%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO537^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 1.68s 1.47s
% Output : Refutation 1.68s
% 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 : 172 ( 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 : 167 ( 167 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 6 con; 0-2 aty)
% ( 0 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 46 ^; 21 !; 20 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_2,type,
epsa: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_3,type,
epsb: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_12,type,
sK0: ( $i > $i ) > ( $i > $i ) > $o ).
thf(func_def_13,type,
sK1: $i > $i ).
thf(func_def_14,type,
sK2: $i > $i ).
thf(func_def_16,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK5: $i > $i ).
thf(func_def_18,type,
sK6: $i > $i ).
thf(func_def_19,type,
sK7: $i > $i ).
thf(f73,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f48,f52,f53,f72]) ).
thf(f72,plain,
( spl3_2
| ~ spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f71,f42,f38]) ).
thf(f38,definition,
( spl3_2
<=> ! [X2: $i > $i,X1: $i > $i] :
( $false
= ( sK0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f42,definition,
( spl3_3
<=> ! [X1: $i > $i] :
( $false
= ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f71,plain,
( ! [X2: $i > $i,X1: $i > $i] :
( $false
= ( sK0 @ X1 @ X2 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ! [X2: $i > $i,X1: $i > $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f69,f43]) ).
thf(f43,plain,
( ! [X1: $i > $i] :
( $false
= ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) )
@ X1 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f69,plain,
! [X2: $i > $i,X1: $i > $i] :
( ( ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) )
@ sK7 )
= $true )
| ( $false
= ( sK0 @ X1 @ X2 ) ) ),
inference(sigma_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i > $i,X1: $i > $i] :
( ( ( ?? @ ( $i > $i )
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( sK0 @ X1 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $i > $i] :
( ( ( ?? @ ( $i > $i ) @ ( sK0 @ X1 ) )
= $false )
| ( ( ?? @ ( $i > $i )
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: $i > $i] :
( ( $false
= ( ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) )
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f53,plain,
~ spl3_4,
inference(avatar_split_clause,[status(thm)],[f27,f45]) ).
thf(f45,definition,
( spl3_4
<=> ( ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) )
@ ( epsii
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f27,plain,
( ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) )
@ ( epsii
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
!= ( sK0
@ ( ^ [Y0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y1: $i > $i] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 )
@ ( ^ [Y0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y1: $i > $i] :
( Y0
@ ( ^ [Y2: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y3: $i > $i] :
( ?? @ ( $i > $i )
@ ^ [Y4: $i > $i] : ( Y2 @ Y3 @ Y4 ) ) )
@ Y0 )
@ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f20,f25]) ).
thf(f25,plain,
( epsb
= ( ^ [Y0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y1: $i > $i] :
( Y0
@ ( ^ [Y2: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y3: $i > $i] :
( ?? @ ( $i > $i )
@ ^ [Y4: $i > $i] : ( Y2 @ Y3 @ Y4 ) ) )
@ Y0 )
@ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f20]) ).
thf(f21,plain,
( epsb
= ( ^ [Y0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y1: $i > $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( epsb
= ( ^ [Y0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y1: $i > $i] : ( Y0 @ ( epsa @ Y0 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [X1: $i > $i] : ( X0 @ ( epsa @ X0 ) @ X1 ) ) )
= epsb ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [X3: $i > $i] : ( X2 @ ( epsa @ X2 ) @ X3 ) ) )
= epsb ),
file('/export/starexec/sandbox2/tmp/tmp.jhoDv3kJAc/DTF2THF_21991.p',epsbd) ).
thf(f20,plain,
( epsa
= ( ^ [Y0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y1: $i > $i] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( epsa
= ( ^ [Y0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Y1: $i > $i] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( epsa
= ( ^ [X0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [X1: $i > $i] :
? [X2: $i > $i] : ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( epsa
= ( ^ [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [X1: $i > $i] :
? [X3: $i > $i] : ( X2 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jhoDv3kJAc/DTF2THF_21991.p',epsad) ).
thf(f24,plain,
( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) )
!= $true )
& ( ( sK0 @ sK2 @ sK1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f18,f17]) ).
thf(f17,plain,
( ? [X0: ( $i > $i ) > ( $i > $i ) > $o] :
( ( ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) )
!= $true )
& ? [X1: $i > $i,X2: $i > $i] :
( ( X0 @ X2 @ X1 )
= $true ) )
=> ( ( ( sK0 @ ( epsa @ sK0 ) @ ( epsb @ sK0 ) )
!= $true )
& ? [X2: $i > $i,X1: $i > $i] :
( ( sK0 @ X2 @ X1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X2: $i > $i,X1: $i > $i] :
( ( sK0 @ X2 @ X1 )
= $true )
=> ( ( sK0 @ sK2 @ sK1 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: ( $i > $i ) > ( $i > $i ) > $o] :
( ( ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) )
!= $true )
& ? [X1: $i > $i,X2: $i > $i] :
( ( X0 @ X2 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ! [X0: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [X1: $i > $i,X2: $i > $i] :
( ( X0 @ X2 @ X1 )
= $true )
=> ( ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ! [X0: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [X1: $i > $i,X2: $i > $i] : ( X0 @ X2 @ X1 )
=> ( X0 @ ( epsa @ X0 ) @ ( epsb @ X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [X3: $i > $i,X1: $i > $i] : ( X2 @ X1 @ X3 )
=> ( X2 @ ( epsa @ X2 ) @ ( epsb @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X2: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [X3: $i > $i,X1: $i > $i] : ( X2 @ X1 @ X3 )
=> ( X2 @ ( epsa @ X2 ) @ ( epsb @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jhoDv3kJAc/DTF2THF_21991.p',conj) ).
thf(f52,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $false = $true )
| ~ spl3_2 ),
inference(backward_demodulation,[status(thm)],[f23,f39]) ).
thf(f39,plain,
( ! [X2: $i > $i,X1: $i > $i] :
( $false
= ( sK0 @ X1 @ X2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f23,plain,
( ( sK0 @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f48,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f29,f45,f42]) ).
thf(f29,plain,
! [X1: $i > $i] :
( ( ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) )
@ ( epsii
@ ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) ) ) ) )
= $true )
| ( $false
= ( sK0
@ ( epsii
@ ^ [Y0: $i > $i] : ( ?? @ ( $i > $i ) @ ( sK0 @ Y0 ) ) )
@ X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO537^1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 14:33:08 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.43 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : SYO537^1 : TPTP v9.2.1. Released v5.2.0.
% 0.16/0.43 % Domain : Syntactic
% 0.16/0.43 % Problem : Choice on binary relations between functions
% 0.16/0.43 % Version : Especial.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.16/0.43 % Source : [Bro11]
% 0.16/0.43 % Names : CHOICE14 [Bro11]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.11 v9.1.0, 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 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
% 0.16/0.43 % Syntax : Number of formulae : 7 ( 2 unt; 3 typ; 2 def)
% 0.16/0.43 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 1 ( 0 avg)
% 0.16/0.43 % Number of connectives : 18 ( 0 ~; 0 |; 0 &; 16 @)
% 0.16/0.43 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 7 ( 4 avg)
% 0.16/0.43 % Number of types : 2 ( 0 usr)
% 0.16/0.43 % Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 4 ( 3 usr; 0 con; 2-2 aty)
% 0.16/0.43 % Number of variables : 10 ( 4 ^; 2 !; 4 ?; 10 :)
% 0.16/0.43 % SPC : TH0_THM_EQU_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : A choice operator ii is used to define a choice operator on ii*ii
% 0.16/0.43 % (Curried).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 thf(epsii,type,
% 0.16/0.43 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 0.16/0.43
% 0.16/0.43 thf(choiceaxii,axiom,
% 0.16/0.43 ! [P: ( $i > $i ) > $o] :
% 0.16/0.43 ( ? [X: $i > $i] : ( P @ X )
% 0.16/0.43 => ( P @ ( epsii @ P ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(epsa,type,
% 0.16/0.43 epsa: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
% 0.16/0.43
% 0.16/0.43 thf(epsad,definition,
% 0.16/0.43 ( epsa
% 0.16/0.43 = ( ^ [R: ( $i > $i ) > ( $i > $i ) > $o] :
% 0.16/0.43 ( epsii
% 0.16/0.43 @ ^ [X: $i > $i] :
% 0.16/0.43 ? [Y: $i > $i] : ( R @ X @ Y ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(epsb,type,
% 0.16/0.43 epsb: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
% 0.16/0.43
% 0.16/0.43 thf(epsbd,definition,
% 0.16/0.43 ( epsb
% 0.16/0.43 = ( ^ [R: ( $i > $i ) > ( $i > $i ) > $o] :
% 0.16/0.43 ( epsii
% 0.16/0.43 @ ^ [Y: $i > $i] : ( R @ ( epsa @ R ) @ Y ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(conj,conjecture,
% 0.16/0.43 ! [R: ( $i > $i ) > ( $i > $i ) > $o] :
% 0.16/0.43 ( ? [X: $i > $i,Y: $i > $i] : ( R @ X @ Y )
% 0.16/0.43 => ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ) ).
% 0.16/0.43
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 ------------------------
% 1.68/1.43 ---- Embedded in THF ---
% 1.68/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.43 %%% Generated on Tue Feb 24 14:33:09 EST 2026
% 1.68/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.43 %%% Logic specification used:
% 1.68/1.43 %%% thf(spec, logic, $$dhol).
% 1.68/1.43
% 1.68/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jhoDv3kJAc/DTF2DTF21991.p
% See solution above
% 1.68/1.43 ------------------------
% 1.68/1.44 ---- Cleaned THF ---
% 1.68/1.45 thf(epsii,type,
% 1.68/1.45 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 1.68/1.45
% 1.68/1.45 thf(choiceaxii,axiom,
% 1.68/1.45 ! [P: ( $i > $i ) > $o] :
% 1.68/1.45 ( ? [X: $i > $i] : ( P @ X )
% 1.68/1.45 => ( P @ ( epsii @ P ) ) ) ).
% 1.68/1.45
% 1.68/1.45 thf(epsa,type,
% 1.68/1.45 epsa: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
% 1.68/1.45
% 1.68/1.45 thf(epsad,definition,
% 1.68/1.45 ( epsa
% 1.68/1.45 = ( ^ [R: ( $i > $i ) > ( $i > $i ) > $o] :
% 1.68/1.45 ( epsii
% 1.68/1.45 @ ^ [X: $i > $i] :
% 1.68/1.45 ? [Y: $i > $i] : ( R @ X @ Y ) ) ) ) ).
% 1.68/1.45
% 1.68/1.45 thf(epsb,type,
% 1.68/1.45 epsb: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
% 1.68/1.45
% 1.68/1.45 thf(epsbd,definition,
% 1.68/1.45 ( epsb
% 1.68/1.45 = ( ^ [R: ( $i > $i ) > ( $i > $i ) > $o] :
% 1.68/1.45 ( epsii
% 1.68/1.45 @ ^ [Y: $i > $i] : ( R @ ( epsa @ R ) @ Y ) ) ) ) ).
% 1.68/1.45
% 1.68/1.45 thf(conj,conjecture,
% 1.68/1.45 ! [R: ( $i > $i ) > ( $i > $i ) > $o] :
% 1.68/1.45 ( ? [X: $i > $i,Y: $i > $i] : ( R @ X @ Y )
% 1.68/1.45 => ( R @ ( epsa @ R ) @ ( epsb @ R ) ) ) ).
% 1.68/1.45 ------------------------
% 1.68/1.47 % (22089)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_21991 for (2999ds/4Mi)
% 1.68/1.47 % (22092)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_21991 for (2999ds/2Mi)
% 1.68/1.47 % (22088)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21991 for (2999ds/183Mi)
% 1.68/1.47 % (22092)Instruction limit reached!
% 1.68/1.47 % (22092)------------------------------
% 1.68/1.47 % (22092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.47 % (22092)Termination reason: Unknown
% 1.68/1.47 % (22094)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21991 for (2999ds/18Mi)
% 1.68/1.47 % (22092)Termination phase: Saturation
% 1.68/1.47
% 1.68/1.47 % (22092)Memory used [KB]: 895
% 1.68/1.47 % (22092)Time elapsed: 0.003 s
% 1.68/1.47 % (22092)Instructions burned: 2 (million)
% 1.68/1.47 % (22092)------------------------------
% 1.68/1.47 % (22092)------------------------------
% 1.68/1.47 % (22091)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21991 for (2999ds/2Mi)
% 1.68/1.47 % (22093)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_21991 for (2999ds/275Mi)
% 1.68/1.47 % (22090)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_21991 for (2999ds/27Mi)
% 1.68/1.47 % (22091)Instruction limit reached!
% 1.68/1.47 % (22091)------------------------------
% 1.68/1.47 % (22091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.47 % (22091)Termination reason: Unknown
% 1.68/1.47 % (22091)Termination phase: Preprocessing 3
% 1.68/1.47
% 1.68/1.47 % (22091)Memory used [KB]: 895
% 1.68/1.47 % (22091)Time elapsed: 0.002 s
% 1.68/1.47 % (22091)Instructions burned: 2 (million)
% 1.68/1.47 % (22091)------------------------------
% 1.68/1.47 % (22091)------------------------------
% 1.68/1.47 % (22089)Instruction limit reached!
% 1.68/1.47 % (22089)------------------------------
% 1.68/1.47 % (22089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.47 % (22089)Termination reason: Unknown
% 1.68/1.47 % (22089)Termination phase: Saturation
% 1.68/1.47
% 1.68/1.47 % (22089)Memory used [KB]: 5500
% 1.68/1.47 % (22089)Time elapsed: 0.005 s
% 1.68/1.47 % (22089)Instructions burned: 5 (million)
% 1.68/1.47 % (22089)------------------------------
% 1.68/1.47 % (22089)------------------------------
% 1.68/1.47 % (22093)Refutation not found, incomplete strategy
% 1.68/1.47 % (22093)------------------------------
% 1.68/1.47 % (22093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.47 % (22093)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.47
% 1.68/1.47
% 1.68/1.47 % (22093)Memory used [KB]: 5500
% 1.68/1.47 % (22093)Time elapsed: 0.003 s
% 1.68/1.47 % (22093)Instructions burned: 3 (million)
% 1.68/1.47 % (22093)------------------------------
% 1.68/1.47 % (22093)------------------------------
% 1.68/1.47 % (22090)First to succeed.
% 1.68/1.47 % (22090)Refutation found. Thanks to Tanya!
% 1.68/1.47 % SZS status Theorem for DTF2THF_21991
% 1.68/1.47 % SZS output start Proof for DTF2THF_21991
% 1.68/1.47 thf(func_def_0, type, epsii: (($i > $i) > $o) > $i > $i).
% 1.68/1.47 thf(func_def_2, type, epsa: (($i > $i) > ($i > $i) > $o) > $i > $i).
% 1.68/1.47 thf(func_def_3, type, epsb: (($i > $i) > ($i > $i) > $o) > $i > $i).
% 1.68/1.47 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.68/1.47 thf(func_def_12, type, sK0: ($i > $i) > ($i > $i) > $o).
% 1.68/1.47 thf(func_def_13, type, sK1: $i > $i).
% 1.68/1.47 thf(func_def_14, type, sK2: $i > $i).
% 1.68/1.47 thf(func_def_16, type, ph4: !>[X0: $tType]:(X0)).
% 1.68/1.47 thf(func_def_17, type, sK5: $i > $i).
% 1.68/1.47 thf(func_def_18, type, sK6: $i > $i).
% 1.68/1.47 thf(func_def_19, type, sK7: $i > $i).
% 1.68/1.47 thf(f73,plain,(
% 1.68/1.47 $false),
% 1.68/1.47 inference(avatar_sat_refutation,[status(thm)],[f48,f52,f53,f72])).
% 1.68/1.47 thf(f72,plain,(
% 1.68/1.47 spl3_2 | ~spl3_3),
% 1.68/1.47 inference(avatar_split_clause,[status(thm)],[f71,f42,f38])).
% 1.68/1.47 thf(f38,definition,(
% 1.68/1.47 spl3_2 <=> ! [X2 : $i > $i,X1 : $i > $i] : ($false = (sK0 @ X1 @ X2))),
% 1.68/1.47 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.68/1.47 thf(f42,definition,(
% 1.68/1.47 spl3_3 <=> ! [X1 : $i > $i] : ($false = (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0)))) @ X1))),
% 1.68/1.47 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.68/1.47 thf(f71,plain,(
% 1.68/1.47 ( ! [X2 : $i > $i,X1 : $i > $i] : (($false = (sK0 @ X1 @ X2))) ) | ~spl3_3),
% 1.68/1.47 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.68/1.47 thf(f70,plain,(
% 1.68/1.47 ( ! [X2 : $i > $i,X1 : $i > $i] : (($false = $true) | ($false = (sK0 @ X1 @ X2))) ) | ~spl3_3),
% 1.68/1.47 inference(forward_demodulation,[status(thm)],[f69,f43])).
% 1.68/1.47 thf(f43,plain,(
% 1.68/1.47 ( ! [X1 : $i > $i] : (($false = (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0)))) @ X1))) ) | ~spl3_3),
% 1.68/1.47 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.68/1.47 thf(f69,plain,(
% 1.68/1.47 ( ! [X2 : $i > $i,X1 : $i > $i] : (((sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0)))) @ sK7) = $true) | ($false = (sK0 @ X1 @ X2))) )),
% 1.68/1.47 inference(sigma_clausification,[status(thm)],[f68])).
% 1.68/1.47 thf(f68,plain,(
% 1.68/1.47 ( ! [X2 : $i > $i,X1 : $i > $i] : (((?? @ ($i > $i) @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0)))))) = $true) | ($false = (sK0 @ X1 @ X2))) )),
% 1.68/1.47 inference(pi_clausification,[status(thm)],[f67])).
% 1.68/1.47 thf(f67,plain,(
% 1.68/1.47 ( ! [X1 : $i > $i] : (((?? @ ($i > $i) @ (sK0 @ X1)) = $false) | ((?? @ ($i > $i) @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0)))))) = $true)) )),
% 1.68/1.47 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.68/1.47 thf(f64,plain,(
% 1.68/1.47 ( ! [X1 : $i > $i] : (($false = ((^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0))) @ X1)) | (((^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0))) @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0))))) = $true)) )),
% 1.68/1.47 introduced(definition,[],[choice_axiom])).
% 1.68/1.47 thf(f53,plain,(
% 1.68/1.47 ~spl3_4),
% 1.68/1.47 inference(avatar_split_clause,[status(thm)],[f27,f45])).
% 1.68/1.47 thf(f45,definition,(
% 1.68/1.47 spl3_4 <=> ((sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0)))) @ (epsii @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0))))))) = $true)),
% 1.68/1.47 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.68/1.47 thf(f27,plain,(
% 1.68/1.47 ((sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0)))) @ (epsii @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0))))))) != $true)),
% 1.68/1.47 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.68/1.47 thf(f26,plain,(
% 1.68/1.47 ($true != (sK0 @ ((^[Y0 : ($i > $i) > ($i > $i) > $o]: (epsii @ (^[Y1 : $i > $i]: (?? @ ($i > $i) @ (^[Y2 : $i > $i]: (Y0 @ Y1 @ Y2)))))) @ sK0) @ ((^[Y0 : ($i > $i) > ($i > $i) > $o]: (epsii @ (^[Y1 : $i > $i]: (Y0 @ ((^[Y2 : ($i > $i) > ($i > $i) > $o]: (epsii @ (^[Y3 : $i > $i]: (?? @ ($i > $i) @ (^[Y4 : $i > $i]: (Y2 @ Y3 @ Y4)))))) @ Y0) @ Y1)))) @ sK0)))),
% 1.68/1.47 inference(definition_unfolding,[status(thm)],[f24,f20,f25])).
% 1.68/1.47 thf(f25,plain,(
% 1.68/1.47 (epsb = (^[Y0 : ($i > $i) > ($i > $i) > $o]: (epsii @ (^[Y1 : $i > $i]: (Y0 @ ((^[Y2 : ($i > $i) > ($i > $i) > $o]: (epsii @ (^[Y3 : $i > $i]: (?? @ ($i > $i) @ (^[Y4 : $i > $i]: (Y2 @ Y3 @ Y4)))))) @ Y0) @ Y1)))))),
% 1.68/1.47 inference(definition_unfolding,[status(thm)],[f21,f20])).
% 1.68/1.48 thf(f21,plain,(
% 1.68/1.48 (epsb = (^[Y0 : ($i > $i) > ($i > $i) > $o]: (epsii @ (^[Y1 : $i > $i]: (Y0 @ (epsa @ Y0) @ Y1)))))),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f8])).
% 1.68/1.48 thf(f8,plain,(
% 1.68/1.48 (epsb = (^[Y0 : ($i > $i) > ($i > $i) > $o]: (epsii @ (^[Y1 : $i > $i]: (Y0 @ (epsa @ Y0) @ Y1)))))),
% 1.68/1.48 inference(fool_elimination,[status(thm)],[f7])).
% 1.68/1.48 thf(f7,plain,(
% 1.68/1.48 ((^[X0 : ($i > $i) > ($i > $i) > $o] : (epsii @ (^[X1 : $i > $i] : (X0 @ (epsa @ X0) @ X1)))) = epsb)),
% 1.68/1.48 inference(rectify,[status(thm)],[f3])).
% 1.68/1.48 thf(f3,axiom,(
% 1.68/1.48 ((^[X2 : ($i > $i) > ($i > $i) > $o] : (epsii @ (^[X3 : $i > $i] : (X2 @ (epsa @ X2) @ X3)))) = epsb)),
% 1.68/1.48 file('/export/starexec/sandbox2/tmp/tmp.jhoDv3kJAc/DTF2THF_21991.p',epsbd)).
% 1.68/1.48 thf(f20,plain,(
% 1.68/1.48 (epsa = (^[Y0 : ($i > $i) > ($i > $i) > $o]: (epsii @ (^[Y1 : $i > $i]: (?? @ ($i > $i) @ (^[Y2 : $i > $i]: (Y0 @ Y1 @ Y2)))))))),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f12])).
% 1.68/1.48 thf(f12,plain,(
% 1.68/1.48 (epsa = (^[Y0 : ($i > $i) > ($i > $i) > $o]: (epsii @ (^[Y1 : $i > $i]: (?? @ ($i > $i) @ (^[Y2 : $i > $i]: (Y0 @ Y1 @ Y2)))))))),
% 1.68/1.48 inference(fool_elimination,[status(thm)],[f11])).
% 1.68/1.48 thf(f11,plain,(
% 1.68/1.48 (epsa = (^[X0 : ($i > $i) > ($i > $i) > $o] : (epsii @ (^[X1 : $i > $i] : (? [X2 : $i > $i] : (X0 @ X1 @ X2))))))),
% 1.68/1.48 inference(rectify,[status(thm)],[f2])).
% 1.68/1.48 thf(f2,axiom,(
% 1.68/1.48 (epsa = (^[X2 : ($i > $i) > ($i > $i) > $o] : (epsii @ (^[X1 : $i > $i] : (? [X3 : $i > $i] : (X2 @ X1 @ X3))))))),
% 1.68/1.48 file('/export/starexec/sandbox2/tmp/tmp.jhoDv3kJAc/DTF2THF_21991.p',epsad)).
% 1.68/1.48 thf(f24,plain,(
% 1.68/1.48 ((sK0 @ (epsa @ sK0) @ (epsb @ sK0)) != $true)),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.48 thf(f19,plain,(
% 1.68/1.48 ((sK0 @ (epsa @ sK0) @ (epsb @ sK0)) != $true) & ((sK0 @ sK2 @ sK1) = $true)),
% 1.68/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f18,f17])).
% 1.68/1.48 thf(f17,plain,(
% 1.68/1.48 ? [X0 : ($i > $i) > ($i > $i) > $o] : (((X0 @ (epsa @ X0) @ (epsb @ X0)) != $true) & ? [X1 : $i > $i,X2 : $i > $i] : ((X0 @ X2 @ X1) = $true)) => (((sK0 @ (epsa @ sK0) @ (epsb @ sK0)) != $true) & ? [X2 : $i > $i,X1 : $i > $i] : ((sK0 @ X2 @ X1) = $true))),
% 1.68/1.48 introduced(definition,[],[choice_axiom])).
% 1.68/1.48 thf(f18,plain,(
% 1.68/1.48 ? [X2 : $i > $i,X1 : $i > $i] : ((sK0 @ X2 @ X1) = $true) => ((sK0 @ sK2 @ sK1) = $true)),
% 1.68/1.48 introduced(definition,[],[choice_axiom])).
% 1.68/1.48 thf(f15,plain,(
% 1.68/1.48 ? [X0 : ($i > $i) > ($i > $i) > $o] : (((X0 @ (epsa @ X0) @ (epsb @ X0)) != $true) & ? [X1 : $i > $i,X2 : $i > $i] : ((X0 @ X2 @ X1) = $true))),
% 1.68/1.48 inference(ennf_transformation,[status(thm)],[f14])).
% 1.68/1.48 thf(f14,plain,(
% 1.68/1.48 ~! [X0 : ($i > $i) > ($i > $i) > $o] : (? [X1 : $i > $i,X2 : $i > $i] : ((X0 @ X2 @ X1) = $true) => ((X0 @ (epsa @ X0) @ (epsb @ X0)) = $true))),
% 1.68/1.48 inference(fool_elimination,[status(thm)],[f13])).
% 1.68/1.48 thf(f13,plain,(
% 1.68/1.48 ~! [X0 : ($i > $i) > ($i > $i) > $o] : (? [X1 : $i > $i,X2 : $i > $i] : (X0 @ X2 @ X1) => (X0 @ (epsa @ X0) @ (epsb @ X0)))),
% 1.68/1.48 inference(rectify,[status(thm)],[f5])).
% 1.68/1.48 thf(f5,negated_conjecture,(
% 1.68/1.48 ~! [X2 : ($i > $i) > ($i > $i) > $o] : (? [X3 : $i > $i,X1 : $i > $i] : (X2 @ X1 @ X3) => (X2 @ (epsa @ X2) @ (epsb @ X2)))),
% 1.68/1.48 inference(negated_conjecture,[status(cth)],[f4])).
% 1.68/1.48 thf(f4,conjecture,(
% 1.68/1.48 ! [X2 : ($i > $i) > ($i > $i) > $o] : (? [X3 : $i > $i,X1 : $i > $i] : (X2 @ X1 @ X3) => (X2 @ (epsa @ X2) @ (epsb @ X2)))),
% 1.68/1.48 file('/export/starexec/sandbox2/tmp/tmp.jhoDv3kJAc/DTF2THF_21991.p',conj)).
% 1.68/1.48 thf(f52,plain,(
% 1.68/1.48 ~spl3_2),
% 1.68/1.48 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.68/1.48 thf(f51,plain,(
% 1.68/1.48 $false | ~spl3_2),
% 1.68/1.48 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.68/1.48 thf(f49,plain,(
% 1.68/1.48 ($false = $true) | ~spl3_2),
% 1.68/1.48 inference(backward_demodulation,[status(thm)],[f23,f39])).
% 1.68/1.48 thf(f39,plain,(
% 1.68/1.48 ( ! [X2 : $i > $i,X1 : $i > $i] : (($false = (sK0 @ X1 @ X2))) ) | ~spl3_2),
% 1.68/1.48 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.68/1.48 thf(f23,plain,(
% 1.68/1.48 ((sK0 @ sK2 @ sK1) = $true)),
% 1.68/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.48 thf(f48,plain,(
% 1.68/1.48 spl3_3 | spl3_4),
% 1.68/1.48 inference(avatar_split_clause,[status(thm)],[f29,f45,f42])).
% 1.68/1.48 thf(f29,plain,(
% 1.68/1.48 ( ! [X1 : $i > $i] : (((sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0)))) @ (epsii @ (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0))))))) = $true) | ($false = (sK0 @ (epsii @ (^[Y0 : $i > $i]: (?? @ ($i > $i) @ (sK0 @ Y0)))) @ X1))) )),
% 1.68/1.48 introduced(definition,[],[choice_axiom])).
% 1.68/1.48 % SZS output end Proof for DTF2THF_21991
% 1.68/1.48 % (22090)------------------------------
% 1.68/1.48 % (22090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.48 % (22090)Termination reason: Refutation
% 1.68/1.48
% 1.68/1.48 % (22090)Memory used [KB]: 5500
% 1.68/1.48 % (22090)Time elapsed: 0.007 s
% 1.68/1.48 % (22090)Instructions burned: 4 (million)
% 1.68/1.48 % (22090)------------------------------
% 1.68/1.48 % (22090)------------------------------
% 1.68/1.48 % (22087)Success in time 0.023 s
%------------------------------------------------------------------------------