%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU891^5 : 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 : n006.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 1.39s 1.27s
% Output : Refutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 183 ( 76 equ; 0 cnn)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 200 ( 35 ~; 36 |; 32 &; 86 @)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 10 !; 22 ?; 32 :)
% 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,
cF: b > a ).
thf(func_def_3,type,
cS: b > $o ).
thf(func_def_4,type,
cR: b > $o ).
thf(func_def_6,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
sK0: a ).
thf(func_def_10,type,
sK1: b ).
thf(func_def_11,type,
sK2: b ).
thf(f47,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f34,f35,f36,f39,f46]) ).
thf(f46,plain,
( ~ spl3_4
| ~ spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f45,f18,f31]) ).
thf(f31,definition,
( spl3_4
<=> ( ( cR @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f18,definition,
( spl3_1
<=> ( ( cF @ sK1 )
= sK0 ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f45,plain,
( ( ( cR @ sK1 )
!= $true )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( sK0 != sK0 )
| ( ( cR @ sK1 )
!= $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f12,f20]) ).
thf(f20,plain,
( ( ( cF @ sK1 )
= sK0 )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f12,plain,
! [X3: b] :
( ( sK0
!= ( cF @ X3 ) )
| ( $true
!= ( cR @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( ( cF @ sK1 )
= sK0 )
& ( ( cR @ sK1 )
= $true ) )
| ( ( $true
= ( cS @ sK2 ) )
& ( sK0
= ( cF @ sK2 ) ) ) )
& ! [X3: b] :
( ( sK0
!= ( cF @ X3 ) )
| ( ( $true
!= ( cR @ X3 ) )
& ( ( cS @ X3 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f9,f8,f7]) ).
thf(f7,plain,
( ? [X0: a] :
( ( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
= $true ) )
| ? [X2: b] :
( ( ( cS @ X2 )
= $true )
& ( ( cF @ X2 )
= X0 ) ) )
& ! [X3: b] :
( ( ( cF @ X3 )
!= X0 )
| ( ( $true
!= ( cR @ X3 ) )
& ( ( cS @ X3 )
!= $true ) ) ) )
=> ( ( ? [X1: b] :
( ( ( cF @ X1 )
= sK0 )
& ( ( cR @ X1 )
= $true ) )
| ? [X2: b] :
( ( ( cS @ X2 )
= $true )
& ( ( cF @ X2 )
= sK0 ) ) )
& ! [X3: b] :
( ( sK0
!= ( cF @ X3 ) )
| ( ( $true
!= ( cR @ X3 ) )
& ( ( cS @ X3 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X1: b] :
( ( ( cF @ X1 )
= sK0 )
& ( ( cR @ X1 )
= $true ) )
=> ( ( ( cF @ sK1 )
= sK0 )
& ( ( cR @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X2: b] :
( ( ( cS @ X2 )
= $true )
& ( ( cF @ X2 )
= sK0 ) )
=> ( ( $true
= ( cS @ sK2 ) )
& ( sK0
= ( cF @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a] :
( ( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
= $true ) )
| ? [X2: b] :
( ( ( cS @ X2 )
= $true )
& ( ( cF @ X2 )
= X0 ) ) )
& ! [X3: b] :
( ( ( cF @ X3 )
!= X0 )
| ( ( $true
!= ( cR @ X3 ) )
& ( ( cS @ X3 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
= $true ) )
| ? [X2: b] :
( ( ( cS @ X2 )
= $true )
& ( ( cF @ X2 )
= X0 ) ) )
=> ? [X3: b] :
( ( ( ( cS @ X3 )
= $true )
| ( $true
= ( cR @ X3 ) ) )
& ( ( cF @ X3 )
= X0 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ( ? [X1: b] :
( ( cR @ X1 )
& ( ( cF @ X1 )
= X0 ) )
| ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( cS @ X2 ) ) )
=> ? [X3: b] :
( ( ( cF @ X3 )
= X0 )
& ( ( cR @ X3 )
| ( cS @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ( ? [X1: b] :
( ( cR @ X1 )
& ( ( cF @ X1 )
= X0 ) )
| ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( cS @ X1 ) ) )
=> ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ( ? [X1: b] :
( ( cR @ X1 )
& ( ( cF @ X1 )
= X0 ) )
| ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( cS @ X1 ) ) )
=> ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pD94xhTgse/DTF2THF_25024.p',cTHM34B_pme) ).
thf(f39,plain,
( ~ spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f22,f27]) ).
thf(f27,definition,
( spl3_3
<=> ( $true
= ( cS @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f22,definition,
( spl3_2
<=> ( sK0
= ( cF @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
!= ( cS @ sK2 ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true
!= ( cS @ sK2 ) )
| ( sK0 != sK0 )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f11,f24]) ).
thf(f24,plain,
( ( sK0
= ( cF @ sK2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f11,plain,
! [X3: b] :
( ( sK0
!= ( cF @ X3 ) )
| ( ( cS @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f36,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f16,f27,f18]) ).
thf(f16,plain,
( ( $true
= ( cS @ sK2 ) )
| ( ( cF @ sK1 )
= sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f35,plain,
( spl3_4
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f22,f31]) ).
thf(f13,plain,
( ( sK0
= ( cF @ sK2 ) )
| ( ( cR @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f34,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f14,f31,f27]) ).
thf(f14,plain,
( ( ( cR @ sK1 )
= $true )
| ( $true
= ( cS @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f25,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f22,f18]) ).
thf(f15,plain,
( ( sK0
= ( cF @ sK2 ) )
| ( ( cF @ sK1 )
= sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU891^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n006.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 12:36:00 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
% 0.27/0.48 ---- Original DTF file ---
% 0.27/0.48 thf(spec,logic,$$dhol).
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 % File : SEU891^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.48 % Domain : Set Theory
% 0.27/0.48 % Problem : TPS problem THM34B
% 0.27/0.48 % Version : Especial.
% 0.27/0.48 % English :
% 0.27/0.48
% 0.27/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.48 % Source : [Bro09]
% 0.27/0.48 % Names : tps_0314 [Bro09]
% 0.27/0.48 % : THM34B [TPS]
% 0.27/0.48
% 0.27/0.48 % Status : Theorem
% 0.27/0.48 % 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
% 0.27/0.48 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.27/0.48 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.27/0.48 % Maximal formula atoms : 7 ( 7 avg)
% 0.27/0.48 % Number of connectives : 13 ( 0 ~; 2 |; 3 &; 7 @)
% 0.27/0.48 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.27/0.48 % Maximal formula depth : 7 ( 7 avg)
% 0.27/0.48 % Number of types : 3 ( 2 usr)
% 0.27/0.48 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.27/0.48 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.27/0.48 % Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 0.27/0.48 % SPC : TH0_THM_EQU_NAR
% 0.27/0.48
% 0.27/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.48 % : Polymorphic definitions expanded.
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 thf(b_type,type,
% 0.27/0.48 b: $tType ).
% 0.27/0.48
% 0.27/0.48 thf(a_type,type,
% 0.27/0.48 a: $tType ).
% 0.27/0.48
% 0.27/0.48 thf(cF,type,
% 0.27/0.48 cF: b > a ).
% 0.27/0.48
% 0.27/0.48 thf(cS,type,
% 0.27/0.48 cS: b > $o ).
% 0.27/0.48
% 0.27/0.48 thf(cR,type,
% 0.27/0.48 cR: b > $o ).
% 0.27/0.48
% 0.27/0.48 thf(cTHM34B_pme,conjecture,
% 0.27/0.48 ! [Xx: a] :
% 0.27/0.48 ( ( ? [Xt: b] :
% 0.27/0.48 ( ( cR @ Xt )
% 0.27/0.48 & ( Xx
% 0.27/0.48 = ( cF @ Xt ) ) )
% 0.27/0.48 | ? [Xt: b] :
% 0.27/0.48 ( ( cS @ Xt )
% 0.27/0.48 & ( Xx
% 0.27/0.48 = ( cF @ Xt ) ) ) )
% 0.27/0.48 => ? [Xt: b] :
% 0.27/0.48 ( ( ( cR @ Xt )
% 0.27/0.48 | ( cS @ Xt ) )
% 0.27/0.48 & ( Xx
% 0.27/0.48 = ( cF @ Xt ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 ------------------------
% 1.39/1.24 ---- Embedded in THF ---
% 1.39/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.24 %%% Generated on Tue Feb 24 12:36:01 EST 2026
% 1.39/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.24 %%% Logic specification used:
% 1.39/1.24 %%% thf(spec, logic, $$dhol).
% 1.39/1.24
% 1.39/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pD94xhTgse/DTF2DTF25024.p
% See solution above
% 1.39/1.24 ------------------------
% 1.39/1.25 ---- Cleaned THF ---
% 1.39/1.25 thf(b_type,type,
% 1.39/1.25 b: $tType ).
% 1.39/1.25
% 1.39/1.25 thf(a_type,type,
% 1.39/1.25 a: $tType ).
% 1.39/1.25
% 1.39/1.25 thf(cF,type,
% 1.39/1.25 cF: b > a ).
% 1.39/1.25
% 1.39/1.25 thf(cS,type,
% 1.39/1.25 cS: b > $o ).
% 1.39/1.25
% 1.39/1.25 thf(cR,type,
% 1.39/1.25 cR: b > $o ).
% 1.39/1.25
% 1.39/1.25 thf(cTHM34B_pme,conjecture,
% 1.39/1.25 ! [Xx: a] :
% 1.39/1.25 ( ( ? [Xt: b] :
% 1.39/1.25 ( ( cR @ Xt )
% 1.39/1.25 & ( Xx
% 1.39/1.25 = ( cF @ Xt ) ) )
% 1.39/1.25 | ? [Xt: b] :
% 1.39/1.25 ( ( cS @ Xt )
% 1.39/1.25 & ( Xx
% 1.39/1.25 = ( cF @ Xt ) ) ) )
% 1.39/1.25 => ? [Xt: b] :
% 1.39/1.25 ( ( ( cR @ Xt )
% 1.39/1.25 | ( cS @ Xt ) )
% 1.39/1.25 & ( Xx
% 1.39/1.25 = ( cF @ Xt ) ) ) ) ).
% 1.39/1.25 ------------------------
% 1.39/1.26 % (25123)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_25024 for (3000ds/27Mi)
% 1.39/1.27 % (25123)First to succeed.
% 1.39/1.27 % (25123)Refutation found. Thanks to Tanya!
% 1.39/1.27 % SZS status Theorem for DTF2THF_25024
% 1.39/1.27 % SZS output start Proof for DTF2THF_25024
% 1.39/1.27 thf(type_def_5, type, b: $tType).
% 1.39/1.27 thf(type_def_6, type, a: $tType).
% 1.39/1.27 thf(func_def_0, type, b: $tType).
% 1.39/1.27 thf(func_def_1, type, a: $tType).
% 1.39/1.27 thf(func_def_2, type, cF: b > a).
% 1.39/1.27 thf(func_def_3, type, cS: b > $o).
% 1.39/1.27 thf(func_def_4, type, cR: b > $o).
% 1.39/1.27 thf(func_def_6, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.39/1.27 thf(func_def_9, type, sK0: a).
% 1.39/1.27 thf(func_def_10, type, sK1: b).
% 1.39/1.27 thf(func_def_11, type, sK2: b).
% 1.39/1.27 thf(f47,plain,(
% 1.39/1.27 $false),
% 1.39/1.27 inference(avatar_sat_refutation,[status(thm)],[f25,f34,f35,f36,f39,f46])).
% 1.39/1.27 thf(f46,plain,(
% 1.39/1.27 ~spl3_4 | ~spl3_1),
% 1.39/1.27 inference(avatar_split_clause,[status(thm)],[f45,f18,f31])).
% 1.39/1.27 thf(f31,definition,(
% 1.39/1.27 spl3_4 <=> ((cR @ sK1) = $true)),
% 1.39/1.27 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.39/1.27 thf(f18,definition,(
% 1.39/1.27 spl3_1 <=> ((cF @ sK1) = sK0)),
% 1.39/1.27 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.39/1.27 thf(f45,plain,(
% 1.39/1.27 ((cR @ sK1) != $true) | ~spl3_1),
% 1.39/1.27 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.39/1.27 thf(f43,plain,(
% 1.39/1.27 (sK0 != sK0) | ((cR @ sK1) != $true) | ~spl3_1),
% 1.39/1.27 inference(superposition,[status(thm)],[f12,f20])).
% 1.39/1.27 thf(f20,plain,(
% 1.39/1.27 ((cF @ sK1) = sK0) | ~spl3_1),
% 1.39/1.27 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.39/1.27 thf(f12,plain,(
% 1.39/1.27 ( ! [X3 : b] : ((sK0 != (cF @ X3)) | ($true != (cR @ X3))) )),
% 1.39/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.39/1.27 thf(f10,plain,(
% 1.39/1.27 ((((cF @ sK1) = sK0) & ((cR @ sK1) = $true)) | (($true = (cS @ sK2)) & (sK0 = (cF @ sK2)))) & ! [X3 : b] : ((sK0 != (cF @ X3)) | (($true != (cR @ X3)) & ((cS @ X3) != $true)))),
% 1.39/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f9,f8,f7])).
% 1.39/1.27 thf(f7,plain,(
% 1.39/1.27 ? [X0 : a] : ((? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) = $true)) | ? [X2 : b] : (((cS @ X2) = $true) & ((cF @ X2) = X0))) & ! [X3 : b] : (((cF @ X3) != X0) | (($true != (cR @ X3)) & ((cS @ X3) != $true)))) => ((? [X1 : b] : (((cF @ X1) = sK0) & ((cR @ X1) = $true)) | ? [X2 : b] : (((cS @ X2) = $true) & ((cF @ X2) = sK0))) & ! [X3 : b] : ((sK0 != (cF @ X3)) | (($true != (cR @ X3)) & ((cS @ X3) != $true))))),
% 1.39/1.27 introduced(definition,[],[choice_axiom])).
% 1.39/1.27 thf(f8,plain,(
% 1.39/1.27 ? [X1 : b] : (((cF @ X1) = sK0) & ((cR @ X1) = $true)) => (((cF @ sK1) = sK0) & ((cR @ sK1) = $true))),
% 1.39/1.27 introduced(definition,[],[choice_axiom])).
% 1.39/1.27 thf(f9,plain,(
% 1.39/1.27 ? [X2 : b] : (((cS @ X2) = $true) & ((cF @ X2) = sK0)) => (($true = (cS @ sK2)) & (sK0 = (cF @ sK2)))),
% 1.39/1.27 introduced(definition,[],[choice_axiom])).
% 1.39/1.27 thf(f6,plain,(
% 1.39/1.27 ? [X0 : a] : ((? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) = $true)) | ? [X2 : b] : (((cS @ X2) = $true) & ((cF @ X2) = X0))) & ! [X3 : b] : (((cF @ X3) != X0) | (($true != (cR @ X3)) & ((cS @ X3) != $true))))),
% 1.39/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.39/1.27 thf(f5,plain,(
% 1.39/1.27 ~! [X0 : a] : ((? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) = $true)) | ? [X2 : b] : (((cS @ X2) = $true) & ((cF @ X2) = X0))) => ? [X3 : b] : ((((cS @ X3) = $true) | ($true = (cR @ X3))) & ((cF @ X3) = X0)))),
% 1.39/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.39/1.27 thf(f4,plain,(
% 1.39/1.27 ~! [X0 : a] : ((? [X1 : b] : ((cR @ X1) & ((cF @ X1) = X0)) | ? [X2 : b] : (((cF @ X2) = X0) & (cS @ X2))) => ? [X3 : b] : (((cF @ X3) = X0) & ((cR @ X3) | (cS @ X3))))),
% 1.39/1.27 inference(rectify,[status(thm)],[f2])).
% 1.39/1.27 thf(f2,negated_conjecture,(
% 1.39/1.27 ~! [X0 : a] : ((? [X1 : b] : ((cR @ X1) & ((cF @ X1) = X0)) | ? [X1 : b] : (((cF @ X1) = X0) & (cS @ X1))) => ? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) | (cS @ X1))))),
% 1.39/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.39/1.27 thf(f1,conjecture,(
% 1.39/1.27 ! [X0 : a] : ((? [X1 : b] : ((cR @ X1) & ((cF @ X1) = X0)) | ? [X1 : b] : (((cF @ X1) = X0) & (cS @ X1))) => ? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) | (cS @ X1))))),
% 1.39/1.27 file('/export/starexec/sandbox2/tmp/tmp.pD94xhTgse/DTF2THF_25024.p',cTHM34B_pme)).
% 1.39/1.27 thf(f39,plain,(
% 1.39/1.27 ~spl3_3 | ~spl3_2),
% 1.39/1.27 inference(avatar_split_clause,[status(thm)],[f38,f22,f27])).
% 1.39/1.27 thf(f27,definition,(
% 1.39/1.27 spl3_3 <=> ($true = (cS @ sK2))),
% 1.39/1.27 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.39/1.27 thf(f22,definition,(
% 1.39/1.27 spl3_2 <=> (sK0 = (cF @ sK2))),
% 1.39/1.27 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.39/1.27 thf(f38,plain,(
% 1.39/1.27 ($true != (cS @ sK2)) | ~spl3_2),
% 1.39/1.27 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.39/1.27 thf(f37,plain,(
% 1.39/1.27 ($true != (cS @ sK2)) | (sK0 != sK0) | ~spl3_2),
% 1.39/1.27 inference(superposition,[status(thm)],[f11,f24])).
% 1.39/1.27 thf(f24,plain,(
% 1.39/1.27 (sK0 = (cF @ sK2)) | ~spl3_2),
% 1.39/1.27 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.39/1.27 thf(f11,plain,(
% 1.39/1.27 ( ! [X3 : b] : ((sK0 != (cF @ X3)) | ((cS @ X3) != $true)) )),
% 1.39/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.39/1.27 thf(f36,plain,(
% 1.39/1.27 spl3_1 | spl3_3),
% 1.39/1.27 inference(avatar_split_clause,[status(thm)],[f16,f27,f18])).
% 1.39/1.27 thf(f16,plain,(
% 1.39/1.27 ($true = (cS @ sK2)) | ((cF @ sK1) = sK0)),
% 1.39/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.39/1.27 thf(f35,plain,(
% 1.39/1.27 spl3_4 | spl3_2),
% 1.39/1.27 inference(avatar_split_clause,[status(thm)],[f13,f22,f31])).
% 1.39/1.27 thf(f13,plain,(
% 1.39/1.27 (sK0 = (cF @ sK2)) | ((cR @ sK1) = $true)),
% 1.39/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.39/1.27 thf(f34,plain,(
% 1.39/1.27 spl3_3 | spl3_4),
% 1.39/1.27 inference(avatar_split_clause,[status(thm)],[f14,f31,f27])).
% 1.39/1.27 thf(f14,plain,(
% 1.39/1.27 ((cR @ sK1) = $true) | ($true = (cS @ sK2))),
% 1.39/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.39/1.27 thf(f25,plain,(
% 1.39/1.27 spl3_1 | spl3_2),
% 1.39/1.27 inference(avatar_split_clause,[status(thm)],[f15,f22,f18])).
% 1.39/1.27 thf(f15,plain,(
% 1.39/1.27 (sK0 = (cF @ sK2)) | ((cF @ sK1) = sK0)),
% 1.39/1.27 inference(cnf_transformation,[status(thm)],[f10])).
% 1.39/1.27 % SZS output end Proof for DTF2THF_25024
% 1.39/1.27 % (25123)------------------------------
% 1.39/1.27 % (25123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.27 % (25123)Termination reason: Refutation
% 1.39/1.27
% 1.39/1.27 % (25123)Memory used [KB]: 5500
% 1.39/1.27 % (25123)Time elapsed: 0.004 s
% 1.39/1.27 % (25123)Instructions burned: 2 (million)
% 1.39/1.27 % (25123)------------------------------
% 1.39/1.27 % (25123)------------------------------
% 1.39/1.27 % (25120)Success in time 0.013 s
%------------------------------------------------------------------------------