%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO536^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 09:54:29 AM UTC 2026
% Result : Theorem 1.69s 1.32s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 176 ( 44 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 287 ( 19 ~; 14 |; 4 &; 218 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 95 ( 95 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 8 con; 0-2 aty)
% ( 0 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 46 ^; 21 !; 20 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_3,type,
epsa: ( ( $i > $i ) > $i > $o ) > $i > $i ).
thf(func_def_4,type,
epsb: ( ( $i > $i ) > $i > $o ) > $i ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK0: ( $i > $i ) > $i > $o ).
thf(func_def_14,type,
sK1: $i > $i ).
thf(func_def_17,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f78,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f53,f57,f58,f77]) ).
thf(f77,plain,
( spl3_2
| ~ spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f76,f47,f43]) ).
thf(f43,definition,
( spl3_2
<=> ! [X2: $i,X1: $i > $i] :
( ( sK0 @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f47,definition,
( spl3_3
<=> ! [X1: $i] :
( ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
@ X1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f76,plain,
( ! [X2: $i,X1: $i > $i] :
( ( sK0 @ X1 @ X2 )
= $false )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X2: $i,X1: $i > $i] :
( ( $true = $false )
| ( ( sK0 @ X1 @ X2 )
= $false ) )
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f74,f48]) ).
thf(f48,plain,
( ! [X1: $i] :
( ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
@ X1 )
= $false )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f74,plain,
! [X2: $i,X1: $i > $i] :
( ( ( sK0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
@ sK7 ) ) ),
inference(sigma_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X1: $i > $i] :
( ( ( sK0 @ X1 @ X2 )
= $false )
| ( $true
= ( ?? @ $i
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: $i > $i] :
( ( $false
= ( ?? @ $i @ ( sK0 @ X1 ) ) )
| ( $true
= ( ?? @ $i
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: $i > $i] :
( ( ( ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f58,plain,
~ spl3_4,
inference(avatar_split_clause,[status(thm)],[f32,f50]) ).
thf(f50,definition,
( spl3_4
<=> ( $true
= ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
@ ( eps
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f32,plain,
( $true
!= ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
@ ( eps
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
!= ( sK0
@ ( ^ [Y0: ( $i > $i ) > $i > $o] :
( epsii
@ ^ [Y1: $i > $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 )
@ ( ^ [Y0: ( $i > $i ) > $i > $o] :
( eps
@ ^ [Y1: $i] :
( Y0
@ ( ^ [Y2: ( $i > $i ) > $i > $o] :
( epsii
@ ^ [Y3: $i > $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y3 @ Y4 ) ) )
@ Y0 )
@ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f26,f30]) ).
thf(f30,plain,
( epsb
= ( ^ [Y0: ( $i > $i ) > $i > $o] :
( eps
@ ^ [Y1: $i] :
( Y0
@ ( ^ [Y2: ( $i > $i ) > $i > $o] :
( epsii
@ ^ [Y3: $i > $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y3 @ Y4 ) ) )
@ Y0 )
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f27,f26]) ).
thf(f27,plain,
( epsb
= ( ^ [Y0: ( $i > $i ) > $i > $o] :
( eps
@ ^ [Y1: $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( epsb
= ( ^ [Y0: ( $i > $i ) > $i > $o] :
( eps
@ ^ [Y1: $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [X0: ( $i > $i ) > $i > $o] :
( eps
@ ^ [X1: $i] : ( X0 @ ( epsa @ X0 ) @ X1 ) ) )
= epsb ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X2: ( $i > $i ) > $i > $o] :
( eps
@ ^ [X3: $i] : ( X2 @ ( epsa @ X2 ) @ X3 ) ) )
= epsb ),
file('/export/starexec/sandbox/tmp/tmp.8AelPxxG1l/DTF2THF_30644.p',epsbd) ).
thf(f26,plain,
( epsa
= ( ^ [Y0: ( $i > $i ) > $i > $o] :
( epsii
@ ^ [Y1: $i > $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( epsa
= ( ^ [Y0: ( $i > $i ) > $i > $o] :
( epsii
@ ^ [Y1: $i > $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: ( $i > $i ) > $i > $o] :
( epsii
@ ^ [X1: $i > $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) )
= epsa ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X2: ( $i > $i ) > $i > $o] :
( epsii
@ ^ [X1: $i > $i] :
? [X3: $i] : ( X2 @ X1 @ X3 ) ) )
= epsa ),
file('/export/starexec/sandbox/tmp/tmp.8AelPxxG1l/DTF2THF_30644.p',epsad) ).
thf(f28,plain,
( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( sK0 @ sK1 @ sK2 )
= $true )
& ( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f19,f22,f21]) ).
thf(f21,plain,
( ? [X0: ( $i > $i ) > $i > $o] :
( ? [X1: $i > $i,X2: $i] :
( $true
= ( X0 @ X1 @ X2 ) )
& ( $true
!= ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) ) )
=> ( ? [X2: $i,X1: $i > $i] :
( $true
= ( sK0 @ X1 @ X2 ) )
& ( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X2: $i,X1: $i > $i] :
( $true
= ( sK0 @ X1 @ X2 ) )
=> ( ( sK0 @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
? [X0: ( $i > $i ) > $i > $o] :
( ? [X1: $i > $i,X2: $i] :
( $true
= ( X0 @ X1 @ X2 ) )
& ( $true
!= ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: ( $i > $i ) > $i > $o] :
( ? [X1: $i > $i,X2: $i] :
( $true
= ( X0 @ X1 @ X2 ) )
=> ( $true
= ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: ( $i > $i ) > $i > $o] :
( ? [X1: $i > $i,X2: $i] : ( X0 @ X1 @ X2 )
=> ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X2: ( $i > $i ) > $i > $o] :
( ? [X1: $i > $i,X3: $i] : ( X2 @ X1 @ X3 )
=> ( X2 @ ( epsa @ X2 ) @ ( epsb @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X2: ( $i > $i ) > $i > $o] :
( ? [X1: $i > $i,X3: $i] : ( X2 @ X1 @ X3 )
=> ( X2 @ ( epsa @ X2 ) @ ( epsb @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8AelPxxG1l/DTF2THF_30644.p',conj) ).
thf(f57,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $true = $false )
| ~ spl3_2 ),
inference(backward_demodulation,[status(thm)],[f29,f44]) ).
thf(f44,plain,
( ! [X2: $i,X1: $i > $i] :
( ( sK0 @ X1 @ X2 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f29,plain,
( ( sK0 @ sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f53,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f34,f50,f47]) ).
thf(f34,plain,
! [X1: $i] :
( ( $true
= ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
@ ( eps
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ) ) )
| ( ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) )
@ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO536^1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % 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 14:33:10 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : SYO536^1 : TPTP v9.2.1. Released v5.2.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : Choice on relations between functions and individuals
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro11]
% 0.30/0.46 % Names : CHOICE13 [Bro11]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0
% 0.30/0.46 % Syntax : Number of formulae : 9 ( 2 unt; 4 typ; 2 def)
% 0.30/0.46 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 1 ( 0 avg)
% 0.30/0.46 % Number of connectives : 22 ( 0 ~; 0 |; 0 &; 19 @)
% 0.30/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 4 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.30/0.46 % Number of variables : 12 ( 4 ^; 3 !; 5 ?; 12 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : Choice operators on i and ii are used to define a choice operator
% 0.30/0.46 % on ii*i (Curried).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(eps,type,
% 0.30/0.46 eps: ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(choiceax,axiom,
% 0.30/0.46 ! [P: $i > $o] :
% 0.30/0.46 ( ? [X: $i] : ( P @ X )
% 0.30/0.46 => ( P @ ( eps @ P ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(epsii,type,
% 0.30/0.46 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(choiceaxii,axiom,
% 0.30/0.46 ! [P: ( $i > $i ) > $o] :
% 0.30/0.46 ( ? [X: $i > $i] : ( P @ X )
% 0.30/0.46 => ( P @ ( epsii @ P ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(epsa,type,
% 0.30/0.46 epsa: ( ( $i > $i ) > $i > $o ) > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(epsad,definition,
% 0.30/0.46 ( epsa
% 0.30/0.46 = ( ^ [R: ( $i > $i ) > $i > $o] :
% 0.30/0.46 ( epsii
% 0.30/0.46 @ ^ [X: $i > $i] :
% 0.30/0.46 ? [Y: $i] : ( R @ X @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(epsb,type,
% 0.30/0.46 epsb: ( ( $i > $i ) > $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(epsbd,definition,
% 0.30/0.46 ( epsb
% 0.30/0.46 = ( ^ [R: ( $i > $i ) > $i > $o] :
% 0.30/0.46 ( eps
% 0.30/0.46 @ ^ [Y: $i] : ( R @ ( epsa @ R ) @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(conj,conjecture,
% 0.30/0.46 ! [R: ( $i > $i ) > $i > $o] :
% 0.30/0.46 ( ? [X: $i > $i,Y: $i] : ( R @ X @ Y )
% 0.30/0.46 => ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.28 %%% Generated on Tue Feb 24 14:33:11 EST 2026
% 1.49/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.28 %%% Logic specification used:
% 1.49/1.28 %%% thf(spec, logic, $$dhol).
% 1.49/1.28
% 1.49/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8AelPxxG1l/DTF2DTF30644.p
% See solution above
% 1.49/1.28 ------------------------
% 1.49/1.29 ---- Cleaned THF ---
% 1.49/1.30 thf(eps,type,
% 1.49/1.30 eps: ( $i > $o ) > $i ).
% 1.49/1.30
% 1.49/1.30 thf(choiceax,axiom,
% 1.49/1.30 ! [P: $i > $o] :
% 1.49/1.30 ( ? [X: $i] : ( P @ X )
% 1.49/1.30 => ( P @ ( eps @ P ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(epsii,type,
% 1.49/1.30 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 1.49/1.30
% 1.49/1.30 thf(choiceaxii,axiom,
% 1.49/1.30 ! [P: ( $i > $i ) > $o] :
% 1.49/1.30 ( ? [X: $i > $i] : ( P @ X )
% 1.49/1.30 => ( P @ ( epsii @ P ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(epsa,type,
% 1.49/1.30 epsa: ( ( $i > $i ) > $i > $o ) > $i > $i ).
% 1.49/1.30
% 1.49/1.30 thf(epsad,definition,
% 1.49/1.30 ( epsa
% 1.49/1.30 = ( ^ [R: ( $i > $i ) > $i > $o] :
% 1.49/1.30 ( epsii
% 1.49/1.30 @ ^ [X: $i > $i] :
% 1.49/1.30 ? [Y: $i] : ( R @ X @ Y ) ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(epsb,type,
% 1.49/1.30 epsb: ( ( $i > $i ) > $i > $o ) > $i ).
% 1.49/1.30
% 1.49/1.30 thf(epsbd,definition,
% 1.49/1.30 ( epsb
% 1.49/1.30 = ( ^ [R: ( $i > $i ) > $i > $o] :
% 1.49/1.30 ( eps
% 1.49/1.30 @ ^ [Y: $i] : ( R @ ( epsa @ R ) @ Y ) ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(conj,conjecture,
% 1.49/1.30 ! [R: ( $i > $i ) > $i > $o] :
% 1.49/1.30 ( ? [X: $i > $i,Y: $i] : ( R @ X @ Y )
% 1.49/1.30 => ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ) ).
% 1.49/1.30 ------------------------
% 1.69/1.31 % (30851)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30644 for (2999ds/2Mi)
% 1.69/1.32 % (30851)Instruction limit reached!
% 1.69/1.32 % (30851)------------------------------
% 1.69/1.32 % (30851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (30851)Termination reason: Unknown
% 1.69/1.32 % (30851)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (30851)Memory used [KB]: 5500
% 1.69/1.32 % (30851)Time elapsed: 0.003 s
% 1.69/1.32 % (30851)Instructions burned: 3 (million)
% 1.69/1.32 % (30851)------------------------------
% 1.69/1.32 % (30851)------------------------------
% 1.69/1.32 % (30849)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_30644 for (2999ds/27Mi)
% 1.69/1.32 % (30849)First to succeed.
% 1.69/1.32 % (30852)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_30644 for (2999ds/2Mi)
% 1.69/1.32 % (30852)Instruction limit reached!
% 1.69/1.32 % (30852)------------------------------
% 1.69/1.32 % (30852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (30852)Termination reason: Unknown
% 1.69/1.32 % (30852)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (30852)Memory used [KB]: 1023
% 1.69/1.32 % (30852)Time elapsed: 0.003 s
% 1.69/1.32 % (30852)Instructions burned: 3 (million)
% 1.69/1.32 % (30852)------------------------------
% 1.69/1.32 % (30852)------------------------------
% 1.69/1.32 % (30849)Refutation found. Thanks to Tanya!
% 1.69/1.32 % SZS status Theorem for DTF2THF_30644
% 1.69/1.32 % SZS output start Proof for DTF2THF_30644
% 1.69/1.32 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.69/1.32 thf(func_def_2, type, epsii: (($i > $i) > $o) > $i > $i).
% 1.69/1.32 thf(func_def_3, type, epsa: (($i > $i) > $i > $o) > $i > $i).
% 1.69/1.32 thf(func_def_4, type, epsb: (($i > $i) > $i > $o) > $i).
% 1.69/1.32 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.69/1.32 thf(func_def_13, type, sK0: ($i > $i) > $i > $o).
% 1.69/1.32 thf(func_def_14, type, sK1: $i > $i).
% 1.69/1.32 thf(func_def_17, type, ph4: !>[X0: $tType]:(X0)).
% 1.69/1.32 thf(f78,plain,(
% 1.69/1.32 $false),
% 1.69/1.32 inference(avatar_sat_refutation,[status(thm)],[f53,f57,f58,f77])).
% 1.69/1.32 thf(f77,plain,(
% 1.69/1.32 spl3_2 | ~spl3_3),
% 1.69/1.32 inference(avatar_split_clause,[status(thm)],[f76,f47,f43])).
% 1.69/1.32 thf(f43,definition,(
% 1.69/1.32 spl3_2 <=> ! [X2 : $i,X1 : $i > $i] : ((sK0 @ X1 @ X2) = $false)),
% 1.69/1.32 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.69/1.32 thf(f47,definition,(
% 1.69/1.32 spl3_3 <=> ! [X1 : $i] : ((sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))) @ X1) = $false)),
% 1.69/1.32 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.69/1.32 thf(f76,plain,(
% 1.69/1.32 ( ! [X2 : $i,X1 : $i > $i] : (((sK0 @ X1 @ X2) = $false)) ) | ~spl3_3),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.69/1.32 thf(f75,plain,(
% 1.69/1.32 ( ! [X2 : $i,X1 : $i > $i] : (($true = $false) | ((sK0 @ X1 @ X2) = $false)) ) | ~spl3_3),
% 1.69/1.32 inference(forward_demodulation,[status(thm)],[f74,f48])).
% 1.69/1.32 thf(f48,plain,(
% 1.69/1.32 ( ! [X1 : $i] : (((sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))) @ X1) = $false)) ) | ~spl3_3),
% 1.69/1.32 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.69/1.32 thf(f74,plain,(
% 1.69/1.32 ( ! [X2 : $i,X1 : $i > $i] : (((sK0 @ X1 @ X2) = $false) | ($true = (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))) @ sK7))) )),
% 1.69/1.32 inference(sigma_clausification,[status(thm)],[f73])).
% 1.69/1.32 thf(f73,plain,(
% 1.69/1.32 ( ! [X2 : $i,X1 : $i > $i] : (((sK0 @ X1 @ X2) = $false) | ($true = (?? @ $i @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))))))) )),
% 1.69/1.32 inference(pi_clausification,[status(thm)],[f72])).
% 1.69/1.32 thf(f72,plain,(
% 1.69/1.32 ( ! [X1 : $i > $i] : (($false = (?? @ $i @ (sK0 @ X1))) | ($true = (?? @ $i @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))))))) )),
% 1.69/1.32 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.69/1.32 thf(f69,plain,(
% 1.69/1.32 ( ! [X1 : $i > $i] : ((((^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0))) @ X1) = $false) | ($true = ((^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0))) @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0))))))) )),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f58,plain,(
% 1.69/1.32 ~spl3_4),
% 1.69/1.32 inference(avatar_split_clause,[status(thm)],[f32,f50])).
% 1.69/1.32 thf(f50,definition,(
% 1.69/1.32 spl3_4 <=> ($true = (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))) @ (eps @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0))))))))),
% 1.69/1.32 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.69/1.32 thf(f32,plain,(
% 1.69/1.32 ($true != (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))) @ (eps @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0))))))))),
% 1.69/1.32 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.69/1.32 thf(f31,plain,(
% 1.69/1.32 ($true != (sK0 @ ((^[Y0 : ($i > $i) > $i > $o]: (epsii @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0) @ ((^[Y0 : ($i > $i) > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : ($i > $i) > $i > $o]: (epsii @ (^[Y3 : $i > $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))) @ Y0) @ Y1)))) @ sK0)))),
% 1.69/1.32 inference(definition_unfolding,[status(thm)],[f28,f26,f30])).
% 1.69/1.32 thf(f30,plain,(
% 1.69/1.32 (epsb = (^[Y0 : ($i > $i) > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : ($i > $i) > $i > $o]: (epsii @ (^[Y3 : $i > $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))) @ Y0) @ Y1)))))),
% 1.69/1.32 inference(definition_unfolding,[status(thm)],[f27,f26])).
% 1.69/1.32 thf(f27,plain,(
% 1.69/1.32 (epsb = (^[Y0 : ($i > $i) > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ (epsa @ Y0) @ Y1)))))),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.32 thf(f17,plain,(
% 1.69/1.32 (epsb = (^[Y0 : ($i > $i) > $i > $o]: (eps @ (^[Y1 : $i]: (Y0 @ (epsa @ Y0) @ Y1)))))),
% 1.69/1.32 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.32 thf(f16,plain,(
% 1.69/1.32 ((^[X0 : ($i > $i) > $i > $o] : (eps @ (^[X1 : $i] : (X0 @ (epsa @ X0) @ X1)))) = epsb)),
% 1.69/1.32 inference(rectify,[status(thm)],[f4])).
% 1.69/1.32 thf(f4,axiom,(
% 1.69/1.32 ((^[X2 : ($i > $i) > $i > $o] : (eps @ (^[X3 : $i] : (X2 @ (epsa @ X2) @ X3)))) = epsb)),
% 1.69/1.32 file('/export/starexec/sandbox/tmp/tmp.8AelPxxG1l/DTF2THF_30644.p',epsbd)).
% 1.69/1.32 thf(f26,plain,(
% 1.69/1.32 (epsa = (^[Y0 : ($i > $i) > $i > $o]: (epsii @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f11])).
% 1.69/1.32 thf(f11,plain,(
% 1.69/1.32 (epsa = (^[Y0 : ($i > $i) > $i > $o]: (epsii @ (^[Y1 : $i > $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 1.69/1.32 inference(fool_elimination,[status(thm)],[f10])).
% 1.69/1.32 thf(f10,plain,(
% 1.69/1.32 ((^[X0 : ($i > $i) > $i > $o] : (epsii @ (^[X1 : $i > $i] : (? [X2 : $i] : (X0 @ X1 @ X2))))) = epsa)),
% 1.69/1.32 inference(rectify,[status(thm)],[f3])).
% 1.69/1.32 thf(f3,axiom,(
% 1.69/1.32 ((^[X2 : ($i > $i) > $i > $o] : (epsii @ (^[X1 : $i > $i] : (? [X3 : $i] : (X2 @ X1 @ X3))))) = epsa)),
% 1.69/1.32 file('/export/starexec/sandbox/tmp/tmp.8AelPxxG1l/DTF2THF_30644.p',epsad)).
% 1.69/1.32 thf(f28,plain,(
% 1.69/1.32 ((sK0 @ (epsa @ sK0) @ (epsb @ sK0)) != $true)),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.32 thf(f23,plain,(
% 1.69/1.32 ((sK0 @ sK1 @ sK2) = $true) & ((sK0 @ (epsa @ sK0) @ (epsb @ sK0)) != $true)),
% 1.69/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f19,f22,f21])).
% 1.69/1.32 thf(f21,plain,(
% 1.69/1.32 ? [X0 : ($i > $i) > $i > $o] : (? [X1 : $i > $i,X2 : $i] : ($true = (X0 @ X1 @ X2)) & ($true != (X0 @ (epsa @ X0) @ (epsb @ X0)))) => (? [X2 : $i,X1 : $i > $i] : ($true = (sK0 @ X1 @ X2)) & ((sK0 @ (epsa @ sK0) @ (epsb @ sK0)) != $true))),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f22,plain,(
% 1.69/1.32 ? [X2 : $i,X1 : $i > $i] : ($true = (sK0 @ X1 @ X2)) => ((sK0 @ sK1 @ sK2) = $true)),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 thf(f19,plain,(
% 1.69/1.32 ? [X0 : ($i > $i) > $i > $o] : (? [X1 : $i > $i,X2 : $i] : ($true = (X0 @ X1 @ X2)) & ($true != (X0 @ (epsa @ X0) @ (epsb @ X0))))),
% 1.69/1.32 inference(ennf_transformation,[status(thm)],[f9])).
% 1.69/1.32 thf(f9,plain,(
% 1.69/1.32 ~! [X0 : ($i > $i) > $i > $o] : (? [X1 : $i > $i,X2 : $i] : ($true = (X0 @ X1 @ X2)) => ($true = (X0 @ (epsa @ X0) @ (epsb @ X0))))),
% 1.69/1.32 inference(fool_elimination,[status(thm)],[f8])).
% 1.69/1.32 thf(f8,plain,(
% 1.69/1.32 ~! [X0 : ($i > $i) > $i > $o] : (? [X1 : $i > $i,X2 : $i] : (X0 @ X1 @ X2) => (X0 @ (epsa @ X0) @ (epsb @ X0)))),
% 1.69/1.32 inference(rectify,[status(thm)],[f6])).
% 1.69/1.32 thf(f6,negated_conjecture,(
% 1.69/1.32 ~! [X2 : ($i > $i) > $i > $o] : (? [X1 : $i > $i,X3 : $i] : (X2 @ X1 @ X3) => (X2 @ (epsa @ X2) @ (epsb @ X2)))),
% 1.69/1.32 inference(negated_conjecture,[status(cth)],[f5])).
% 1.69/1.32 thf(f5,conjecture,(
% 1.69/1.32 ! [X2 : ($i > $i) > $i > $o] : (? [X1 : $i > $i,X3 : $i] : (X2 @ X1 @ X3) => (X2 @ (epsa @ X2) @ (epsb @ X2)))),
% 1.69/1.32 file('/export/starexec/sandbox/tmp/tmp.8AelPxxG1l/DTF2THF_30644.p',conj)).
% 1.69/1.32 thf(f57,plain,(
% 1.69/1.32 ~spl3_2),
% 1.69/1.32 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.69/1.32 thf(f56,plain,(
% 1.69/1.32 $false | ~spl3_2),
% 1.69/1.32 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.69/1.32 thf(f54,plain,(
% 1.69/1.32 ($true = $false) | ~spl3_2),
% 1.69/1.32 inference(backward_demodulation,[status(thm)],[f29,f44])).
% 1.69/1.32 thf(f44,plain,(
% 1.69/1.32 ( ! [X2 : $i,X1 : $i > $i] : (((sK0 @ X1 @ X2) = $false)) ) | ~spl3_2),
% 1.69/1.32 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.69/1.32 thf(f29,plain,(
% 1.69/1.32 ((sK0 @ sK1 @ sK2) = $true)),
% 1.69/1.32 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.32 thf(f53,plain,(
% 1.69/1.32 spl3_3 | spl3_4),
% 1.69/1.32 inference(avatar_split_clause,[status(thm)],[f34,f50,f47])).
% 1.69/1.32 thf(f34,plain,(
% 1.69/1.32 ( ! [X1 : $i] : (($true = (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))) @ (eps @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))))))) | ((sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ $i @ (sK0 @ Y0)))) @ X1) = $false)) )),
% 1.69/1.32 introduced(definition,[],[choice_axiom])).
% 1.69/1.32 % SZS output end Proof for DTF2THF_30644
% 1.69/1.32 % (30849)------------------------------
% 1.69/1.32 % (30849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (30849)Termination reason: Refutation
% 1.69/1.32
% 1.69/1.32 % (30849)Memory used [KB]: 5500
% 1.69/1.32 % (30849)Time elapsed: 0.006 s
% 1.69/1.32 % (30849)Instructions burned: 4 (million)
% 1.69/1.32 % (30849)------------------------------
% 1.69/1.32 % (30849)------------------------------
% 1.69/1.32 % (30845)Success in time 0.021 s
%------------------------------------------------------------------------------