%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU849^5 : 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 : n022.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 09:37:35 AM UTC 2026
% Result : Theorem 1.62s 1.32s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 4 unt; 0 typ; 7 def)
% Number of atoms : 346 ( 99 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 354 ( 71 ~; 87 |; 41 &; 135 @)
% ( 12 <=>; 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 : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 65 ( 24 ^; 28 !; 13 ?; 65 :)
% 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_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(f95,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f23,f28,f33,f51,f83,f87,f88,f94]) ).
thf(f94,plain,
( ~ spl3_1
| ~ spl3_5
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f93]) ).
thf(f93,plain,
( $false
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8 ),
inference(forward_demodulation,[status(thm)],[f91,f82]) ).
thf(f82,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f80,definition,
( spl3_8
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f91,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ~ spl3_1
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true != $true )
| ~ spl3_1
| ~ spl3_5 ),
inference(superposition,[status(thm)],[f18,f69]) ).
thf(f69,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl3_5
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f18,plain,
( ! [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
| ( ( sK0 @ X3 )
= $true ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl3_1
<=> ! [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
| ( ( sK0 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f88,plain,
( spl3_5
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f65,f20,f67]) ).
thf(f20,definition,
( spl3_2
<=> ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= sK1 ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f65,plain,
( ( $true
= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(duplicate_literal_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true
= ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( $true
= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
!= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK5 )
!= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(negative_extensionality,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= sK1 )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f87,plain,
( spl3_2
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
| spl3_2
| ~ spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $true = $false )
| spl3_2
| ~ spl3_7 ),
inference(forward_demodulation,[status(thm)],[f65,f78]) ).
thf(f78,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl3_7
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f83,plain,
( spl3_7
| spl3_8
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f62,f20,f80,f76]) ).
thf(f62,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| spl3_2 ),
inference(duplicate_literal_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $false
= ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f51,plain,
( ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f50]) ).
thf(f50,plain,
( $false
| ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true = $false )
| ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(backward_demodulation,[status(thm)],[f32,f44]) ).
thf(f44,plain,
( ( ( sK1 @ sK2 )
= $false )
| ~ spl3_2
| spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true != $true )
| ( ( sK1 @ sK2 )
= $false )
| ~ spl3_2
| spl3_3 ),
inference(superposition,[status(thm)],[f27,f40]) ).
thf(f40,plain,
( ! [X1: a] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ! [X1: a] :
( ( ( ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= $true )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ! [X1: a] :
( ( ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= ( sK1 @ X1 ) )
| ~ spl3_2 ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
( ! [X1: a] :
( ( sK1 @ X1 )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ~ spl3_2 ),
inference(argument_congruence,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= sK1 )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f27,plain,
( ( $true
!= ( sK0 @ sK2 ) )
| spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl3_3
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f32,plain,
( ( ( sK1 @ sK2 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl3_4
<=> ( ( sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f33,plain,
( spl3_4
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f20,f30]) ).
thf(f15,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= sK1 )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= sK1 )
| ( ( ( sK1 @ sK2 )
= $true )
& ( $true
!= ( sK0 @ sK2 ) ) ) )
& ( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= sK1 )
| ! [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
| ( ( sK0 @ X3 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= X1 )
| ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
!= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 )
| ! [X3: a] :
( ( $true
!= ( X1 @ X3 ) )
| ( $true
= ( X0 @ X3 ) ) ) ) )
=> ( ( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= sK1 )
| ? [X2: a] :
( ( $true
= ( sK1 @ X2 ) )
& ( $true
!= ( sK0 @ X2 ) ) ) )
& ( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= sK1 )
| ! [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
| ( ( sK0 @ X3 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X2: a] :
( ( $true
= ( sK1 @ X2 ) )
& ( $true
!= ( sK0 @ X2 ) ) )
=> ( ( ( sK1 @ sK2 )
= $true )
& ( $true
!= ( sK0 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= X1 )
| ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
!= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 )
| ! [X3: a] :
( ( $true
!= ( X1 @ X3 ) )
| ( $true
= ( X0 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= X1 )
| ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
!= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 )
| ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
= $true ) )
<~> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) )
<=> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X1 )
<=> ! [X3: a] :
( ( $true
= ( X1 @ X3 ) )
=> ( $true
= ( X0 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( X1
= ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) )
<=> ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ( X0
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ( X0
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.M55bG1ZwQH/DTF2THF_3405.p',cGAZING_THM39_pme) ).
thf(f28,plain,
( ~ spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f20,f25]) ).
thf(f14,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= sK1 )
| ( $true
!= ( sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f23,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f20,f17]) ).
thf(f13,plain,
! [X3: a] :
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
= sK1 )
| ( $true
!= ( sK1 @ X3 ) )
| ( ( sK0 @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU849^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:35:36 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEU849^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : TPS problem GAZING-THM39
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.19/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0342 [Bro09]
% 0.19/0.46 % : 39 [Bar92]
% 0.19/0.46 % : GAZING-THM39 [TPS]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % 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, 0.00 v6.1.0, 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
% 0.19/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.46 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 4 @)
% 0.19/0.46 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.46 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % : Polymorphic definitions expanded.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(cGAZING_THM39_pme,conjecture,
% 0.19/0.46 ! [S: a > $o,T: a > $o] :
% 0.19/0.46 ( ( ( ^ [Xx: a] :
% 0.19/0.46 ( ( S @ Xx )
% 0.19/0.46 & ( T @ Xx ) ) )
% 0.19/0.46 = S )
% 0.19/0.46 <=> ! [Xx: a] :
% 0.19/0.46 ( ( S @ Xx )
% 0.19/0.46 => ( T @ Xx ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.42/1.29 ---- Embedded in THF ---
% 1.42/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.42/1.29 %%% Generated on Tue Feb 24 12:35:37 EST 2026
% 1.42/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.42/1.29 %%% Logic specification used:
% 1.42/1.29 %%% thf(spec, logic, $$dhol).
% 1.42/1.29
% 1.42/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.M55bG1ZwQH/DTF2DTF3405.p
% See solution above
% 1.42/1.29 ------------------------
% 1.62/1.30 ---- Cleaned THF ---
% 1.62/1.30 thf(a_type,type,
% 1.62/1.30 a: $tType ).
% 1.62/1.30
% 1.62/1.30 thf(cGAZING_THM39_pme,conjecture,
% 1.62/1.30 ! [S: a > $o,T: a > $o] :
% 1.62/1.30 ( ( ( ^ [Xx: a] :
% 1.62/1.30 ( ( S @ Xx )
% 1.62/1.30 & ( T @ Xx ) ) )
% 1.62/1.30 = S )
% 1.62/1.30 <=> ! [Xx: a] :
% 1.62/1.30 ( ( S @ Xx )
% 1.62/1.30 => ( T @ Xx ) ) ) ).
% 1.62/1.30 ------------------------
% 1.62/1.32 % (3569)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_3405 for (2999ds/27Mi)
% 1.62/1.32 % (3568)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_3405 for (2999ds/4Mi)
% 1.62/1.32 % (3568)Instruction limit reached!
% 1.62/1.32 % (3568)------------------------------
% 1.62/1.32 % (3568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (3568)Termination reason: Unknown
% 1.62/1.32 % (3568)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (3568)Memory used [KB]: 5500
% 1.62/1.32 % (3568)Time elapsed: 0.003 s
% 1.62/1.32 % (3568)Instructions burned: 4 (million)
% 1.62/1.32 % (3568)------------------------------
% 1.62/1.32 % (3568)------------------------------
% 1.62/1.32 % (3569)First to succeed.
% 1.62/1.32 % (3569)Refutation found. Thanks to Tanya!
% 1.62/1.32 % SZS status Theorem for DTF2THF_3405
% 1.62/1.32 % SZS output start Proof for DTF2THF_3405
% 1.62/1.32 thf(type_def_5, type, a: $tType).
% 1.62/1.32 thf(func_def_0, type, a: $tType).
% 1.62/1.32 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.62/1.32 thf(func_def_8, type, sK0: a > $o).
% 1.62/1.32 thf(func_def_9, type, sK1: a > $o).
% 1.62/1.32 thf(func_def_10, type, sK2: a).
% 1.62/1.32 thf(func_def_12, type, ph4: !>[X0: $tType]:(X0)).
% 1.62/1.32 thf(func_def_13, type, sK5: a).
% 1.62/1.32 thf(f95,plain,(
% 1.62/1.32 $false),
% 1.62/1.32 inference(avatar_sat_refutation,[status(thm)],[f23,f28,f33,f51,f83,f87,f88,f94])).
% 1.62/1.32 thf(f94,plain,(
% 1.62/1.32 ~spl3_1 | ~spl3_5 | ~spl3_8),
% 1.62/1.32 inference(avatar_contradiction_clause,[status(thm)],[f93])).
% 1.62/1.32 thf(f93,plain,(
% 1.62/1.32 $false | (~spl3_1 | ~spl3_5 | ~spl3_8)),
% 1.62/1.32 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.62/1.32 thf(f92,plain,(
% 1.62/1.32 ($true = $false) | (~spl3_1 | ~spl3_5 | ~spl3_8)),
% 1.62/1.32 inference(forward_demodulation,[status(thm)],[f91,f82])).
% 1.62/1.32 thf(f82,plain,(
% 1.62/1.32 ($false = (sK0 @ sK5)) | ~spl3_8),
% 1.62/1.32 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.62/1.32 thf(f80,definition,(
% 1.62/1.32 spl3_8 <=> ($false = (sK0 @ sK5))),
% 1.62/1.32 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.62/1.32 thf(f91,plain,(
% 1.62/1.32 ($true = (sK0 @ sK5)) | (~spl3_1 | ~spl3_5)),
% 1.62/1.32 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.62/1.32 thf(f90,plain,(
% 1.62/1.32 ($true = (sK0 @ sK5)) | ($true != $true) | (~spl3_1 | ~spl3_5)),
% 1.62/1.32 inference(superposition,[status(thm)],[f18,f69])).
% 1.62/1.32 thf(f69,plain,(
% 1.62/1.32 ($true = (sK1 @ sK5)) | ~spl3_5),
% 1.62/1.32 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.62/1.32 thf(f67,definition,(
% 1.62/1.32 spl3_5 <=> ($true = (sK1 @ sK5))),
% 1.62/1.32 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.62/1.32 thf(f18,plain,(
% 1.62/1.32 ( ! [X3 : a] : (($true != (sK1 @ X3)) | ((sK0 @ X3) = $true)) ) | ~spl3_1),
% 1.62/1.32 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.62/1.32 thf(f17,definition,(
% 1.62/1.32 spl3_1 <=> ! [X3 : a] : (($true != (sK1 @ X3)) | ((sK0 @ X3) = $true))),
% 1.62/1.32 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.62/1.32 thf(f88,plain,(
% 1.62/1.32 spl3_5 | spl3_2),
% 1.62/1.32 inference(avatar_split_clause,[status(thm)],[f65,f20,f67])).
% 1.62/1.32 thf(f20,definition,(
% 1.62/1.32 spl3_2 <=> ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) = sK1)),
% 1.62/1.32 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.62/1.32 thf(f65,plain,(
% 1.62/1.32 ($true = (sK1 @ sK5)) | spl3_2),
% 1.62/1.32 inference(duplicate_literal_removal,[status(thm)],[f63])).
% 1.62/1.32 thf(f63,plain,(
% 1.62/1.32 ($true = (sK1 @ sK5)) | ($true = (sK1 @ sK5)) | spl3_2),
% 1.62/1.32 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.62/1.32 thf(f59,plain,(
% 1.62/1.32 ($true = ((sK0 @ sK5) & (sK1 @ sK5))) | ($true = (sK1 @ sK5)) | spl3_2),
% 1.62/1.32 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.62/1.32 thf(f58,plain,(
% 1.62/1.32 (((sK0 @ sK5) & (sK1 @ sK5)) != (sK1 @ sK5)) | spl3_2),
% 1.62/1.32 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.62/1.32 thf(f57,plain,(
% 1.62/1.32 (((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) @ sK5) != (sK1 @ sK5)) | spl3_2),
% 1.62/1.32 inference(negative_extensionality,[status(thm)],[f21])).
% 1.62/1.32 thf(f21,plain,(
% 1.62/1.32 ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) != sK1) | spl3_2),
% 1.62/1.32 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.62/1.32 thf(f87,plain,(
% 1.62/1.32 spl3_2 | ~spl3_7),
% 1.62/1.32 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 1.62/1.32 thf(f86,plain,(
% 1.62/1.32 $false | (spl3_2 | ~spl3_7)),
% 1.62/1.32 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.62/1.32 thf(f85,plain,(
% 1.62/1.32 ($true = $false) | (spl3_2 | ~spl3_7)),
% 1.62/1.32 inference(forward_demodulation,[status(thm)],[f65,f78])).
% 1.62/1.32 thf(f78,plain,(
% 1.62/1.32 ($false = (sK1 @ sK5)) | ~spl3_7),
% 1.62/1.32 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.62/1.32 thf(f76,definition,(
% 1.62/1.32 spl3_7 <=> ($false = (sK1 @ sK5))),
% 1.62/1.32 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.62/1.32 thf(f83,plain,(
% 1.62/1.32 spl3_7 | spl3_8 | spl3_2),
% 1.62/1.32 inference(avatar_split_clause,[status(thm)],[f62,f20,f80,f76])).
% 1.62/1.32 thf(f62,plain,(
% 1.62/1.32 ($false = (sK1 @ sK5)) | ($false = (sK0 @ sK5)) | spl3_2),
% 1.62/1.32 inference(duplicate_literal_removal,[status(thm)],[f61])).
% 1.62/1.32 thf(f61,plain,(
% 1.62/1.32 ($false = (sK0 @ sK5)) | ($false = (sK1 @ sK5)) | ($false = (sK1 @ sK5)) | spl3_2),
% 1.62/1.32 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.62/1.32 thf(f60,plain,(
% 1.62/1.32 ($false = ((sK0 @ sK5) & (sK1 @ sK5))) | ($false = (sK1 @ sK5)) | spl3_2),
% 1.62/1.32 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.62/1.32 thf(f51,plain,(
% 1.62/1.32 ~spl3_2 | spl3_3 | ~spl3_4),
% 1.62/1.32 inference(avatar_contradiction_clause,[status(thm)],[f50])).
% 1.62/1.32 thf(f50,plain,(
% 1.62/1.32 $false | (~spl3_2 | spl3_3 | ~spl3_4)),
% 1.62/1.32 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.62/1.32 thf(f45,plain,(
% 1.62/1.32 ($true = $false) | (~spl3_2 | spl3_3 | ~spl3_4)),
% 1.62/1.32 inference(backward_demodulation,[status(thm)],[f32,f44])).
% 1.62/1.32 thf(f44,plain,(
% 1.62/1.32 ((sK1 @ sK2) = $false) | (~spl3_2 | spl3_3)),
% 1.62/1.32 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.62/1.32 thf(f43,plain,(
% 1.62/1.32 ($true != $true) | ((sK1 @ sK2) = $false) | (~spl3_2 | spl3_3)),
% 1.62/1.32 inference(superposition,[status(thm)],[f27,f40])).
% 1.62/1.32 thf(f40,plain,(
% 1.62/1.32 ( ! [X1 : a] : (($true = (sK0 @ X1)) | ((sK1 @ X1) = $false)) ) | ~spl3_2),
% 1.62/1.32 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.62/1.32 thf(f36,plain,(
% 1.62/1.32 ( ! [X1 : a] : ((((sK0 @ X1) & (sK1 @ X1)) = $true) | ((sK1 @ X1) = $false)) ) | ~spl3_2),
% 1.62/1.32 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.62/1.32 thf(f35,plain,(
% 1.62/1.32 ( ! [X1 : a] : ((((sK0 @ X1) & (sK1 @ X1)) = (sK1 @ X1))) ) | ~spl3_2),
% 1.62/1.32 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.62/1.32 thf(f34,plain,(
% 1.62/1.32 ( ! [X1 : a] : (((sK1 @ X1) = ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) @ X1))) ) | ~spl3_2),
% 1.62/1.32 inference(argument_congruence,[status(thm)],[f22])).
% 1.62/1.32 thf(f22,plain,(
% 1.62/1.32 ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) = sK1) | ~spl3_2),
% 1.62/1.32 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.62/1.32 thf(f27,plain,(
% 1.62/1.32 ($true != (sK0 @ sK2)) | spl3_3),
% 1.62/1.32 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.62/1.32 thf(f25,definition,(
% 1.62/1.32 spl3_3 <=> ($true = (sK0 @ sK2))),
% 1.62/1.32 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.62/1.32 thf(f32,plain,(
% 1.62/1.32 ((sK1 @ sK2) = $true) | ~spl3_4),
% 1.62/1.32 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.62/1.32 thf(f30,definition,(
% 1.62/1.32 spl3_4 <=> ((sK1 @ sK2) = $true)),
% 1.62/1.32 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.62/1.32 thf(f33,plain,(
% 1.62/1.32 spl3_4 | ~spl3_2),
% 1.62/1.32 inference(avatar_split_clause,[status(thm)],[f15,f20,f30])).
% 1.62/1.32 thf(f15,plain,(
% 1.62/1.32 ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) != sK1) | ((sK1 @ sK2) = $true)),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.62/1.32 thf(f12,plain,(
% 1.62/1.32 (((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) != sK1) | (((sK1 @ sK2) = $true) & ($true != (sK0 @ sK2)))) & (((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) = sK1) | ! [X3 : a] : (($true != (sK1 @ X3)) | ((sK0 @ X3) = $true)))),
% 1.62/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10])).
% 1.62/1.32 thf(f10,plain,(
% 1.62/1.32 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) != X1) | ? [X2 : a] : (((X1 @ X2) = $true) & ((X0 @ X2) != $true))) & (((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X1) | ! [X3 : a] : (($true != (X1 @ X3)) | ($true = (X0 @ X3))))) => ((((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) != sK1) | ? [X2 : a] : (($true = (sK1 @ X2)) & ($true != (sK0 @ X2)))) & (((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) = sK1) | ! [X3 : a] : (($true != (sK1 @ X3)) | ((sK0 @ X3) = $true))))),
% 1.62/1.32 introduced(definition,[],[choice_axiom])).
% 1.62/1.32 thf(f11,plain,(
% 1.62/1.32 ? [X2 : a] : (($true = (sK1 @ X2)) & ($true != (sK0 @ X2))) => (((sK1 @ sK2) = $true) & ($true != (sK0 @ sK2)))),
% 1.62/1.32 introduced(definition,[],[choice_axiom])).
% 1.62/1.32 thf(f9,plain,(
% 1.62/1.32 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) != X1) | ? [X2 : a] : (((X1 @ X2) = $true) & ((X0 @ X2) != $true))) & (((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X1) | ! [X3 : a] : (($true != (X1 @ X3)) | ($true = (X0 @ X3)))))),
% 1.62/1.32 inference(rectify,[status(thm)],[f8])).
% 1.62/1.32 thf(f8,plain,(
% 1.62/1.32 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) != X1) | ? [X2 : a] : (((X1 @ X2) = $true) & ((X0 @ X2) != $true))) & (((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X1) | ! [X2 : a] : (((X1 @ X2) != $true) | ((X0 @ X2) = $true))))),
% 1.62/1.32 inference(nnf_transformation,[status(thm)],[f7])).
% 1.62/1.32 thf(f7,plain,(
% 1.62/1.32 ? [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X1 @ X2) != $true) | ((X0 @ X2) = $true)) <~> ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X1))),
% 1.62/1.32 inference(ennf_transformation,[status(thm)],[f6])).
% 1.62/1.32 thf(f6,plain,(
% 1.62/1.32 ~! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X1 @ X2) = $true) => ((X0 @ X2) = $true)) <=> ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X1))),
% 1.62/1.32 inference(rectify,[status(thm)],[f5])).
% 1.62/1.32 thf(f5,plain,(
% 1.62/1.32 ~! [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X1) <=> ! [X3 : a] : (($true = (X1 @ X3)) => ($true = (X0 @ X3))))),
% 1.62/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.32 thf(f4,plain,(
% 1.62/1.32 ~! [X0 : a > $o,X1 : a > $o] : ((X1 = (^[X2 : a] : ((X1 @ X2) & (X0 @ X2)))) <=> ! [X3 : a] : ((X1 @ X3) => (X0 @ X3)))),
% 1.62/1.32 inference(rectify,[status(thm)],[f2])).
% 1.62/1.32 thf(f2,negated_conjecture,(
% 1.62/1.32 ~! [X1 : a > $o,X0 : a > $o] : ((X0 = (^[X2 : a] : ((X0 @ X2) & (X1 @ X2)))) <=> ! [X2 : a] : ((X0 @ X2) => (X1 @ X2)))),
% 1.62/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.32 thf(f1,conjecture,(
% 1.62/1.32 ! [X1 : a > $o,X0 : a > $o] : ((X0 = (^[X2 : a] : ((X0 @ X2) & (X1 @ X2)))) <=> ! [X2 : a] : ((X0 @ X2) => (X1 @ X2)))),
% 1.62/1.32 file('/export/starexec/sandbox2/tmp/tmp.M55bG1ZwQH/DTF2THF_3405.p',cGAZING_THM39_pme)).
% 1.62/1.32 thf(f28,plain,(
% 1.62/1.32 ~spl3_3 | ~spl3_2),
% 1.62/1.32 inference(avatar_split_clause,[status(thm)],[f14,f20,f25])).
% 1.62/1.32 thf(f14,plain,(
% 1.62/1.32 ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) != sK1) | ($true != (sK0 @ sK2))),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.62/1.32 thf(f23,plain,(
% 1.62/1.32 spl3_1 | spl3_2),
% 1.62/1.32 inference(avatar_split_clause,[status(thm)],[f13,f20,f17])).
% 1.62/1.32 thf(f13,plain,(
% 1.62/1.32 ( ! [X3 : a] : (((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) = sK1) | ($true != (sK1 @ X3)) | ((sK0 @ X3) = $true)) )),
% 1.62/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.62/1.32 % SZS output end Proof for DTF2THF_3405
% 1.62/1.32 % (3569)------------------------------
% 1.62/1.32 % (3569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (3569)Termination reason: Refutation
% 1.62/1.32
% 1.62/1.32 % (3569)Memory used [KB]: 5500
% 1.62/1.32 % (3569)Time elapsed: 0.005 s
% 1.62/1.32 % (3569)Instructions burned: 6 (million)
% 1.62/1.32 % (3569)------------------------------
% 1.62/1.32 % (3569)------------------------------
% 1.62/1.32 % (3564)Success in time 0.015 s
%------------------------------------------------------------------------------