%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU890^5 : 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 : n008.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 09:37:40 AM UTC 2026
% Result : Theorem 1.50s 1.27s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 1 unt; 0 typ; 6 def)
% Number of atoms : 280 ( 124 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 366 ( 76 ~; 76 |; 43 &; 156 @)
% ( 10 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 26 !; 36 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
c: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(func_def_0,type,
c: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_3,type,
cG: c > b ).
thf(func_def_4,type,
cF: b > a ).
thf(func_def_5,type,
cS: c > $o ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: b ).
thf(func_def_11,type,
sK2: c ).
thf(func_def_12,type,
sK3: c ).
thf(f60,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f30,f35,f40,f44,f45,f50,f51,f55,f59]) ).
thf(f59,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6 ),
inference(subsumption_resolution,[status(thm)],[f57,f39]) ).
thf(f39,plain,
( ( ( cS @ sK2 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl4_4
<=> ( ( cS @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f57,plain,
( ( ( cS @ sK2 )
!= $true )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(subsumption_resolution,[status(thm)],[f56,f49]) ).
thf(f49,plain,
( ( ( cF @ sK1 )
= sK0 )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl4_6
<=> ( ( cF @ sK1 )
= sK0 ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f56,plain,
( ( ( cF @ sK1 )
!= sK0 )
| ( ( cS @ sK2 )
!= $true )
| ~ spl4_1
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f43,f25]) ).
thf(f25,plain,
( ( ( cG @ sK2 )
= sK1 )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl4_1
<=> ( ( cG @ sK2 )
= sK1 ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f43,plain,
( ! [X3: c] :
( ( ( cF @ ( cG @ X3 ) )
!= sK0 )
| ( ( cS @ X3 )
!= $true ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl4_5
<=> ! [X3: c] :
( ( ( cF @ ( cG @ X3 ) )
!= sK0 )
| ( ( cS @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f55,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f54]) ).
thf(f54,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(subsumption_resolution,[status(thm)],[f53,f34]) ).
thf(f34,plain,
( ( $true
= ( cS @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl4_3
<=> ( $true
= ( cS @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f53,plain,
( ( $true
!= ( cS @ sK3 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $true
!= ( cS @ sK3 ) )
| ( sK0 != sK0 )
| ~ spl4_2
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f43,f29]) ).
thf(f29,plain,
( ( sK0
= ( cF @ ( cG @ sK3 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl4_2
<=> ( sK0
= ( cF @ ( cG @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f51,plain,
( spl4_2
| spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f14,f47,f27]) ).
thf(f14,plain,
( ( ( cF @ sK1 )
= sK0 )
| ( sK0
= ( cF @ ( cG @ sK3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ! [X1: b] :
( ! [X2: c] :
( ( ( cG @ X2 )
!= X1 )
| ( ( cS @ X2 )
!= $true ) )
| ( ( cF @ X1 )
!= sK0 ) )
| ! [X3: c] :
( ( ( cS @ X3 )
!= $true )
| ( ( cF @ ( cG @ X3 ) )
!= sK0 ) ) )
& ( ( ( ( cG @ sK2 )
= sK1 )
& ( ( cS @ sK2 )
= $true )
& ( ( cF @ sK1 )
= sK0 ) )
| ( ( $true
= ( cS @ sK3 ) )
& ( sK0
= ( cF @ ( cG @ sK3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a] :
( ( ! [X1: b] :
( ! [X2: c] :
( ( ( cG @ X2 )
!= X1 )
| ( ( cS @ X2 )
!= $true ) )
| ( ( cF @ X1 )
!= X0 ) )
| ! [X3: c] :
( ( ( cS @ X3 )
!= $true )
| ( ( cF @ ( cG @ X3 ) )
!= X0 ) ) )
& ( ? [X4: b] :
( ? [X5: c] :
( ( ( cG @ X5 )
= X4 )
& ( ( cS @ X5 )
= $true ) )
& ( ( cF @ X4 )
= X0 ) )
| ? [X6: c] :
( ( ( cS @ X6 )
= $true )
& ( ( cF @ ( cG @ X6 ) )
= X0 ) ) ) )
=> ( ( ! [X1: b] :
( ! [X2: c] :
( ( ( cG @ X2 )
!= X1 )
| ( ( cS @ X2 )
!= $true ) )
| ( ( cF @ X1 )
!= sK0 ) )
| ! [X3: c] :
( ( ( cS @ X3 )
!= $true )
| ( ( cF @ ( cG @ X3 ) )
!= sK0 ) ) )
& ( ? [X4: b] :
( ? [X5: c] :
( ( ( cG @ X5 )
= X4 )
& ( ( cS @ X5 )
= $true ) )
& ( sK0
= ( cF @ X4 ) ) )
| ? [X6: c] :
( ( ( cS @ X6 )
= $true )
& ( ( cF @ ( cG @ X6 ) )
= sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X4: b] :
( ? [X5: c] :
( ( ( cG @ X5 )
= X4 )
& ( ( cS @ X5 )
= $true ) )
& ( sK0
= ( cF @ X4 ) ) )
=> ( ? [X5: c] :
( ( sK1
= ( cG @ X5 ) )
& ( ( cS @ X5 )
= $true ) )
& ( ( cF @ sK1 )
= sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: c] :
( ( sK1
= ( cG @ X5 ) )
& ( ( cS @ X5 )
= $true ) )
=> ( ( ( cG @ sK2 )
= sK1 )
& ( ( cS @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: c] :
( ( ( cS @ X6 )
= $true )
& ( ( cF @ ( cG @ X6 ) )
= sK0 ) )
=> ( ( $true
= ( cS @ sK3 ) )
& ( sK0
= ( cF @ ( cG @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a] :
( ( ! [X1: b] :
( ! [X2: c] :
( ( ( cG @ X2 )
!= X1 )
| ( ( cS @ X2 )
!= $true ) )
| ( ( cF @ X1 )
!= X0 ) )
| ! [X3: c] :
( ( ( cS @ X3 )
!= $true )
| ( ( cF @ ( cG @ X3 ) )
!= X0 ) ) )
& ( ? [X4: b] :
( ? [X5: c] :
( ( ( cG @ X5 )
= X4 )
& ( ( cS @ X5 )
= $true ) )
& ( ( cF @ X4 )
= X0 ) )
| ? [X6: c] :
( ( ( cS @ X6 )
= $true )
& ( ( cF @ ( cG @ X6 ) )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a] :
( ( ! [X2: b] :
( ! [X3: c] :
( ( ( cG @ X3 )
!= X2 )
| ( ( cS @ X3 )
!= $true ) )
| ( ( cF @ X2 )
!= X0 ) )
| ! [X1: c] :
( ( ( cS @ X1 )
!= $true )
| ( ( cF @ ( cG @ X1 ) )
!= X0 ) ) )
& ( ? [X2: b] :
( ? [X3: c] :
( ( ( cG @ X3 )
= X2 )
& ( ( cS @ X3 )
= $true ) )
& ( ( cF @ X2 )
= X0 ) )
| ? [X1: c] :
( ( ( cS @ X1 )
= $true )
& ( ( cF @ ( cG @ X1 ) )
= X0 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a] :
( ? [X1: c] :
( ( ( cS @ X1 )
= $true )
& ( ( cF @ ( cG @ X1 ) )
= X0 ) )
<~> ? [X2: b] :
( ? [X3: c] :
( ( ( cG @ X3 )
= X2 )
& ( ( cS @ X3 )
= $true ) )
& ( ( cF @ X2 )
= X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ? [X2: b] :
( ? [X3: c] :
( ( ( cG @ X3 )
= X2 )
& ( ( cS @ X3 )
= $true ) )
& ( ( cF @ X2 )
= X0 ) )
<=> ? [X1: c] :
( ( ( cS @ X1 )
= $true )
& ( ( cF @ ( cG @ X1 ) )
= X0 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: c] :
( ( cS @ X1 )
& ( ( cF @ ( cG @ X1 ) )
= X0 ) )
<=> ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ? [X3: c] :
( ( ( cG @ X3 )
= X2 )
& ( cS @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: c] :
( ( cS @ X1 )
& ( ( cF @ ( cG @ X1 ) )
= X0 ) )
<=> ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ? [X2: c] :
( ( ( cG @ X2 )
= X1 )
& ( cS @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: c] :
( ( cS @ X1 )
& ( ( cF @ ( cG @ X1 ) )
= X0 ) )
<=> ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ? [X2: c] :
( ( ( cG @ X2 )
= X1 )
& ( cS @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JJUqKInH9j/DTF2THF_24980.p',cTHM29_pme) ).
thf(f50,plain,
( spl4_3
| spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f15,f47,f32]) ).
thf(f15,plain,
( ( $true
= ( cS @ sK3 ) )
| ( ( cF @ sK1 )
= sK0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f45,plain,
( spl4_4
| spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f17,f32,f37]) ).
thf(f17,plain,
( ( ( cS @ sK2 )
= $true )
| ( $true
= ( cS @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f44,plain,
( spl4_5
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f21,f42,f42]) ).
thf(f21,plain,
! [X2: c,X3: c] :
( ( ( cF @ ( cG @ X3 ) )
!= sK0 )
| ( ( cS @ X2 )
!= $true )
| ( ( cS @ X3 )
!= $true )
| ( sK0
!= ( cF @ ( cG @ X2 ) ) ) ),
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: c,X3: c,X1: b] :
( ( ( cG @ X2 )
!= X1 )
| ( ( cS @ X2 )
!= $true )
| ( ( cF @ X1 )
!= sK0 )
| ( ( cS @ X3 )
!= $true )
| ( ( cF @ ( cG @ X3 ) )
!= sK0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f40,plain,
( spl4_2
| spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f16,f37,f27]) ).
thf(f16,plain,
( ( sK0
= ( cF @ ( cG @ sK3 ) ) )
| ( ( cS @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f35,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f19,f32,f23]) ).
thf(f19,plain,
( ( ( cG @ sK2 )
= sK1 )
| ( $true
= ( cS @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f30,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f27,f23]) ).
thf(f18,plain,
( ( sK0
= ( cF @ ( cG @ sK3 ) ) )
| ( ( cG @ sK2 )
= sK1 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU890^5 : 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
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:36:09 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU890^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : TPS problem THM29
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0299 [Bro09]
% 0.30/0.46 % : THM29 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 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 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.30/0.46 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 5 ( 5 avg)
% 0.30/0.46 % Number of connectives : 10 ( 0 ~; 0 |; 3 &; 6 @)
% 0.30/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.30/0.46 % Number of types : 4 ( 3 usr)
% 0.30/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.30/0.46 % Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 % : Polymorphic definitions expanded.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(c_type,type,
% 0.30/0.46 c: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(b_type,type,
% 0.30/0.46 b: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(a_type,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(cG,type,
% 0.30/0.46 cG: c > b ).
% 0.30/0.46
% 0.30/0.46 thf(cF,type,
% 0.30/0.46 cF: b > a ).
% 0.30/0.46
% 0.30/0.46 thf(cS,type,
% 0.30/0.46 cS: c > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cTHM29_pme,conjecture,
% 0.30/0.46 ! [Xx: a] :
% 0.30/0.46 ( ? [Xt: b] :
% 0.30/0.46 ( ? [Xt0: c] :
% 0.30/0.46 ( ( cS @ Xt0 )
% 0.30/0.46 & ( Xt
% 0.30/0.46 = ( cG @ Xt0 ) ) )
% 0.30/0.46 & ( Xx
% 0.30/0.46 = ( cF @ Xt ) ) )
% 0.30/0.46 <=> ? [Xt: c] :
% 0.30/0.46 ( ( cS @ Xt )
% 0.30/0.46 & ( Xx
% 0.30/0.46 = ( cF @ ( cG @ Xt ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.50/1.23 ---- Embedded in THF ---
% 1.50/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.24 %%% Generated on Tue Feb 24 12:36:10 EST 2026
% 1.50/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.24 %%% Logic specification used:
% 1.50/1.24 %%% thf(spec, logic, $$dhol).
% 1.50/1.24
% 1.50/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.JJUqKInH9j/DTF2DTF24980.p
% See solution above
% 1.50/1.24 ------------------------
% 1.50/1.24 ---- Cleaned THF ---
% 1.50/1.25 thf(c_type,type,
% 1.50/1.25 c: $tType ).
% 1.50/1.25
% 1.50/1.25 thf(b_type,type,
% 1.50/1.25 b: $tType ).
% 1.50/1.25
% 1.50/1.25 thf(a_type,type,
% 1.50/1.25 a: $tType ).
% 1.50/1.25
% 1.50/1.25 thf(cG,type,
% 1.50/1.25 cG: c > b ).
% 1.50/1.25
% 1.50/1.25 thf(cF,type,
% 1.50/1.25 cF: b > a ).
% 1.50/1.25
% 1.50/1.25 thf(cS,type,
% 1.50/1.25 cS: c > $o ).
% 1.50/1.25
% 1.50/1.25 thf(cTHM29_pme,conjecture,
% 1.50/1.25 ! [Xx: a] :
% 1.50/1.25 ( ? [Xt: b] :
% 1.50/1.25 ( ? [Xt0: c] :
% 1.50/1.25 ( ( cS @ Xt0 )
% 1.50/1.25 & ( Xt
% 1.50/1.25 = ( cG @ Xt0 ) ) )
% 1.50/1.25 & ( Xx
% 1.50/1.25 = ( cF @ Xt ) ) )
% 1.50/1.25 <=> ? [Xt: c] :
% 1.50/1.25 ( ( cS @ Xt )
% 1.50/1.25 & ( Xx
% 1.50/1.25 = ( cF @ ( cG @ Xt ) ) ) ) ) ).
% 1.50/1.25 ------------------------
% 1.50/1.27 % (25194)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24980 for (3000ds/183Mi)
% 1.50/1.27 % (25200)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24980 for (3000ds/18Mi)
% 1.50/1.27 % (25199)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_24980 for (3000ds/275Mi)
% 1.50/1.27 % (25197)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24980 for (3000ds/2Mi)
% 1.50/1.27 % (25198)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_24980 for (3000ds/2Mi)
% 1.50/1.27 % (25196)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_24980 for (3000ds/27Mi)
% 1.50/1.27 % (25195)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_24980 for (3000ds/4Mi)
% 1.50/1.27 % (25198)Instruction limit reached!
% 1.50/1.27 % (25198)------------------------------
% 1.50/1.27 % (25198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (25198)Termination reason: Unknown
% 1.50/1.27 % (25198)Termination phase: Property scanning
% 1.50/1.27
% 1.50/1.27 % (25198)Memory used [KB]: 895
% 1.50/1.27 % (25198)Time elapsed: 0.003 s
% 1.50/1.27 % (25198)Instructions burned: 2 (million)
% 1.50/1.27 % (25198)------------------------------
% 1.50/1.27 % (25198)------------------------------
% 1.50/1.27 % (25197)Instruction limit reached!
% 1.50/1.27 % (25197)------------------------------
% 1.50/1.27 % (25197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (25197)Termination reason: Unknown
% 1.50/1.27 % (25197)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (25197)Memory used [KB]: 5500
% 1.50/1.27 % (25197)Time elapsed: 0.004 s
% 1.50/1.27 % (25197)Instructions burned: 2 (million)
% 1.50/1.27 % (25197)------------------------------
% 1.50/1.27 % (25197)------------------------------
% 1.50/1.27 % (25194)First to succeed.
% 1.50/1.27 % (25195)Also succeeded, but the first one will report.
% 1.50/1.27 % (25194)Refutation found. Thanks to Tanya!
% 1.50/1.27 % SZS status Theorem for DTF2THF_24980
% 1.50/1.27 % SZS output start Proof for DTF2THF_24980
% 1.50/1.27 thf(type_def_5, type, c: $tType).
% 1.50/1.27 thf(type_def_6, type, b: $tType).
% 1.50/1.27 thf(type_def_8, type, a: $tType).
% 1.50/1.27 thf(func_def_0, type, c: $tType).
% 1.50/1.27 thf(func_def_1, type, b: $tType).
% 1.50/1.27 thf(func_def_2, type, a: $tType).
% 1.50/1.27 thf(func_def_3, type, cG: c > b).
% 1.50/1.27 thf(func_def_4, type, cF: b > a).
% 1.50/1.27 thf(func_def_5, type, cS: c > $o).
% 1.50/1.27 thf(func_def_9, type, sK0: a).
% 1.50/1.27 thf(func_def_10, type, sK1: b).
% 1.50/1.27 thf(func_def_11, type, sK2: c).
% 1.50/1.27 thf(func_def_12, type, sK3: c).
% 1.50/1.27 thf(f60,plain,(
% 1.50/1.27 $false),
% 1.50/1.27 inference(avatar_sat_refutation,[status(thm)],[f30,f35,f40,f44,f45,f50,f51,f55,f59])).
% 1.50/1.27 thf(f59,plain,(
% 1.50/1.27 ~spl4_1 | ~spl4_4 | ~spl4_5 | ~spl4_6),
% 1.50/1.27 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.50/1.27 thf(f58,plain,(
% 1.50/1.27 $false | (~spl4_1 | ~spl4_4 | ~spl4_5 | ~spl4_6)),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f57,f39])).
% 1.50/1.27 thf(f39,plain,(
% 1.50/1.27 ((cS @ sK2) = $true) | ~spl4_4),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.50/1.27 thf(f37,definition,(
% 1.50/1.27 spl4_4 <=> ((cS @ sK2) = $true)),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.50/1.27 thf(f57,plain,(
% 1.50/1.27 ((cS @ sK2) != $true) | (~spl4_1 | ~spl4_5 | ~spl4_6)),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f56,f49])).
% 1.50/1.27 thf(f49,plain,(
% 1.50/1.27 ((cF @ sK1) = sK0) | ~spl4_6),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.50/1.27 thf(f47,definition,(
% 1.50/1.27 spl4_6 <=> ((cF @ sK1) = sK0)),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.50/1.27 thf(f56,plain,(
% 1.50/1.27 ((cF @ sK1) != sK0) | ((cS @ sK2) != $true) | (~spl4_1 | ~spl4_5)),
% 1.50/1.27 inference(superposition,[status(thm)],[f43,f25])).
% 1.50/1.27 thf(f25,plain,(
% 1.50/1.27 ((cG @ sK2) = sK1) | ~spl4_1),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.50/1.27 thf(f23,definition,(
% 1.50/1.27 spl4_1 <=> ((cG @ sK2) = sK1)),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.50/1.27 thf(f43,plain,(
% 1.50/1.27 ( ! [X3 : c] : (((cF @ (cG @ X3)) != sK0) | ((cS @ X3) != $true)) ) | ~spl4_5),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.50/1.27 thf(f42,definition,(
% 1.50/1.27 spl4_5 <=> ! [X3 : c] : (((cF @ (cG @ X3)) != sK0) | ((cS @ X3) != $true))),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.50/1.27 thf(f55,plain,(
% 1.50/1.27 ~spl4_2 | ~spl4_3 | ~spl4_5),
% 1.50/1.27 inference(avatar_contradiction_clause,[status(thm)],[f54])).
% 1.50/1.27 thf(f54,plain,(
% 1.50/1.27 $false | (~spl4_2 | ~spl4_3 | ~spl4_5)),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f53,f34])).
% 1.50/1.27 thf(f34,plain,(
% 1.50/1.27 ($true = (cS @ sK3)) | ~spl4_3),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.50/1.27 thf(f32,definition,(
% 1.50/1.27 spl4_3 <=> ($true = (cS @ sK3))),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.50/1.27 thf(f53,plain,(
% 1.50/1.27 ($true != (cS @ sK3)) | (~spl4_2 | ~spl4_5)),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.50/1.27 thf(f52,plain,(
% 1.50/1.27 ($true != (cS @ sK3)) | (sK0 != sK0) | (~spl4_2 | ~spl4_5)),
% 1.50/1.27 inference(superposition,[status(thm)],[f43,f29])).
% 1.50/1.27 thf(f29,plain,(
% 1.50/1.27 (sK0 = (cF @ (cG @ sK3))) | ~spl4_2),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.50/1.27 thf(f27,definition,(
% 1.50/1.27 spl4_2 <=> (sK0 = (cF @ (cG @ sK3)))),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.50/1.27 thf(f51,plain,(
% 1.50/1.27 spl4_2 | spl4_6),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f14,f47,f27])).
% 1.50/1.27 thf(f14,plain,(
% 1.50/1.27 ((cF @ sK1) = sK0) | (sK0 = (cF @ (cG @ sK3)))),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.27 thf(f13,plain,(
% 1.50/1.27 (! [X1 : b] : (! [X2 : c] : (((cG @ X2) != X1) | ((cS @ X2) != $true)) | ((cF @ X1) != sK0)) | ! [X3 : c] : (((cS @ X3) != $true) | ((cF @ (cG @ X3)) != sK0))) & (((((cG @ sK2) = sK1) & ((cS @ sK2) = $true)) & ((cF @ sK1) = sK0)) | (($true = (cS @ sK3)) & (sK0 = (cF @ (cG @ sK3)))))),
% 1.50/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f12,f11,f10,f9])).
% 1.50/1.27 thf(f9,plain,(
% 1.50/1.27 ? [X0 : a] : ((! [X1 : b] : (! [X2 : c] : (((cG @ X2) != X1) | ((cS @ X2) != $true)) | ((cF @ X1) != X0)) | ! [X3 : c] : (((cS @ X3) != $true) | ((cF @ (cG @ X3)) != X0))) & (? [X4 : b] : (? [X5 : c] : (((cG @ X5) = X4) & ((cS @ X5) = $true)) & ((cF @ X4) = X0)) | ? [X6 : c] : (((cS @ X6) = $true) & ((cF @ (cG @ X6)) = X0)))) => ((! [X1 : b] : (! [X2 : c] : (((cG @ X2) != X1) | ((cS @ X2) != $true)) | ((cF @ X1) != sK0)) | ! [X3 : c] : (((cS @ X3) != $true) | ((cF @ (cG @ X3)) != sK0))) & (? [X4 : b] : (? [X5 : c] : (((cG @ X5) = X4) & ((cS @ X5) = $true)) & (sK0 = (cF @ X4))) | ? [X6 : c] : (((cS @ X6) = $true) & ((cF @ (cG @ X6)) = sK0))))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f10,plain,(
% 1.50/1.27 ? [X4 : b] : (? [X5 : c] : (((cG @ X5) = X4) & ((cS @ X5) = $true)) & (sK0 = (cF @ X4))) => (? [X5 : c] : ((sK1 = (cG @ X5)) & ((cS @ X5) = $true)) & ((cF @ sK1) = sK0))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f11,plain,(
% 1.50/1.27 ? [X5 : c] : ((sK1 = (cG @ X5)) & ((cS @ X5) = $true)) => (((cG @ sK2) = sK1) & ((cS @ sK2) = $true))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f12,plain,(
% 1.50/1.27 ? [X6 : c] : (((cS @ X6) = $true) & ((cF @ (cG @ X6)) = sK0)) => (($true = (cS @ sK3)) & (sK0 = (cF @ (cG @ sK3))))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f8,plain,(
% 1.50/1.27 ? [X0 : a] : ((! [X1 : b] : (! [X2 : c] : (((cG @ X2) != X1) | ((cS @ X2) != $true)) | ((cF @ X1) != X0)) | ! [X3 : c] : (((cS @ X3) != $true) | ((cF @ (cG @ X3)) != X0))) & (? [X4 : b] : (? [X5 : c] : (((cG @ X5) = X4) & ((cS @ X5) = $true)) & ((cF @ X4) = X0)) | ? [X6 : c] : (((cS @ X6) = $true) & ((cF @ (cG @ X6)) = X0))))),
% 1.50/1.27 inference(rectify,[status(thm)],[f7])).
% 1.50/1.27 thf(f7,plain,(
% 1.50/1.27 ? [X0 : a] : ((! [X2 : b] : (! [X3 : c] : (((cG @ X3) != X2) | ((cS @ X3) != $true)) | ((cF @ X2) != X0)) | ! [X1 : c] : (((cS @ X1) != $true) | ((cF @ (cG @ X1)) != X0))) & (? [X2 : b] : (? [X3 : c] : (((cG @ X3) = X2) & ((cS @ X3) = $true)) & ((cF @ X2) = X0)) | ? [X1 : c] : (((cS @ X1) = $true) & ((cF @ (cG @ X1)) = X0))))),
% 1.50/1.27 inference(nnf_transformation,[status(thm)],[f6])).
% 1.50/1.27 thf(f6,plain,(
% 1.50/1.27 ? [X0 : a] : (? [X1 : c] : (((cS @ X1) = $true) & ((cF @ (cG @ X1)) = X0)) <~> ? [X2 : b] : (? [X3 : c] : (((cG @ X3) = X2) & ((cS @ X3) = $true)) & ((cF @ X2) = X0)))),
% 1.50/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.27 thf(f5,plain,(
% 1.50/1.27 ~! [X0 : a] : (? [X2 : b] : (? [X3 : c] : (((cG @ X3) = X2) & ((cS @ X3) = $true)) & ((cF @ X2) = X0)) <=> ? [X1 : c] : (((cS @ X1) = $true) & ((cF @ (cG @ X1)) = X0)))),
% 1.50/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.27 thf(f4,plain,(
% 1.50/1.27 ~! [X0 : a] : (? [X1 : c] : ((cS @ X1) & ((cF @ (cG @ X1)) = X0)) <=> ? [X2 : b] : (((cF @ X2) = X0) & ? [X3 : c] : (((cG @ X3) = X2) & (cS @ X3))))),
% 1.50/1.27 inference(rectify,[status(thm)],[f2])).
% 1.50/1.27 thf(f2,negated_conjecture,(
% 1.50/1.27 ~! [X0 : a] : (? [X1 : c] : ((cS @ X1) & ((cF @ (cG @ X1)) = X0)) <=> ? [X1 : b] : (((cF @ X1) = X0) & ? [X2 : c] : (((cG @ X2) = X1) & (cS @ X2))))),
% 1.50/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.27 thf(f1,conjecture,(
% 1.50/1.27 ! [X0 : a] : (? [X1 : c] : ((cS @ X1) & ((cF @ (cG @ X1)) = X0)) <=> ? [X1 : b] : (((cF @ X1) = X0) & ? [X2 : c] : (((cG @ X2) = X1) & (cS @ X2))))),
% 1.50/1.27 file('/export/starexec/sandbox2/tmp/tmp.JJUqKInH9j/DTF2THF_24980.p',cTHM29_pme)).
% 1.50/1.27 thf(f50,plain,(
% 1.50/1.27 spl4_3 | spl4_6),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f15,f47,f32])).
% 1.50/1.27 thf(f15,plain,(
% 1.50/1.27 ($true = (cS @ sK3)) | ((cF @ sK1) = sK0)),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.27 thf(f45,plain,(
% 1.50/1.27 spl4_4 | spl4_3),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f17,f32,f37])).
% 1.50/1.27 thf(f17,plain,(
% 1.50/1.27 ((cS @ sK2) = $true) | ($true = (cS @ sK3))),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.27 thf(f44,plain,(
% 1.50/1.27 spl4_5 | spl4_5),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f21,f42,f42])).
% 1.50/1.27 thf(f21,plain,(
% 1.50/1.27 ( ! [X2 : c,X3 : c] : (((cF @ (cG @ X3)) != sK0) | ((cS @ X2) != $true) | ((cS @ X3) != $true) | (sK0 != (cF @ (cG @ X2)))) )),
% 1.50/1.27 inference(equality_resolution,[status(thm)],[f20])).
% 1.50/1.27 thf(f20,plain,(
% 1.50/1.27 ( ! [X2 : c,X3 : c,X1 : b] : (((cG @ X2) != X1) | ((cS @ X2) != $true) | ((cF @ X1) != sK0) | ((cS @ X3) != $true) | ((cF @ (cG @ X3)) != sK0)) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.27 thf(f40,plain,(
% 1.50/1.27 spl4_2 | spl4_4),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f16,f37,f27])).
% 1.50/1.27 thf(f16,plain,(
% 1.50/1.27 (sK0 = (cF @ (cG @ sK3))) | ((cS @ sK2) = $true)),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.27 thf(f35,plain,(
% 1.50/1.27 spl4_1 | spl4_3),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f19,f32,f23])).
% 1.50/1.27 thf(f19,plain,(
% 1.50/1.27 ((cG @ sK2) = sK1) | ($true = (cS @ sK3))),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.27 thf(f30,plain,(
% 1.50/1.27 spl4_1 | spl4_2),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f18,f27,f23])).
% 1.50/1.27 thf(f18,plain,(
% 1.50/1.27 (sK0 = (cF @ (cG @ sK3))) | ((cG @ sK2) = sK1)),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.27 % SZS output end Proof for DTF2THF_24980
% 1.50/1.27 % (25194)------------------------------
% 1.50/1.27 % (25194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (25194)Termination reason: Refutation
% 1.50/1.27
% 1.50/1.27 % (25194)Memory used [KB]: 5500
% 1.50/1.27 % (25194)Time elapsed: 0.006 s
% 1.50/1.27 % (25194)Instructions burned: 3 (million)
% 1.50/1.27 % (25194)------------------------------
% 1.50/1.27 % (25194)------------------------------
% 1.50/1.27 % (25193)Success in time 0.021 s
%------------------------------------------------------------------------------