%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU848^5 : 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 : n023.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 09:37:34 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% 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 : 351 ( 100 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 352 ( 71 ~; 116 |; 12 &; 135 @)
% ( 11 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 62 ( 23 ^; 26 !; 13 ?; 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_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(f112,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f27,f32,f50,f60,f64,f103,f111]) ).
thf(f111,plain,
( spl3_5
| ~ spl3_2
| ~ spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f110,f47,f20,f43]) ).
thf(f43,definition,
( spl3_5
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f20,definition,
( spl3_2
<=> ! [X3: a] :
( ( ( sK0 @ X3 )
= $true )
| ( ( sK1 @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f47,definition,
( spl3_6
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f110,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_2
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( $true != $true )
| ( ( sK0 @ sK5 )
= $true )
| ~ spl3_2
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f21,f49]) ).
thf(f49,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f21,plain,
( ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
= $true ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f103,plain,
( ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
| ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(forward_demodulation,[status(thm)],[f92,f83]) ).
thf(f83,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_1
| spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true != $true )
| ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_1
| spl3_4 ),
inference(superposition,[status(thm)],[f31,f73]) ).
thf(f73,plain,
( ! [X1: a] :
( ( ( sK0 @ X1 )
= $true )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ! [X1: a] :
( ( ( sK0 @ X1 )
= $true )
| ( ( ( sK1 @ X1 )
| ( sK0 @ X1 ) )
= $false ) )
| ~ spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
| ( sK0 @ X1 ) )
= ( sK0 @ X1 ) )
| ~ spl3_1 ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( ! [X1: a] :
( ( sK0 @ X1 )
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ X1 ) )
| ~ spl3_1 ),
inference(argument_congruence,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
= sK0 )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl3_1
<=> ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
= sK0 ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f31,plain,
( ( ( sK0 @ sK2 )
!= $true )
| spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl3_4
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f92,plain,
( ( ( sK0 @ sK2 )
= $true )
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( ( sK0 @ sK2 )
= $true )
| ( $false = $true )
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f74,f26]) ).
thf(f26,plain,
( ( ( sK1 @ sK2 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl3_3
<=> ( ( sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f74,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( sK0 @ X1 )
= $true ) )
| ~ spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f64,plain,
( ~ spl3_5
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f63]) ).
thf(f63,plain,
( $false
| ~ spl3_5
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $false = $true )
| ~ spl3_5
| ~ spl3_8 ),
inference(backward_demodulation,[status(thm)],[f45,f58]) ).
thf(f58,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl3_8
<=> ( $false
= ( sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f45,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f60,plain,
( spl3_8
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f39,f16,f56]) ).
thf(f39,plain,
( ( $false
= ( sK0 @ sK5 ) )
| spl3_1 ),
inference(duplicate_literal_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( sK0 @ sK5 ) )
| spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ( $false
= ( ( sK1 @ sK5 )
| ( sK0 @ sK5 ) ) )
| spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( sK0 @ sK5 )
!= ( ( sK1 @ sK5 )
| ( sK0 @ sK5 ) ) )
| spl3_1 ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ sK5 )
!= ( sK0 @ sK5 ) )
| spl3_1 ),
inference(negative_extensionality,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
!= sK0 )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f50,plain,
( spl3_5
| spl3_6
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f41,f16,f47,f43]) ).
thf(f41,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| spl3_1 ),
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true )
| spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ( sK1 @ sK5 )
| ( sK0 @ sK5 ) ) )
| spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f32,plain,
( ~ spl3_4
| ~ spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f14,f16,f29]) ).
thf(f14,plain,
( ( ( sK0 @ sK2 )
!= $true )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
!= sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
!= sK0 )
| ( ( ( sK0 @ sK2 )
!= $true )
& ( ( sK1 @ sK2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
= sK0 )
| ! [X3: a] :
( ( ( sK0 @ X3 )
= $true )
| ( ( sK1 @ X3 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
!= X0 )
| ? [X2: a] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 )
| ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) ) ) )
=> ( ( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
!= sK0 )
| ? [X2: a] :
( ( ( sK0 @ X2 )
!= $true )
& ( ( sK1 @ X2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
= sK0 )
| ! [X3: a] :
( ( ( sK0 @ X3 )
= $true )
| ( ( sK1 @ X3 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: a] :
( ( ( sK0 @ X2 )
!= $true )
& ( ( sK1 @ X2 )
= $true ) )
=> ( ( ( sK0 @ sK2 )
!= $true )
& ( ( sK1 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
!= X0 )
| ? [X2: a] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 )
| ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
!= X0 )
| ? [X2: a] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 )
| ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) )
<~> ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 )
<=> ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) )
<=> ( ( ^ [X3: a] :
( ( X0 @ X3 )
| ( X1 @ X3 ) ) )
= X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) )
<=> ( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) )
<=> ( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.rmQsGkKnxH/DTF2THF_20820.p',cGAZING_THM38_pme) ).
thf(f27,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f13,f24,f16]) ).
thf(f13,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
!= sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f22,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f12,f20,f16]) ).
thf(f12,plain,
! [X3: a] :
( ( ( sK0 @ X3 )
= $true )
| ( ( sK1 @ X3 )
!= $true )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) )
= sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU848^5 : 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 : n023.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 12:36:19 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
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEU848^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.47 % Domain : Set Theory
% 0.27/0.47 % Problem : TPS problem GAZING-THM38
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.27/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : tps_0282 [Bro09]
% 0.27/0.47 % : 38 [Bar92]
% 0.27/0.47 % : GAZING-THM38 [TPS]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % 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, 0.00 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
% 0.27/0.47 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.27/0.47 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.27/0.47 % Number of connectives : 7 ( 0 ~; 1 |; 0 &; 4 @)
% 0.27/0.47 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 7 ( 7 avg)
% 0.27/0.47 % Number of types : 2 ( 1 usr)
% 0.27/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.27/0.47 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.47 % : Polymorphic definitions expanded.
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(a_type,type,
% 0.27/0.47 a: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(cGAZING_THM38_pme,conjecture,
% 0.27/0.47 ! [S: a > $o,T: a > $o] :
% 0.27/0.47 ( ( ( ^ [Xz: a] :
% 0.27/0.47 ( ( S @ Xz )
% 0.27/0.47 | ( T @ Xz ) ) )
% 0.27/0.47 = S )
% 0.27/0.47 <=> ! [Xx: a] :
% 0.27/0.47 ( ( T @ Xx )
% 0.27/0.47 => ( S @ Xx ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 12:36:20 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rmQsGkKnxH/DTF2DTF20820.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(a_type,type,
% 1.47/1.27 a: $tType ).
% 1.47/1.27
% 1.47/1.27 thf(cGAZING_THM38_pme,conjecture,
% 1.47/1.27 ! [S: a > $o,T: a > $o] :
% 1.47/1.27 ( ( ( ^ [Xz: a] :
% 1.47/1.27 ( ( S @ Xz )
% 1.47/1.27 | ( T @ Xz ) ) )
% 1.47/1.27 = S )
% 1.47/1.27 <=> ! [Xx: a] :
% 1.47/1.27 ( ( T @ Xx )
% 1.47/1.27 => ( S @ Xx ) ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.29 % (21105)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_20820 for (2999ds/2Mi)
% 1.47/1.29 % (21103)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_20820 for (2999ds/27Mi)
% 1.47/1.29 % (21105)Refutation not found, incomplete strategy
% 1.47/1.29 % (21105)------------------------------
% 1.47/1.29 % (21105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (21105)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (21105)Memory used [KB]: 5500
% 1.47/1.29 % (21105)Time elapsed: 0.002 s
% 1.47/1.29 % (21105)Instructions burned: 1 (million)
% 1.47/1.29 % (21105)------------------------------
% 1.47/1.29 % (21105)------------------------------
% 1.47/1.29 % (21103)First to succeed.
% 1.47/1.29 % (21103)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_20820
% 1.47/1.29 % SZS output start Proof for DTF2THF_20820
% 1.47/1.29 thf(type_def_5, type, a: $tType).
% 1.47/1.29 thf(func_def_0, type, a: $tType).
% 1.47/1.29 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.47/1.29 thf(func_def_8, type, sK0: a > $o).
% 1.47/1.29 thf(func_def_9, type, sK1: a > $o).
% 1.47/1.29 thf(func_def_10, type, sK2: a).
% 1.47/1.29 thf(func_def_12, type, ph4: !>[X0: $tType]:(X0)).
% 1.47/1.29 thf(func_def_13, type, sK5: a).
% 1.47/1.29 thf(f112,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(avatar_sat_refutation,[status(thm)],[f22,f27,f32,f50,f60,f64,f103,f111])).
% 1.47/1.29 thf(f111,plain,(
% 1.47/1.29 spl3_5 | ~spl3_2 | ~spl3_6),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f110,f47,f20,f43])).
% 1.47/1.29 thf(f43,definition,(
% 1.47/1.29 spl3_5 <=> ((sK0 @ sK5) = $true)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.47/1.29 thf(f20,definition,(
% 1.47/1.29 spl3_2 <=> ! [X3 : a] : (((sK0 @ X3) = $true) | ((sK1 @ X3) != $true))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.47/1.29 thf(f47,definition,(
% 1.47/1.29 spl3_6 <=> ((sK1 @ sK5) = $true)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.47/1.29 thf(f110,plain,(
% 1.47/1.29 ((sK0 @ sK5) = $true) | (~spl3_2 | ~spl3_6)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.47/1.29 thf(f108,plain,(
% 1.47/1.29 ($true != $true) | ((sK0 @ sK5) = $true) | (~spl3_2 | ~spl3_6)),
% 1.47/1.29 inference(superposition,[status(thm)],[f21,f49])).
% 1.47/1.29 thf(f49,plain,(
% 1.47/1.29 ((sK1 @ sK5) = $true) | ~spl3_6),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.47/1.29 thf(f21,plain,(
% 1.47/1.29 ( ! [X3 : a] : (((sK1 @ X3) != $true) | ((sK0 @ X3) = $true)) ) | ~spl3_2),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.47/1.29 thf(f103,plain,(
% 1.47/1.29 ~spl3_1 | ~spl3_3 | spl3_4),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f102])).
% 1.47/1.29 thf(f102,plain,(
% 1.47/1.29 $false | (~spl3_1 | ~spl3_3 | spl3_4)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.47/1.29 thf(f101,plain,(
% 1.47/1.29 ($false = $true) | (~spl3_1 | ~spl3_3 | spl3_4)),
% 1.47/1.29 inference(forward_demodulation,[status(thm)],[f92,f83])).
% 1.47/1.29 thf(f83,plain,(
% 1.47/1.29 ($false = (sK0 @ sK2)) | (~spl3_1 | spl3_4)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.47/1.29 thf(f80,plain,(
% 1.47/1.29 ($true != $true) | ($false = (sK0 @ sK2)) | (~spl3_1 | spl3_4)),
% 1.47/1.29 inference(superposition,[status(thm)],[f31,f73])).
% 1.47/1.29 thf(f73,plain,(
% 1.47/1.29 ( ! [X1 : a] : (((sK0 @ X1) = $true) | ((sK0 @ X1) = $false)) ) | ~spl3_1),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.47/1.29 thf(f72,plain,(
% 1.47/1.29 ( ! [X1 : a] : (((sK0 @ X1) = $true) | (((sK1 @ X1) | (sK0 @ X1)) = $false)) ) | ~spl3_1),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.47/1.29 thf(f70,plain,(
% 1.47/1.29 ( ! [X1 : a] : ((((sK1 @ X1) | (sK0 @ X1)) = (sK0 @ X1))) ) | ~spl3_1),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.47/1.29 thf(f69,plain,(
% 1.47/1.29 ( ! [X1 : a] : (((sK0 @ X1) = ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) @ X1))) ) | ~spl3_1),
% 1.47/1.29 inference(argument_congruence,[status(thm)],[f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = sK0) | ~spl3_1),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.47/1.29 thf(f16,definition,(
% 1.47/1.29 spl3_1 <=> ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = sK0)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.47/1.29 thf(f31,plain,(
% 1.47/1.29 ((sK0 @ sK2) != $true) | spl3_4),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.47/1.29 thf(f29,definition,(
% 1.47/1.29 spl3_4 <=> ((sK0 @ sK2) = $true)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.47/1.29 thf(f92,plain,(
% 1.47/1.29 ((sK0 @ sK2) = $true) | (~spl3_1 | ~spl3_3)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.47/1.29 thf(f88,plain,(
% 1.47/1.29 ((sK0 @ sK2) = $true) | ($false = $true) | (~spl3_1 | ~spl3_3)),
% 1.47/1.29 inference(superposition,[status(thm)],[f74,f26])).
% 1.47/1.29 thf(f26,plain,(
% 1.47/1.29 ((sK1 @ sK2) = $true) | ~spl3_3),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.47/1.29 thf(f24,definition,(
% 1.47/1.29 spl3_3 <=> ((sK1 @ sK2) = $true)),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.47/1.29 thf(f74,plain,(
% 1.47/1.29 ( ! [X1 : a] : (($false = (sK1 @ X1)) | ((sK0 @ X1) = $true)) ) | ~spl3_1),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.47/1.29 thf(f64,plain,(
% 1.47/1.29 ~spl3_5 | ~spl3_8),
% 1.47/1.29 inference(avatar_contradiction_clause,[status(thm)],[f63])).
% 1.47/1.29 thf(f63,plain,(
% 1.47/1.29 $false | (~spl3_5 | ~spl3_8)),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.47/1.29 thf(f62,plain,(
% 1.47/1.29 ($false = $true) | (~spl3_5 | ~spl3_8)),
% 1.47/1.29 inference(backward_demodulation,[status(thm)],[f45,f58])).
% 1.47/1.29 thf(f58,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | ~spl3_8),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.47/1.29 thf(f56,definition,(
% 1.47/1.29 spl3_8 <=> ($false = (sK0 @ sK5))),
% 1.47/1.29 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.47/1.29 thf(f45,plain,(
% 1.47/1.29 ((sK0 @ sK5) = $true) | ~spl3_5),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.47/1.29 thf(f60,plain,(
% 1.47/1.29 spl3_8 | spl3_1),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f39,f16,f56])).
% 1.47/1.29 thf(f39,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | spl3_1),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f37])).
% 1.47/1.29 thf(f37,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | ($false = (sK0 @ sK5)) | spl3_1),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.47/1.29 thf(f36,plain,(
% 1.47/1.29 ($false = (sK0 @ sK5)) | ($false = ((sK1 @ sK5) | (sK0 @ sK5))) | spl3_1),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.47/1.29 thf(f34,plain,(
% 1.47/1.29 ((sK0 @ sK5) != ((sK1 @ sK5) | (sK0 @ sK5))) | spl3_1),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.47/1.29 thf(f33,plain,(
% 1.47/1.29 (((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) @ sK5) != (sK0 @ sK5)) | spl3_1),
% 1.47/1.29 inference(negative_extensionality,[status(thm)],[f17])).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) != sK0) | spl3_1),
% 1.47/1.29 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.47/1.29 thf(f50,plain,(
% 1.47/1.29 spl3_5 | spl3_6 | spl3_1),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f41,f16,f47,f43])).
% 1.47/1.29 thf(f41,plain,(
% 1.47/1.29 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true) | spl3_1),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.47/1.29 thf(f40,plain,(
% 1.47/1.29 ((sK0 @ sK5) = $true) | ((sK0 @ sK5) = $true) | ((sK1 @ sK5) = $true) | spl3_1),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.47/1.29 thf(f35,plain,(
% 1.47/1.29 ((sK0 @ sK5) = $true) | ($true = ((sK1 @ sK5) | (sK0 @ sK5))) | spl3_1),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.47/1.29 thf(f32,plain,(
% 1.47/1.29 ~spl3_4 | ~spl3_1),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f14,f16,f29])).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 ((sK0 @ sK2) != $true) | ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) != sK0)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 (((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) != sK0) | (((sK0 @ sK2) != $true) & ((sK1 @ sK2) = $true))) & (((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = sK0) | ! [X3 : a] : (((sK0 @ X3) = $true) | ((sK1 @ X3) != $true)))),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) != X0) | ? [X2 : a] : (((X0 @ X2) != $true) & ((X1 @ X2) = $true))) & (((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = X0) | ! [X3 : a] : (((X0 @ X3) = $true) | ((X1 @ X3) != $true)))) => ((((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) != sK0) | ? [X2 : a] : (((sK0 @ X2) != $true) & ((sK1 @ X2) = $true))) & (((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = sK0) | ! [X3 : a] : (((sK0 @ X3) = $true) | ((sK1 @ X3) != $true))))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 ? [X2 : a] : (((sK0 @ X2) != $true) & ((sK1 @ X2) = $true)) => (((sK0 @ sK2) != $true) & ((sK1 @ sK2) = $true))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) != X0) | ? [X2 : a] : (((X0 @ X2) != $true) & ((X1 @ X2) = $true))) & (((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = X0) | ! [X3 : a] : (((X0 @ X3) = $true) | ((X1 @ X3) != $true))))),
% 1.47/1.29 inference(rectify,[status(thm)],[f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) != X0) | ? [X2 : a] : (((X0 @ X2) != $true) & ((X1 @ X2) = $true))) & (((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = X0) | ! [X2 : a] : (((X0 @ X2) = $true) | ((X1 @ X2) != $true))))),
% 1.47/1.29 inference(nnf_transformation,[status(thm)],[f6])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ? [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X0 @ X2) = $true) | ((X1 @ X2) != $true)) <~> ((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = X0))),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,plain,(
% 1.47/1.29 ~! [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = X0) <=> ! [X2 : a] : (((X1 @ X2) = $true) => ((X0 @ X2) = $true)))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.29 thf(f4,plain,(
% 1.47/1.29 ~! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) <=> ((^[X3 : a] : ((X0 @ X3) | (X1 @ X3))) = X0))),
% 1.47/1.29 inference(rectify,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,negated_conjecture,(
% 1.47/1.29 ~! [X0 : a > $o,X1 : a > $o] : (! [X3 : a] : ((X1 @ X3) => (X0 @ X3)) <=> ((^[X2 : a] : ((X0 @ X2) | (X1 @ X2))) = X0))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.29 thf(f1,conjecture,(
% 1.47/1.29 ! [X0 : a > $o,X1 : a > $o] : (! [X3 : a] : ((X1 @ X3) => (X0 @ X3)) <=> ((^[X2 : a] : ((X0 @ X2) | (X1 @ X2))) = X0))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.rmQsGkKnxH/DTF2THF_20820.p',cGAZING_THM38_pme)).
% 1.47/1.29 thf(f27,plain,(
% 1.47/1.29 ~spl3_1 | spl3_3),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f13,f24,f16])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 ((sK1 @ sK2) = $true) | ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) != sK0)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.29 thf(f22,plain,(
% 1.47/1.29 spl3_1 | spl3_2),
% 1.47/1.29 inference(avatar_split_clause,[status(thm)],[f12,f20,f16])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 ( ! [X3 : a] : (((sK0 @ X3) = $true) | ((sK1 @ X3) != $true) | ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = sK0)) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.29 % SZS output end Proof for DTF2THF_20820
% 1.47/1.29 % (21103)------------------------------
% 1.47/1.29 % (21103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (21103)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (21103)Memory used [KB]: 5500
% 1.47/1.29 % (21103)Time elapsed: 0.005 s
% 1.47/1.29 % (21103)Instructions burned: 6 (million)
% 1.47/1.29 % (21103)------------------------------
% 1.47/1.29 % (21103)------------------------------
% 1.47/1.29 % (21100)Success in time 0.015 s
%------------------------------------------------------------------------------