%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU893^5 : 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 : n005.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 09:37:41 AM UTC 2026
% Result : Theorem 1.34s 1.15s
% Output : Refutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 173 ( 73 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 194 ( 37 ~; 33 |; 29 &; 87 @)
% ( 2 <=>; 6 =>; 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 : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 18 !; 20 ?; 38 :)
% 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_8,type,
sK0: a ).
thf(func_def_9,type,
sK1: b ).
thf(f33,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f29,f32]) ).
thf(f32,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f31]) ).
thf(f31,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[status(thm)],[f30,f20]) ).
thf(f20,plain,
( ( ( cR @ sK1 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl2_1
<=> ( ( cR @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f30,plain,
( ( cR @ sK1 )
!= $true ),
inference(equality_resolution,[status(thm)],[f16]) ).
thf(f16,plain,
! [X3: b] :
( ( ( cF @ sK1 )
!= ( cF @ X3 ) )
| ( ( cR @ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f11,f14]) ).
thf(f14,plain,
( ( cF @ sK1 )
= sK0 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( cF @ sK1 )
= sK0 )
& ( ( ( cS @ sK1 )
= $true )
| ( ( cR @ sK1 )
= $true ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= sK0 )
| ( $true
!= ( cS @ X2 ) ) )
& ! [X3: b] :
( ( ( cR @ X3 )
!= $true )
| ( sK0
!= ( cF @ X3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $true ) ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= X0 )
| ( $true
!= ( cS @ X2 ) ) )
& ! [X3: b] :
( ( ( cR @ X3 )
!= $true )
| ( ( cF @ X3 )
!= X0 ) ) )
=> ( ? [X1: b] :
( ( ( cF @ X1 )
= sK0 )
& ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $true ) ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= sK0 )
| ( $true
!= ( cS @ X2 ) ) )
& ! [X3: b] :
( ( ( cR @ X3 )
!= $true )
| ( sK0
!= ( cF @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X1: b] :
( ( ( cF @ X1 )
= sK0 )
& ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $true ) ) )
=> ( ( ( cF @ sK1 )
= sK0 )
& ( ( ( cS @ sK1 )
= $true )
| ( ( cR @ sK1 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $true ) ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= X0 )
| ( $true
!= ( cS @ X2 ) ) )
& ! [X3: b] :
( ( ( cR @ X3 )
!= $true )
| ( ( cF @ X3 )
!= X0 ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a] :
( ! [X2: b] :
( ( ( cF @ X2 )
!= X0 )
| ( $true
!= ( cS @ X2 ) ) )
& ! [X3: b] :
( ( ( cR @ X3 )
!= $true )
| ( ( cF @ X3 )
!= X0 ) )
& ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $true ) ) )
=> ( ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( $true
= ( cS @ X2 ) ) )
| ? [X3: b] :
( ( ( cF @ X3 )
= X0 )
& ( ( cR @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) )
=> ( ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( cS @ X2 ) )
| ? [X3: b] :
( ( cR @ X3 )
& ( ( cF @ X3 )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) )
=> ( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( cS @ X1 ) )
| ? [X1: b] :
( ( cR @ X1 )
& ( ( cF @ X1 )
= X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) )
=> ( ? [X1: b] :
( ( ( cF @ X1 )
= X0 )
& ( cS @ X1 ) )
| ? [X1: b] :
( ( cR @ X1 )
& ( ( cF @ X1 )
= X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pO9wIBa9fC/DTF2THF_31720.p',cTHM34A_pme) ).
thf(f11,plain,
! [X3: b] :
( ( ( cR @ X3 )
!= $true )
| ( sK0
!= ( cF @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f29,plain,
~ spl2_2,
inference(avatar_split_clause,[status(thm)],[f26,f22]) ).
thf(f22,definition,
( spl2_2
<=> ( ( cS @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f26,plain,
( ( cS @ sK1 )
!= $true ),
inference(equality_resolution,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: b] :
( ( ( cF @ X2 )
!= ( cF @ sK1 ) )
| ( $true
!= ( cS @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f12,f14]) ).
thf(f12,plain,
! [X2: b] :
( ( ( cF @ X2 )
!= sK0 )
| ( $true
!= ( cS @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f25,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f22,f18]) ).
thf(f13,plain,
( ( ( cS @ sK1 )
= $true )
| ( ( cR @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU893^5 : TPTP v9.2.1. Released v4.0.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:35:59 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SEU893^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.42 % Domain : Set Theory
% 0.15/0.42 % Problem : TPS problem THM34A
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bro09]
% 0.15/0.42 % Names : tps_0356 [Bro09]
% 0.15/0.42 % : THM34A [TPS]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % 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
% 0.15/0.42 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.15/0.42 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 7 ( 7 avg)
% 0.15/0.42 % Number of connectives : 13 ( 0 ~; 2 |; 3 &; 7 @)
% 0.15/0.42 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 7 ( 7 avg)
% 0.15/0.42 % Number of types : 3 ( 2 usr)
% 0.15/0.42 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.15/0.42 % Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 0.15/0.42 % SPC : TH0_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.42 % : Polymorphic definitions expanded.
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(b_type,type,
% 0.15/0.42 b: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(a_type,type,
% 0.15/0.42 a: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(cF,type,
% 0.15/0.42 cF: b > a ).
% 0.15/0.42
% 0.15/0.42 thf(cS,type,
% 0.15/0.42 cS: b > $o ).
% 0.15/0.42
% 0.15/0.42 thf(cR,type,
% 0.15/0.42 cR: b > $o ).
% 0.15/0.42
% 0.15/0.42 thf(cTHM34A_pme,conjecture,
% 0.15/0.42 ! [Xx: a] :
% 0.15/0.42 ( ? [Xt: b] :
% 0.15/0.42 ( ( ( cR @ Xt )
% 0.15/0.42 | ( cS @ Xt ) )
% 0.15/0.42 & ( Xx
% 0.15/0.42 = ( cF @ Xt ) ) )
% 0.15/0.42 => ( ? [Xt: b] :
% 0.15/0.42 ( ( cR @ Xt )
% 0.15/0.42 & ( Xx
% 0.15/0.42 = ( cF @ Xt ) ) )
% 0.15/0.42 | ? [Xt: b] :
% 0.15/0.42 ( ( cS @ Xt )
% 0.15/0.42 & ( Xx
% 0.15/0.42 = ( cF @ Xt ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.15/1.12 ---- Embedded in THF ---
% 1.15/1.12 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.15/1.12 %%% Generated on Tue Feb 24 12:36:00 EST 2026
% 1.15/1.12 %%% using '$$dhol' embedding, version 1.3.0.
% 1.15/1.12 %%% Logic specification used:
% 1.15/1.12 %%% thf(spec, logic, $$dhol).
% 1.15/1.12
% 1.15/1.12 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.pO9wIBa9fC/DTF2DTF31720.p
% See solution above
% 1.15/1.12 ------------------------
% 1.34/1.13 ---- Cleaned THF ---
% 1.34/1.13 thf(b_type,type,
% 1.34/1.13 b: $tType ).
% 1.34/1.13
% 1.34/1.13 thf(a_type,type,
% 1.34/1.13 a: $tType ).
% 1.34/1.13
% 1.34/1.13 thf(cF,type,
% 1.34/1.13 cF: b > a ).
% 1.34/1.13
% 1.34/1.13 thf(cS,type,
% 1.34/1.13 cS: b > $o ).
% 1.34/1.13
% 1.34/1.13 thf(cR,type,
% 1.34/1.13 cR: b > $o ).
% 1.34/1.13
% 1.34/1.13 thf(cTHM34A_pme,conjecture,
% 1.34/1.13 ! [Xx: a] :
% 1.34/1.13 ( ? [Xt: b] :
% 1.34/1.13 ( ( ( cR @ Xt )
% 1.34/1.13 | ( cS @ Xt ) )
% 1.34/1.13 & ( Xx
% 1.34/1.13 = ( cF @ Xt ) ) )
% 1.34/1.13 => ( ? [Xt: b] :
% 1.34/1.13 ( ( cR @ Xt )
% 1.34/1.13 & ( Xx
% 1.34/1.13 = ( cF @ Xt ) ) )
% 1.34/1.13 | ? [Xt: b] :
% 1.34/1.13 ( ( cS @ Xt )
% 1.34/1.13 & ( Xx
% 1.34/1.13 = ( cF @ Xt ) ) ) ) ) ).
% 1.34/1.13 ------------------------
% 1.34/1.14 % (31818)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31720 for (3000ds/183Mi)
% 1.34/1.15 % (31818)First to succeed.
% 1.34/1.15 % (31818)Refutation found. Thanks to Tanya!
% 1.34/1.15 % SZS status Theorem for DTF2THF_31720
% 1.34/1.15 % SZS output start Proof for DTF2THF_31720
% 1.34/1.15 thf(type_def_5, type, b: $tType).
% 1.34/1.15 thf(type_def_6, type, a: $tType).
% 1.34/1.15 thf(func_def_0, type, b: $tType).
% 1.34/1.15 thf(func_def_1, type, a: $tType).
% 1.34/1.15 thf(func_def_2, type, cF: b > a).
% 1.34/1.15 thf(func_def_3, type, cS: b > $o).
% 1.34/1.15 thf(func_def_4, type, cR: b > $o).
% 1.34/1.15 thf(func_def_8, type, sK0: a).
% 1.34/1.15 thf(func_def_9, type, sK1: b).
% 1.34/1.15 thf(f33,plain,(
% 1.34/1.15 $false),
% 1.34/1.15 inference(avatar_sat_refutation,[status(thm)],[f25,f29,f32])).
% 1.34/1.15 thf(f32,plain,(
% 1.34/1.15 ~spl2_1),
% 1.34/1.15 inference(avatar_contradiction_clause,[status(thm)],[f31])).
% 1.34/1.15 thf(f31,plain,(
% 1.34/1.15 $false | ~spl2_1),
% 1.34/1.15 inference(subsumption_resolution,[status(thm)],[f30,f20])).
% 1.34/1.15 thf(f20,plain,(
% 1.34/1.15 ((cR @ sK1) = $true) | ~spl2_1),
% 1.34/1.15 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.34/1.15 thf(f18,definition,(
% 1.34/1.15 spl2_1 <=> ((cR @ sK1) = $true)),
% 1.34/1.15 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.34/1.15 thf(f30,plain,(
% 1.34/1.15 ((cR @ sK1) != $true)),
% 1.34/1.15 inference(equality_resolution,[status(thm)],[f16])).
% 1.34/1.15 thf(f16,plain,(
% 1.34/1.15 ( ! [X3 : b] : (((cF @ sK1) != (cF @ X3)) | ((cR @ X3) != $true)) )),
% 1.34/1.15 inference(definition_unfolding,[status(thm)],[f11,f14])).
% 1.34/1.15 thf(f14,plain,(
% 1.34/1.15 ((cF @ sK1) = sK0)),
% 1.34/1.15 inference(cnf_transformation,[status(thm)],[f10])).
% 1.34/1.15 thf(f10,plain,(
% 1.34/1.15 (((cF @ sK1) = sK0) & (((cS @ sK1) = $true) | ((cR @ sK1) = $true))) & ! [X2 : b] : (((cF @ X2) != sK0) | ($true != (cS @ X2))) & ! [X3 : b] : (((cR @ X3) != $true) | (sK0 != (cF @ X3)))),
% 1.34/1.15 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.34/1.15 thf(f8,plain,(
% 1.34/1.15 ? [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & (((cS @ X1) = $true) | ((cR @ X1) = $true))) & ! [X2 : b] : (((cF @ X2) != X0) | ($true != (cS @ X2))) & ! [X3 : b] : (((cR @ X3) != $true) | ((cF @ X3) != X0))) => (? [X1 : b] : (((cF @ X1) = sK0) & (((cS @ X1) = $true) | ((cR @ X1) = $true))) & ! [X2 : b] : (((cF @ X2) != sK0) | ($true != (cS @ X2))) & ! [X3 : b] : (((cR @ X3) != $true) | (sK0 != (cF @ X3))))),
% 1.34/1.15 introduced(definition,[],[choice_axiom])).
% 1.34/1.15 thf(f9,plain,(
% 1.34/1.15 ? [X1 : b] : (((cF @ X1) = sK0) & (((cS @ X1) = $true) | ((cR @ X1) = $true))) => (((cF @ sK1) = sK0) & (((cS @ sK1) = $true) | ((cR @ sK1) = $true)))),
% 1.34/1.15 introduced(definition,[],[choice_axiom])).
% 1.34/1.15 thf(f7,plain,(
% 1.34/1.15 ? [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & (((cS @ X1) = $true) | ((cR @ X1) = $true))) & ! [X2 : b] : (((cF @ X2) != X0) | ($true != (cS @ X2))) & ! [X3 : b] : (((cR @ X3) != $true) | ((cF @ X3) != X0)))),
% 1.34/1.15 inference(flattening,[status(thm)],[f6])).
% 1.34/1.15 thf(f6,plain,(
% 1.34/1.15 ? [X0 : a] : ((! [X2 : b] : (((cF @ X2) != X0) | ($true != (cS @ X2))) & ! [X3 : b] : (((cR @ X3) != $true) | ((cF @ X3) != X0))) & ? [X1 : b] : (((cF @ X1) = X0) & (((cS @ X1) = $true) | ((cR @ X1) = $true))))),
% 1.34/1.15 inference(ennf_transformation,[status(thm)],[f5])).
% 1.34/1.15 thf(f5,plain,(
% 1.34/1.15 ~! [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & (((cS @ X1) = $true) | ((cR @ X1) = $true))) => (? [X2 : b] : (((cF @ X2) = X0) & ($true = (cS @ X2))) | ? [X3 : b] : (((cF @ X3) = X0) & ((cR @ X3) = $true))))),
% 1.34/1.15 inference(fool_elimination,[status(thm)],[f4])).
% 1.34/1.15 thf(f4,plain,(
% 1.34/1.15 ~! [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) | (cS @ X1))) => (? [X2 : b] : (((cF @ X2) = X0) & (cS @ X2)) | ? [X3 : b] : ((cR @ X3) & ((cF @ X3) = X0))))),
% 1.34/1.15 inference(rectify,[status(thm)],[f2])).
% 1.34/1.15 thf(f2,negated_conjecture,(
% 1.34/1.15 ~! [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) | (cS @ X1))) => (? [X1 : b] : (((cF @ X1) = X0) & (cS @ X1)) | ? [X1 : b] : ((cR @ X1) & ((cF @ X1) = X0))))),
% 1.34/1.15 inference(negated_conjecture,[status(cth)],[f1])).
% 1.34/1.15 thf(f1,conjecture,(
% 1.34/1.15 ! [X0 : a] : (? [X1 : b] : (((cF @ X1) = X0) & ((cR @ X1) | (cS @ X1))) => (? [X1 : b] : (((cF @ X1) = X0) & (cS @ X1)) | ? [X1 : b] : ((cR @ X1) & ((cF @ X1) = X0))))),
% 1.34/1.15 file('/export/starexec/sandbox/tmp/tmp.pO9wIBa9fC/DTF2THF_31720.p',cTHM34A_pme)).
% 1.34/1.15 thf(f11,plain,(
% 1.34/1.15 ( ! [X3 : b] : (((cR @ X3) != $true) | (sK0 != (cF @ X3))) )),
% 1.34/1.15 inference(cnf_transformation,[status(thm)],[f10])).
% 1.34/1.15 thf(f29,plain,(
% 1.34/1.15 ~spl2_2),
% 1.34/1.15 inference(avatar_split_clause,[status(thm)],[f26,f22])).
% 1.34/1.15 thf(f22,definition,(
% 1.34/1.15 spl2_2 <=> ((cS @ sK1) = $true)),
% 1.34/1.15 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.34/1.15 thf(f26,plain,(
% 1.34/1.15 ((cS @ sK1) != $true)),
% 1.34/1.15 inference(equality_resolution,[status(thm)],[f15])).
% 1.34/1.15 thf(f15,plain,(
% 1.34/1.15 ( ! [X2 : b] : (((cF @ X2) != (cF @ sK1)) | ($true != (cS @ X2))) )),
% 1.34/1.15 inference(definition_unfolding,[status(thm)],[f12,f14])).
% 1.34/1.15 thf(f12,plain,(
% 1.34/1.15 ( ! [X2 : b] : (((cF @ X2) != sK0) | ($true != (cS @ X2))) )),
% 1.34/1.15 inference(cnf_transformation,[status(thm)],[f10])).
% 1.34/1.15 thf(f25,plain,(
% 1.34/1.15 spl2_1 | spl2_2),
% 1.34/1.15 inference(avatar_split_clause,[status(thm)],[f13,f22,f18])).
% 1.34/1.15 thf(f13,plain,(
% 1.34/1.15 ((cS @ sK1) = $true) | ((cR @ sK1) = $true)),
% 1.34/1.15 inference(cnf_transformation,[status(thm)],[f10])).
% 1.34/1.15 % SZS output end Proof for DTF2THF_31720
% 1.34/1.15 % (31818)------------------------------
% 1.34/1.15 % (31818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.15 % (31818)Termination reason: Refutation
% 1.34/1.15
% 1.34/1.15 % (31818)Memory used [KB]: 5500
% 1.34/1.15 % (31818)Time elapsed: 0.003 s
% 1.34/1.15 % (31818)Instructions burned: 1 (million)
% 1.34/1.15 % (31818)------------------------------
% 1.34/1.15 % (31818)------------------------------
% 1.34/1.15 % (31817)Success in time 0.012 s
%------------------------------------------------------------------------------