,(
% 1.63/1.35 ((sK1 @ sK4) = $true) | ((sK1 @ sK4) = $true) | spl2_1),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.63/1.35 thf(f27,plain,(
% 1.63/1.35 ((sK1 @ sK4) = $true) | (((~ (sK0 @ sK4)) & (sK1 @ sK4)) = $true) | spl2_1),
% 1.63/1.35 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.63/1.35 thf(f26,plain,(
% 1.63/1.35 (((~ (sK0 @ sK4)) & (sK1 @ sK4)) != (sK1 @ sK4)) | spl2_1),
% 1.63/1.35 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.63/1.35 thf(f25,plain,(
% 1.63/1.35 (((^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0))) @ sK4) != (sK1 @ sK4)) | spl2_1),
% 1.63/1.35 inference(negative_extensionality,[status(thm)],[f14])).
% 1.63/1.35 thf(f14,plain,(
% 1.63/1.35 (sK1 != (^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) | spl2_1),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f13])).
% 1.63/1.35 thf(f39,plain,(
% 1.63/1.35 ((sK1 @ sK4) = $false) | ~spl2_3),
% 1.63/1.35 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.63/1.35 thf(f44,plain,(
% 1.63/1.35 spl2_3 | spl2_4 | spl2_1),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f31,f13,f41,f37])).
% 1.63/1.36 thf(f31,plain,(
% 1.63/1.36 ((sK0 @ sK4) = $true) | ((sK1 @ sK4) = $false) | spl2_1),
% 1.63/1.36 inference(not_proxy_clausification,[status(thm)],[f30])).
% 1.63/1.36 thf(f30,plain,(
% 1.63/1.36 ((~ (sK0 @ sK4)) = $false) | ((sK1 @ sK4) = $false) | spl2_1),
% 1.63/1.36 inference(duplicate_literal_removal,[status(thm)],[f29])).
% 1.63/1.36 thf(f29,plain,(
% 1.63/1.36 ((~ (sK0 @ sK4)) = $false) | ((sK1 @ sK4) = $false) | ((sK1 @ sK4) = $false) | spl2_1),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.63/1.36 thf(f28,plain,(
% 1.63/1.36 ((sK1 @ sK4) = $false) | (((~ (sK0 @ sK4)) & (sK1 @ sK4)) = $false) | spl2_1),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.63/1.36 thf(f21,plain,(
% 1.63/1.36 ~spl2_2 | ~spl2_1),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f11,f13,f17])).
% 1.63/1.36 thf(f11,plain,(
% 1.63/1.36 (sK1 != (^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))))),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.63/1.36 thf(f9,plain,(
% 1.63/1.36 ((sK1 != (^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))))) & ((sK1 = (^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) | ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))))),
% 1.63/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.63/1.36 thf(f8,plain,(
% 1.63/1.36 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0))) != X1) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))))) & (((^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0))) = X1) | ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))))) => (((sK1 != (^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))))) & ((sK1 = (^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) | ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))))))),
% 1.63/1.36 introduced(definition,[],[choice_axiom])).
% 1.63/1.36 thf(f7,plain,(
% 1.63/1.36 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0))) != X1) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))))) & (((^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0))) = X1) | ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))))))),
% 1.63/1.36 inference(nnf_transformation,[status(thm)],[f6])).
% 1.63/1.36 thf(f6,plain,(
% 1.63/1.36 ? [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) <~> ((^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0))) = X1))),
% 1.63/1.36 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.36 thf(f5,plain,(
% 1.63/1.36 ~! [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0))) = X1) <=> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))))),
% 1.63/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.36 thf(f4,plain,(
% 1.63/1.36 ~! [X0 : a > $o,X1 : a > $o] : (((^[X2 : a] : ($false)) = (^[X3 : a] : ((X1 @ X3) & (X0 @ X3)))) <=> (X1 = (^[X4 : a] : ((X1 @ X4) & ~(X0 @ X4)))))),
% 1.63/1.36 inference(rectify,[status(thm)],[f2])).
% 1.63/1.36 thf(f2,negated_conjecture,(
% 1.63/1.36 ~! [X1 : a > $o,X0 : a > $o] : (((^[X2 : a] : ($false)) = (^[X2 : a] : ((X0 @ X2) & (X1 @ X2)))) <=> (X0 = (^[X2 : a] : ((X0 @ X2) & ~(X1 @ X2)))))),
% 1.63/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.36 thf(f1,conjecture,(
% 1.63/1.36 ! [X1 : a > $o,X0 : a > $o] : (((^[X2 : a] : ($false)) = (^[X2 : a] : ((X0 @ X2) & (X1 @ X2)))) <=> (X0 = (^[X2 : a] : ((X0 @ X2) & ~(X1 @ X2)))))),
% 1.63/1.36 file('/export/starexec/sandbox2/tmp/tmp.8nHIETYvzf/DTF2THF_9787.p',cBOOL_PROP_84_pme)).
% 1.63/1.36 thf(f20,plain,(
% 1.63/1.36 spl2_1 | spl2_2),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f10,f17,f13])).
% 1.63/1.36 thf(f10,plain,(
% 1.63/1.36 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | (sK1 = (^[Y0 : a]: ((~ (sK0 @ Y0)) & (sK1 @ Y0))))),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.63/1.36 % SZS output end Proof for DTF2THF_9787
% 1.63/1.36 % (10066)------------------------------
% 1.63/1.36 % (10066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (10066)Termination reason: Refutation
% 1.63/1.36
% 1.63/1.36 % (10066)Memory used [KB]: 5500
% 1.63/1.36 % (10066)Time elapsed: 0.005 s
% 1.63/1.36 % (10066)Instructions burned: 5 (million)
% 1.63/1.36 % (10066)------------------------------
% 1.63/1.36 % (10066)------------------------------
% 1.63/1.36 % (10060)Success in time 0.016 s
%------------------------------------------------------------------------------