%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU883^5 : 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 : n014.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 09:37:39 AM UTC 2026
% Result : Theorem 1.28s 1.12s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 9 unt; 0 typ; 5 def)
% Number of atoms : 292 ( 123 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 333 ( 40 ~; 59 |; 39 &; 170 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 11 con; 0-2 aty)
% ( 0 !!; 20 ??; 0 @@+; 0 @@-)
% Number of variables : 58 ( 38 ^; 14 !; 6 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
f: b > a ).
thf(func_def_3,type,
g: b > $o ).
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK2: a ).
thf(func_def_16,type,
sK3: b ).
thf(func_def_17,type,
sK4: b ).
thf(f74,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f41,f46,f51,f52,f56,f65,f73]) ).
thf(f73,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f68,f50]) ).
thf(f50,plain,
( ( ( f @ sK3 )
= sK2 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl0_4
<=> ( ( f @ sK3 )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f68,plain,
( ( ( f @ sK3 )
!= sK2 )
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $false = $true )
| ( ( f @ sK3 )
!= sK2 )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f36,f55]) ).
thf(f55,plain,
( ! [X2: b] :
( ( ( g @ X2 )
= $false )
| ( ( f @ X2 )
!= sK2 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl0_5
<=> ! [X2: b] :
( ( ( f @ X2 )
!= sK2 )
| ( ( g @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f36,plain,
( ( ( g @ sK3 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl0_1
<=> ( ( g @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f65,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f59,f54,f43,f38]) ).
thf(f38,definition,
( spl0_2
<=> ( sK2
= ( f @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f43,definition,
( spl0_3
<=> ( ( g @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f59,plain,
( ( sK2
!= ( f @ sK4 ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( sK2
!= ( f @ sK4 ) )
| ( $false = $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f45,f55]) ).
thf(f45,plain,
( ( ( g @ sK4 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f56,plain,
( spl0_5
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f19,f54,f54]) ).
thf(f19,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK2 )
| ( ( f @ X2 )
!= sK2 )
| ( ( g @ X2 )
= $false )
| ( ( g @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK2 )
| ( $false
= ( ( f @ X2 )
= sK2 ) )
| ( ( g @ X1 )
= $false )
| ( ( g @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: b,X1: b] :
( ( ( g @ X1 )
= $false )
| ( $false
= ( ( ( f @ X2 )
= sK2 )
& ( g @ X2 ) ) )
| ( ( f @ X1 )
!= sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: b,X1: b] :
( ( ( g @ X1 )
= $false )
| ( ( f @ X1 )
!= sK2 )
| ( $false
= ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( g @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: b] :
( ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( g @ Y0 ) ) ) )
| ( ( g @ X1 )
= $false )
| ( ( f @ X1 )
!= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: b] :
( ( ( g @ X1 )
= $false )
| ( $false
= ( ( f @ X1 )
= sK2 ) )
| ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( g @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: b] :
( ( $false
= ( ( g @ X1 )
& ( ( f @ X1 )
= sK2 ) ) )
| ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( g @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: b] :
( ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( g @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: b] :
( ( g @ Y0 )
& ( ( f @ Y0 )
= sK2 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( g @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) ) )
| ( $false
= ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( g @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( g @ Y0 ) ) )
!= ( ?? @ b
@ ^ [Y0: b] :
( ( g @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( g @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( g @ Y1 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( g @ Y1 ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( g @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( g @ Y1 ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( g @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( ( f @ Y1 )
= Y0 )
& ( g @ Y1 ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( g @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a] :
? [X1: b] :
( ( g @ X1 )
& ( ( f @ X1 )
= X0 ) ) )
!= ( ^ [X2: a] :
? [X3: b] :
( ( ( f @ X3 )
= X2 )
& ( g @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( g @ X1 )
& ( ( f @ X1 )
= X0 ) ) )
!= ( ^ [X0: a] :
? [X2: b] :
( ( ( f @ X2 )
= X0 )
& ( g @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a] :
? [X1: b] :
( ( g @ X1 )
& ( ( f @ X1 )
= X0 ) ) )
= ( ^ [X0: a] :
? [X2: b] :
( ( ( f @ X2 )
= X0 )
& ( g @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YimJaeopdM/DTF2THF_20696.p',cX5212_pme) ).
thf(f52,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f28,f43,f48]) ).
thf(f28,plain,
( ( ( f @ sK3 )
= sK2 )
| ( ( g @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( f @ sK3 )
= sK2 )
| ( ( ( g @ sK4 )
& ( ( f @ sK4 )
= sK2 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $true
= ( ( f @ sK3 )
= sK2 ) )
| ( ( ( g @ sK4 )
& ( ( f @ sK4 )
= sK2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( ( ( f @ sK3 )
= sK2 )
& ( g @ sK3 ) ) )
| ( ( ( g @ sK4 )
& ( ( f @ sK4 )
= sK2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true
= ( ^ [Y0: b] :
( ( g @ Y0 )
& ( ( f @ Y0 )
= sK2 ) )
@ sK4 ) )
| ( $true
= ( ( ( f @ sK3 )
= sK2 )
& ( g @ sK3 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( g @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true )
| ( $true
= ( ( ( f @ sK3 )
= sK2 )
& ( g @ sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true
= ( ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( g @ Y0 ) )
@ sK3 ) )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( g @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ?? @ b
@ ^ [Y0: b] :
( ( ( f @ Y0 )
= sK2 )
& ( g @ Y0 ) ) )
= $true )
| ( ( ?? @ b
@ ^ [Y0: b] :
( ( g @ Y0 )
& ( ( f @ Y0 )
= sK2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f51,plain,
( spl0_4
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f29,f38,f48]) ).
thf(f29,plain,
( ( sK2
= ( f @ sK4 ) )
| ( ( f @ sK3 )
= sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( f @ sK3 )
= sK2 )
| ( ( ( f @ sK4 )
= sK2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f46,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f31,f43,f34]) ).
thf(f31,plain,
( ( ( g @ sK4 )
= $true )
| ( ( g @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( g @ sK3 )
= $true )
| ( ( ( g @ sK4 )
& ( ( f @ sK4 )
= sK2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f41,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f38,f34]) ).
thf(f32,plain,
( ( ( g @ sK3 )
= $true )
| ( sK2
= ( f @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ( f @ sK4 )
= sK2 )
= $true )
| ( ( g @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU883^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n014.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:36:12 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEU883^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.42 % Domain : Set Theory
% 0.16/0.42 % Problem : TPS problem X5212
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0209 [Bro09]
% 0.16/0.42 % : X5212 [TPS]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.00 v6.0.0, 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 v4.0.0
% 0.16/0.42 % Syntax : Number of formulae : 5 ( 1 unt; 4 typ; 0 def)
% 0.16/0.42 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 1 ( 5 avg)
% 0.16/0.42 % Number of connectives : 6 ( 0 ~; 0 |; 2 &; 4 @)
% 0.16/0.42 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 1 ( 1 avg)
% 0.16/0.42 % Number of types : 3 ( 2 usr)
% 0.16/0.42 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.16/0.42 % Number of variables : 4 ( 2 ^; 0 !; 2 ?; 4 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 % : Polymorphic definitions expanded.
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(b_type,type,
% 0.16/0.42 b: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(a_type,type,
% 0.16/0.42 a: $tType ).
% 0.16/0.42
% 0.16/0.42 thf(f,type,
% 0.16/0.42 f: b > a ).
% 0.16/0.42
% 0.16/0.42 thf(g,type,
% 0.16/0.42 g: b > $o ).
% 0.16/0.42
% 0.16/0.42 thf(cX5212_pme,conjecture,
% 0.16/0.42 ( ( ^ [Xz: a] :
% 0.16/0.42 ? [Xx: b] :
% 0.16/0.42 ( ( g @ Xx )
% 0.16/0.42 & ( Xz
% 0.16/0.42 = ( f @ Xx ) ) ) )
% 0.16/0.42 = ( ^ [Xz: a] :
% 0.16/0.42 ? [Xt: b] :
% 0.16/0.42 ( ( g @ Xt )
% 0.16/0.42 & ( Xz
% 0.16/0.42 = ( f @ Xt ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.10/1.10 ---- Embedded in THF ---
% 1.10/1.10 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.10/1.10 %%% Generated on Tue Feb 24 12:36:13 EST 2026
% 1.10/1.10 %%% using '$$dhol' embedding, version 1.3.0.
% 1.10/1.10 %%% Logic specification used:
% 1.10/1.10 %%% thf(spec, logic, $$dhol).
% 1.10/1.10
% 1.10/1.10 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YimJaeopdM/DTF2DTF20696.p
% See solution above
% 1.10/1.10 ------------------------
% 1.10/1.10 ---- Cleaned THF ---
% 1.10/1.10 thf(b_type,type,
% 1.10/1.10 b: $tType ).
% 1.10/1.10
% 1.10/1.10 thf(a_type,type,
% 1.10/1.10 a: $tType ).
% 1.10/1.10
% 1.10/1.10 thf(f,type,
% 1.10/1.10 f: b > a ).
% 1.10/1.10
% 1.10/1.10 thf(g,type,
% 1.10/1.10 g: b > $o ).
% 1.10/1.10
% 1.10/1.10 thf(cX5212_pme,conjecture,
% 1.10/1.10 ( ( ^ [Xz: a] :
% 1.10/1.10 ? [Xx: b] :
% 1.10/1.10 ( ( g @ Xx )
% 1.10/1.10 & ( Xz
% 1.10/1.10 = ( f @ Xx ) ) ) )
% 1.10/1.10 = ( ^ [Xz: a] :
% 1.10/1.10 ? [Xt: b] :
% 1.10/1.10 ( ( g @ Xt )
% 1.10/1.10 & ( Xz
% 1.10/1.10 = ( f @ Xt ) ) ) ) ) ).
% 1.10/1.11 ------------------------
% 1.28/1.12 % (20796)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20696 for (3000ds/183Mi)
% 1.28/1.12 % (20796)First to succeed.
% 1.28/1.12 % (20796)Refutation found. Thanks to Tanya!
% 1.28/1.12 % SZS status Theorem for DTF2THF_20696
% 1.28/1.12 % SZS output start Proof for DTF2THF_20696
% 1.28/1.12 thf(type_def_5, type, b: $tType).
% 1.28/1.12 thf(type_def_6, type, a: $tType).
% 1.28/1.12 thf(func_def_0, type, b: $tType).
% 1.28/1.12 thf(func_def_1, type, a: $tType).
% 1.28/1.12 thf(func_def_2, type, f: b > a).
% 1.28/1.12 thf(func_def_3, type, g: b > $o).
% 1.28/1.12 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 1.28/1.12 thf(func_def_15, type, sK2: a).
% 1.28/1.12 thf(func_def_16, type, sK3: b).
% 1.28/1.12 thf(func_def_17, type, sK4: b).
% 1.28/1.12 thf(f74,plain,(
% 1.28/1.12 $false),
% 1.28/1.12 inference(avatar_sat_refutation,[status(thm)],[f41,f46,f51,f52,f56,f65,f73])).
% 1.28/1.12 thf(f73,plain,(
% 1.28/1.12 ~spl0_1 | ~spl0_4 | ~spl0_5),
% 1.28/1.12 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.28/1.12 thf(f72,plain,(
% 1.28/1.12 $false | (~spl0_1 | ~spl0_4 | ~spl0_5)),
% 1.28/1.12 inference(subsumption_resolution,[status(thm)],[f68,f50])).
% 1.28/1.12 thf(f50,plain,(
% 1.28/1.12 ((f @ sK3) = sK2) | ~spl0_4),
% 1.28/1.12 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.28/1.12 thf(f48,definition,(
% 1.28/1.12 spl0_4 <=> ((f @ sK3) = sK2)),
% 1.28/1.12 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.28/1.12 thf(f68,plain,(
% 1.28/1.12 ((f @ sK3) != sK2) | (~spl0_1 | ~spl0_5)),
% 1.28/1.12 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.28/1.12 thf(f66,plain,(
% 1.28/1.12 ($false = $true) | ((f @ sK3) != sK2) | (~spl0_1 | ~spl0_5)),
% 1.28/1.12 inference(superposition,[status(thm)],[f36,f55])).
% 1.28/1.12 thf(f55,plain,(
% 1.28/1.12 ( ! [X2 : b] : (((g @ X2) = $false) | ((f @ X2) != sK2)) ) | ~spl0_5),
% 1.28/1.12 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.28/1.12 thf(f54,definition,(
% 1.28/1.12 spl0_5 <=> ! [X2 : b] : (((f @ X2) != sK2) | ((g @ X2) = $false))),
% 1.28/1.12 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.28/1.12 thf(f36,plain,(
% 1.28/1.12 ((g @ sK3) = $true) | ~spl0_1),
% 1.28/1.12 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.28/1.12 thf(f34,definition,(
% 1.28/1.12 spl0_1 <=> ((g @ sK3) = $true)),
% 1.28/1.12 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.28/1.12 thf(f65,plain,(
% 1.28/1.12 ~spl0_2 | ~spl0_3 | ~spl0_5),
% 1.28/1.12 inference(avatar_split_clause,[status(thm)],[f59,f54,f43,f38])).
% 1.28/1.12 thf(f38,definition,(
% 1.28/1.12 spl0_2 <=> (sK2 = (f @ sK4))),
% 1.28/1.12 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.28/1.12 thf(f43,definition,(
% 1.28/1.12 spl0_3 <=> ((g @ sK4) = $true)),
% 1.28/1.12 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.28/1.12 thf(f59,plain,(
% 1.28/1.12 (sK2 != (f @ sK4)) | (~spl0_3 | ~spl0_5)),
% 1.28/1.12 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.28/1.12 thf(f58,plain,(
% 1.28/1.12 (sK2 != (f @ sK4)) | ($false = $true) | (~spl0_3 | ~spl0_5)),
% 1.28/1.12 inference(superposition,[status(thm)],[f45,f55])).
% 1.28/1.12 thf(f45,plain,(
% 1.28/1.12 ((g @ sK4) = $true) | ~spl0_3),
% 1.28/1.12 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.28/1.12 thf(f56,plain,(
% 1.28/1.12 spl0_5 | spl0_5),
% 1.28/1.12 inference(avatar_split_clause,[status(thm)],[f19,f54,f54])).
% 1.28/1.12 thf(f19,plain,(
% 1.28/1.12 ( ! [X2 : b,X1 : b] : (((f @ X1) != sK2) | ((f @ X2) != sK2) | ((g @ X2) = $false) | ((g @ X1) = $false)) )),
% 1.28/1.12 inference(equality_proxy_clausification,[status(thm)],[f18])).
% 1.28/1.12 thf(f18,plain,(
% 1.28/1.12 ( ! [X2 : b,X1 : b] : (((f @ X1) != sK2) | ($false = ((f @ X2) = sK2)) | ((g @ X1) = $false) | ((g @ X2) = $false)) )),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.28/1.12 thf(f17,plain,(
% 1.28/1.12 ( ! [X2 : b,X1 : b] : (((g @ X1) = $false) | ($false = (((f @ X2) = sK2) & (g @ X2))) | ((f @ X1) != sK2)) )),
% 1.28/1.12 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.28/1.12 thf(f16,plain,(
% 1.28/1.12 ( ! [X2 : b,X1 : b] : (((g @ X1) = $false) | ((f @ X1) != sK2) | ($false = ((^[Y0 : b]: (((f @ Y0) = sK2) & (g @ Y0))) @ X2))) )),
% 1.28/1.12 inference(pi_clausification,[status(thm)],[f15])).
% 1.28/1.12 thf(f15,plain,(
% 1.28/1.12 ( ! [X1 : b] : (($false = (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (g @ Y0))))) | ((g @ X1) = $false) | ((f @ X1) != sK2)) )),
% 1.28/1.12 inference(equality_proxy_clausification,[status(thm)],[f14])).
% 1.28/1.12 thf(f14,plain,(
% 1.28/1.12 ( ! [X1 : b] : (((g @ X1) = $false) | ($false = ((f @ X1) = sK2)) | ($false = (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (g @ Y0)))))) )),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.28/1.12 thf(f13,plain,(
% 1.28/1.12 ( ! [X1 : b] : (($false = ((g @ X1) & ((f @ X1) = sK2))) | ($false = (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (g @ Y0)))))) )),
% 1.28/1.12 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.28/1.12 thf(f12,plain,(
% 1.28/1.12 ( ! [X1 : b] : (($false = (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (g @ Y0))))) | ($false = ((^[Y0 : b]: ((g @ Y0) & ((f @ Y0) = sK2))) @ X1))) )),
% 1.28/1.12 inference(pi_clausification,[status(thm)],[f11])).
% 1.28/1.12 thf(f11,plain,(
% 1.28/1.12 ($false = (?? @ b @ (^[Y0 : b]: ((g @ Y0) & ((f @ Y0) = sK2))))) | ($false = (?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (g @ Y0)))))),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.28/1.12 thf(f9,plain,(
% 1.28/1.12 ((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (g @ Y0)))) != (?? @ b @ (^[Y0 : b]: ((g @ Y0) & ((f @ Y0) = sK2)))))),
% 1.28/1.12 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.28/1.12 thf(f8,plain,(
% 1.28/1.12 (((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((g @ Y1) & ((f @ Y1) = Y0))))) @ sK2) != ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & (g @ Y1))))) @ sK2))),
% 1.28/1.12 inference(negative_extensionality,[status(thm)],[f7])).
% 1.28/1.12 thf(f7,plain,(
% 1.28/1.12 ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & (g @ Y1))))) != (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((g @ Y1) & ((f @ Y1) = Y0))))))),
% 1.28/1.12 inference(cnf_transformation,[status(thm)],[f6])).
% 1.28/1.12 thf(f6,plain,(
% 1.28/1.12 ((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & (g @ Y1))))) != (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((g @ Y1) & ((f @ Y1) = Y0))))))),
% 1.28/1.12 inference(flattening,[status(thm)],[f5])).
% 1.28/1.12 thf(f5,plain,(
% 1.28/1.12 ~((^[Y0 : a]: (?? @ b @ (^[Y1 : b]: (((f @ Y1) = Y0) & (g @ Y1))))) = (^[Y0 : a]: (?? @ b @ (^[Y1 : b]: ((g @ Y1) & ((f @ Y1) = Y0))))))),
% 1.28/1.12 inference(fool_elimination,[status(thm)],[f4])).
% 1.28/1.12 thf(f4,plain,(
% 1.28/1.12 ~((^[X0 : a] : (? [X1 : b] : ((g @ X1) & ((f @ X1) = X0)))) = (^[X2 : a] : (? [X3 : b] : (((f @ X3) = X2) & (g @ X3)))))),
% 1.28/1.12 inference(rectify,[status(thm)],[f2])).
% 1.28/1.12 thf(f2,negated_conjecture,(
% 1.28/1.12 ~((^[X0 : a] : (? [X1 : b] : ((g @ X1) & ((f @ X1) = X0)))) = (^[X0 : a] : (? [X2 : b] : (((f @ X2) = X0) & (g @ X2)))))),
% 1.28/1.12 inference(negated_conjecture,[status(cth)],[f1])).
% 1.28/1.12 thf(f1,conjecture,(
% 1.28/1.12 ((^[X0 : a] : (? [X1 : b] : ((g @ X1) & ((f @ X1) = X0)))) = (^[X0 : a] : (? [X2 : b] : (((f @ X2) = X0) & (g @ X2)))))),
% 1.28/1.12 file('/export/starexec/sandbox/tmp/tmp.YimJaeopdM/DTF2THF_20696.p',cX5212_pme)).
% 1.28/1.12 thf(f52,plain,(
% 1.28/1.12 spl0_4 | spl0_3),
% 1.28/1.12 inference(avatar_split_clause,[status(thm)],[f28,f43,f48])).
% 1.28/1.12 thf(f28,plain,(
% 1.28/1.12 ((f @ sK3) = sK2) | ((g @ sK4) = $true)),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.28/1.12 thf(f26,plain,(
% 1.28/1.12 ((f @ sK3) = sK2) | (((g @ sK4) & ((f @ sK4) = sK2)) = $true)),
% 1.28/1.12 inference(equality_proxy_clausification,[status(thm)],[f25])).
% 1.28/1.12 thf(f25,plain,(
% 1.28/1.12 ($true = ((f @ sK3) = sK2)) | (((g @ sK4) & ((f @ sK4) = sK2)) = $true)),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.28/1.12 thf(f23,plain,(
% 1.28/1.12 ($true = (((f @ sK3) = sK2) & (g @ sK3))) | (((g @ sK4) & ((f @ sK4) = sK2)) = $true)),
% 1.28/1.12 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.28/1.12 thf(f22,plain,(
% 1.28/1.12 ($true = ((^[Y0 : b]: ((g @ Y0) & ((f @ Y0) = sK2))) @ sK4)) | ($true = (((f @ sK3) = sK2) & (g @ sK3)))),
% 1.28/1.12 inference(sigma_clausification,[status(thm)],[f21])).
% 1.28/1.12 thf(f21,plain,(
% 1.28/1.12 ((?? @ b @ (^[Y0 : b]: ((g @ Y0) & ((f @ Y0) = sK2)))) = $true) | ($true = (((f @ sK3) = sK2) & (g @ sK3)))),
% 1.28/1.12 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.28/1.12 thf(f20,plain,(
% 1.28/1.12 ($true = ((^[Y0 : b]: (((f @ Y0) = sK2) & (g @ Y0))) @ sK3)) | ((?? @ b @ (^[Y0 : b]: ((g @ Y0) & ((f @ Y0) = sK2)))) = $true)),
% 1.28/1.12 inference(sigma_clausification,[status(thm)],[f10])).
% 1.28/1.12 thf(f10,plain,(
% 1.28/1.12 ((?? @ b @ (^[Y0 : b]: (((f @ Y0) = sK2) & (g @ Y0)))) = $true) | ((?? @ b @ (^[Y0 : b]: ((g @ Y0) & ((f @ Y0) = sK2)))) = $true)),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.28/1.12 thf(f51,plain,(
% 1.28/1.12 spl0_4 | spl0_2),
% 1.28/1.12 inference(avatar_split_clause,[status(thm)],[f29,f38,f48])).
% 1.28/1.12 thf(f29,plain,(
% 1.28/1.12 (sK2 = (f @ sK4)) | ((f @ sK3) = sK2)),
% 1.28/1.12 inference(equality_proxy_clausification,[status(thm)],[f27])).
% 1.28/1.12 thf(f27,plain,(
% 1.28/1.12 ((f @ sK3) = sK2) | (((f @ sK4) = sK2) = $true)),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.28/1.12 thf(f46,plain,(
% 1.28/1.12 spl0_1 | spl0_3),
% 1.28/1.12 inference(avatar_split_clause,[status(thm)],[f31,f43,f34])).
% 1.28/1.12 thf(f31,plain,(
% 1.28/1.12 ((g @ sK4) = $true) | ((g @ sK3) = $true)),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.28/1.12 thf(f24,plain,(
% 1.28/1.12 ((g @ sK3) = $true) | (((g @ sK4) & ((f @ sK4) = sK2)) = $true)),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.28/1.12 thf(f41,plain,(
% 1.28/1.12 spl0_1 | spl0_2),
% 1.28/1.12 inference(avatar_split_clause,[status(thm)],[f32,f38,f34])).
% 1.28/1.12 thf(f32,plain,(
% 1.28/1.12 ((g @ sK3) = $true) | (sK2 = (f @ sK4))),
% 1.28/1.12 inference(equality_proxy_clausification,[status(thm)],[f30])).
% 1.28/1.12 thf(f30,plain,(
% 1.28/1.12 (((f @ sK4) = sK2) = $true) | ((g @ sK3) = $true)),
% 1.28/1.12 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.28/1.12 % SZS output end Proof for DTF2THF_20696
% 1.28/1.12 % (20796)------------------------------
% 1.28/1.12 % (20796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.12 % (20796)Termination reason: Refutation
% 1.28/1.12
% 1.28/1.12 % (20796)Memory used [KB]: 5500
% 1.28/1.12 % (20796)Time elapsed: 0.004 s
% 1.28/1.12 % (20796)Instructions burned: 3 (million)
% 1.28/1.12 % (20796)------------------------------
% 1.28/1.12 % (20796)------------------------------
% 1.28/1.12 % (20795)Success in time 0.013 s
%------------------------------------------------------------------------------