%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM766^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 09:24:38 AM UTC 2026
% Result : Theorem 1.81s 1.50s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 256 ( 84 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 625 ( 69 ~; 39 |; 0 &; 504 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 118 ( 0 ^; 116 !; 2 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(func_def_0,type,
frac: $tType ).
thf(func_def_1,type,
x: frac ).
thf(func_def_2,type,
y: frac ).
thf(func_def_3,type,
nat: $tType ).
thf(func_def_4,type,
ts: nat > nat > nat ).
thf(func_def_5,type,
num: frac > nat ).
thf(func_def_6,type,
den: frac > nat ).
thf(func_def_7,type,
pl: nat > nat > nat ).
thf(func_def_9,type,
eq: frac > frac > $o ).
thf(func_def_10,type,
pf: frac > frac > frac ).
thf(func_def_11,type,
fr: nat > nat > frac ).
thf(func_def_12,type,
ind: ( nat > $o ) > nat ).
thf(func_def_13,type,
amone: ( nat > $o ) > $o ).
thf(func_def_19,type,
sK0: nat ).
thf(f290,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f287]) ).
thf(f287,plain,
$true != $true,
inference(superposition,[status(thm)],[f286,f42]) ).
thf(f42,plain,
! [X0: nat,X1: frac] :
( $true
= ( eq @ ( fr @ ( ts @ ( num @ X1 ) @ X0 ) @ ( ts @ ( den @ X1 ) @ X0 ) ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: nat,X1: frac] :
( $true
= ( eq @ ( fr @ ( ts @ ( num @ X1 ) @ X0 ) @ ( ts @ ( den @ X1 ) @ X0 ) ) @ X1 ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: nat,X1: frac] : ( eq @ ( fr @ ( ts @ ( num @ X1 ) @ X0 ) @ ( ts @ ( den @ X1 ) @ X0 ) ) @ X1 ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X5: nat,X1: frac] : ( eq @ ( fr @ ( ts @ ( num @ X1 ) @ X5 ) @ ( ts @ ( den @ X1 ) @ X5 ) ) @ X1 ),
file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz40a) ).
thf(f286,plain,
! [X0: frac] :
( $true
!= ( eq @ X0 @ ( fr @ sK0 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f285,f42]) ).
thf(f285,plain,
! [X0: frac] :
( ( $true
!= ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ x ) )
| ( $true
!= ( eq @ X0 @ ( fr @ sK0 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f284,f43]) ).
thf(f43,plain,
! [X0: nat,X1: nat] :
( ( ts @ X1 @ X0 )
= ( ts @ X0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: nat,X1: nat] :
( ( ts @ X1 @ X0 )
= ( ts @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X1: nat,X2: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz29) ).
thf(f284,plain,
! [X0: frac] :
( ( $true
!= ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) @ x ) )
| ( $true
!= ( eq @ X0 @ ( fr @ sK0 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f283,f43]) ).
thf(f283,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ ( fr @ sK0 @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) )
| ( $true
!= ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) @ x ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f280]) ).
thf(f280,plain,
! [X0: frac] :
( ( $true
!= ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) @ x ) )
| ( $true != $true )
| ( $true
!= ( eq @ X0 @ ( fr @ sK0 @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) ) ),
inference(superposition,[status(thm)],[f144,f46]) ).
thf(f46,plain,
! [X0: frac,X1: nat] :
( $true
= ( eq @ X0 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: frac,X1: nat] :
( $true
= ( eq @ X0 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: frac,X1: nat] : ( eq @ X0 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ ( den @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: frac,X5: nat] : ( eq @ X1 @ ( fr @ ( ts @ ( num @ X1 ) @ X5 ) @ ( ts @ ( den @ X1 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz40) ).
thf(f144,plain,
! [X0: nat,X1: frac] :
( ( $true
!= ( eq @ y @ ( fr @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 ) ) )
| ( ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ X0 ) @ x )
!= $true )
| ( $true
!= ( eq @ X1 @ ( fr @ sK0 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f75,f44]) ).
thf(f44,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f36,f39]) ).
thf(f39,plain,
( ? [X0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 ) )
=> ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
? [X0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 ) ),
inference(ennf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ! [X0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',m) ).
thf(f75,plain,
! [X2: nat,X3: frac,X0: nat,X1: nat] :
( ( $true
!= ( eq @ ( fr @ ( pl @ X0 @ X2 ) @ X1 ) @ x ) )
| ( $true
!= ( eq @ y @ ( fr @ X0 @ X1 ) ) )
| ( $true
!= ( eq @ X3 @ ( fr @ X2 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: nat,X3: frac,X0: nat,X1: nat] :
( ( $true
!= ( eq @ y @ ( fr @ X0 @ X1 ) ) )
| ( $true != $true )
| ( $true
!= ( eq @ ( fr @ ( pl @ X0 @ X2 ) @ X1 ) @ x ) )
| ( $true
!= ( eq @ X3 @ ( fr @ X2 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f61,f49]) ).
thf(f49,plain,
! [X2: nat,X0: nat,X1: nat] :
( $true
= ( eq @ ( pf @ ( fr @ X2 @ X1 ) @ ( fr @ X0 @ X1 ) ) @ ( fr @ ( pl @ X2 @ X0 ) @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: nat,X1: nat,X2: nat] :
( $true
= ( eq @ ( pf @ ( fr @ X2 @ X1 ) @ ( fr @ X0 @ X1 ) ) @ ( fr @ ( pl @ X2 @ X0 ) @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: nat,X1: nat,X2: nat] : ( eq @ ( pf @ ( fr @ X2 @ X1 ) @ ( fr @ X0 @ X1 ) ) @ ( fr @ ( pl @ X2 @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X7: nat,X5: nat,X6: nat] : ( eq @ ( pf @ ( fr @ X6 @ X5 ) @ ( fr @ X7 @ X5 ) ) @ ( fr @ ( pl @ X6 @ X7 ) @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz57) ).
thf(f61,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ X3 ) )
| ( $true
!= ( eq @ X2 @ X1 ) )
| ( $true
!= ( eq @ y @ X0 ) )
| ( $true
!= ( eq @ X3 @ x ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
!= ( eq @ X2 @ X1 ) )
| ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ X3 ) )
| ( $true
!= ( eq @ y @ X0 ) )
| ( $true
!= ( eq @ X3 @ x ) ) ),
inference(superposition,[status(thm)],[f56,f41]) ).
thf(f41,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X1 @ X2 )
= $true )
| ( $true
!= ( eq @ X0 @ X2 ) )
| ( $true
!= ( eq @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
!= ( eq @ X0 @ X2 ) )
| ( ( eq @ X1 @ X2 )
= $true )
| ( $true
!= ( eq @ X1 @ X0 ) ) ),
inference(flattening,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X1 @ X2 )
= $true )
| ( $true
!= ( eq @ X0 @ X2 ) )
| ( $true
!= ( eq @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( eq @ X1 @ X0 ) )
=> ( ( $true
= ( eq @ X0 @ X2 ) )
=> ( ( eq @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X1 @ X0 )
=> ( ( eq @ X0 @ X2 )
=> ( eq @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: frac,X1: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz39) ).
thf(f56,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X1 @ X2 ) @ x ) )
| ( $true
!= ( eq @ X0 @ X2 ) )
| ( $true
!= ( eq @ y @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ y @ X1 ) )
| ( $true
!= ( eq @ X0 @ X2 ) )
| ( $true != $true )
| ( $true
!= ( eq @ ( pf @ X1 @ X2 ) @ x ) ) ),
inference(superposition,[status(thm)],[f51,f47]) ).
thf(f47,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X0 @ X3 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( eq @ X0 @ X2 ) )
| ( $true
!= ( eq @ X3 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
!= ( eq @ X0 @ X2 ) )
| ( $true
= ( eq @ ( pf @ X0 @ X3 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( eq @ X3 @ X1 ) ) ),
inference(flattening,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
= ( eq @ ( pf @ X0 @ X3 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( eq @ X3 @ X1 ) )
| ( $true
!= ( eq @ X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
= ( eq @ X0 @ X2 ) )
=> ( ( $true
= ( eq @ X3 @ X1 ) )
=> ( $true
= ( eq @ ( pf @ X0 @ X3 ) @ ( pf @ X2 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ X0 @ X2 )
=> ( ( eq @ X3 @ X1 )
=> ( eq @ ( pf @ X0 @ X3 ) @ ( pf @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: frac,X4: frac,X2: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X3 @ X4 )
=> ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz56) ).
thf(f51,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ y @ X0 ) @ X1 ) )
| ( $true
!= ( eq @ X1 @ x ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
!= ( eq @ X1 @ x ) )
| ( $true
!= ( eq @ ( pf @ y @ X0 ) @ X1 ) ) ),
inference(superposition,[status(thm)],[f45,f41]) ).
thf(f45,plain,
! [X0: frac] :
( ( eq @ ( pf @ y @ X0 ) @ x )
!= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: frac] :
( ( eq @ ( pf @ y @ X0 ) @ x )
!= $true ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
~ ~ ! [X0: frac] :
( ( eq @ ( pf @ y @ X0 ) @ x )
!= $true ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ~ ! [X0: frac] :
~ ( eq @ ( pf @ y @ X0 ) @ x ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ~ ! [X0: frac] :
~ ( eq @ ( pf @ y @ X0 ) @ x ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
~ ! [X0: frac] :
~ ( eq @ ( pf @ y @ X0 ) @ x ),
file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz67a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM766^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.35 % Computer : n010.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 11:13:33 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.45 ---- Original DTF file ---
% 0.21/0.45 thf(spec,logic,$$dhol).
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 % File : NUM766^1 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.45 % Domain : Number Theory
% 0.21/0.45 % Problem : Landau theorem 67a
% 0.21/0.45 % Version : Especial.
% 0.21/0.45 % English : ~(forall x_0:frac.~(eq (pf y x_0) x))
% 0.21/0.45
% 0.21/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.45 % Source : [Bro09]
% 0.21/0.45 % Names : satz67a [Lan30]
% 0.21/0.45
% 0.21/0.45 % Status : Theorem
% 0.21/0.45 % : Without extensionality : Theorem
% 0.21/0.45 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.3.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.67 v3.7.0
% 0.21/0.45 % Syntax : Number of formulae : 24 ( 8 unt; 13 typ; 0 def)
% 0.21/0.45 % Number of atoms : 16 ( 3 equ; 0 cnn)
% 0.21/0.45 % Maximal formula atoms : 3 ( 1 avg)
% 0.21/0.45 % Number of connectives : 89 ( 8 ~; 0 |; 0 &; 75 @)
% 0.21/0.45 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.21/0.45 % Maximal formula depth : 11 ( 7 avg)
% 0.21/0.45 % Number of types : 3 ( 2 usr)
% 0.21/0.45 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.21/0.45 % Number of symbols : 12 ( 11 usr; 2 con; 0-2 aty)
% 0.21/0.45 % Number of variables : 24 ( 1 ^; 23 !; 0 ?; 24 :)
% 0.21/0.45 % SPC : TH0_THM_EQU_NAR
% 0.21/0.45
% 0.21/0.45 % Comments :
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 thf(frac_type,type,
% 0.21/0.45 frac: $tType ).
% 0.21/0.45
% 0.21/0.45 thf(x,type,
% 0.21/0.45 x: frac ).
% 0.21/0.45
% 0.21/0.45 thf(y,type,
% 0.21/0.45 y: frac ).
% 0.21/0.45
% 0.21/0.45 thf(nat_type,type,
% 0.21/0.45 nat: $tType ).
% 0.21/0.45
% 0.21/0.45 thf(ts,type,
% 0.21/0.45 ts: nat > nat > nat ).
% 0.21/0.45
% 0.21/0.45 thf(num,type,
% 0.21/0.45 num: frac > nat ).
% 0.21/0.45
% 0.21/0.45 thf(den,type,
% 0.21/0.45 den: frac > nat ).
% 0.21/0.45
% 0.21/0.45 thf(pl,type,
% 0.21/0.45 pl: nat > nat > nat ).
% 0.21/0.45
% 0.21/0.45 thf(m,axiom,
% 0.21/0.45 ~ ! [Xx_0: nat] :
% 0.21/0.45 ( ( ts @ ( num @ x ) @ ( den @ y ) )
% 0.21/0.45 != ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xx_0 ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(eq,type,
% 0.21/0.45 eq: frac > frac > $o ).
% 0.21/0.45
% 0.21/0.45 thf(pf,type,
% 0.21/0.45 pf: frac > frac > frac ).
% 0.21/0.45
% 0.21/0.45 thf(fr,type,
% 0.21/0.45 fr: nat > nat > frac ).
% 0.21/0.45
% 0.21/0.45 thf(ind,type,
% 0.21/0.45 ind: ( nat > $o ) > nat ).
% 0.21/0.45
% 0.21/0.45 thf(amone,type,
% 0.21/0.45 amone: ( nat > $o ) > $o ).
% 0.21/0.45
% 0.21/0.45 thf(satz8b,axiom,
% 0.21/0.45 ! [Xx: nat,Xy: nat] :
% 0.21/0.45 ( amone
% 0.21/0.45 @ ^ [Xz: nat] :
% 0.21/0.45 ( Xx
% 0.21/0.45 = ( pl @ Xy @ Xz ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(satz39,axiom,
% 0.21/0.45 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.21/0.45 ( ( eq @ Xx @ Xy )
% 0.21/0.45 => ( ( eq @ Xy @ Xz )
% 0.21/0.45 => ( eq @ Xx @ Xz ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(satz56,axiom,
% 0.21/0.45 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.21/0.45 ( ( eq @ Xx @ Xy )
% 0.21/0.45 => ( ( eq @ Xz @ Xu )
% 0.21/0.45 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(satz40,axiom,
% 0.21/0.45 ! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(satz37,axiom,
% 0.21/0.45 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.21/0.45
% 0.21/0.45 thf(satz29,axiom,
% 0.21/0.45 ! [Xx: nat,Xy: nat] :
% 0.21/0.45 ( ( ts @ Xx @ Xy )
% 0.21/0.45 = ( ts @ Xy @ Xx ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(satz57,axiom,
% 0.21/0.45 ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(oneax,axiom,
% 0.21/0.45 ! [Xp: nat > $o] :
% 0.21/0.45 ( ~ ( ( amone @ Xp )
% 0.21/0.45 => ~ ~ ! [Xx: nat] :
% 0.21/0.45 ~ ( Xp @ Xx ) )
% 0.21/0.45 => ( Xp @ ( ind @ Xp ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(satz40a,axiom,
% 0.21/0.45 ! [Xx: frac,Xn: nat] : ( eq @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) @ Xx ) ).
% 0.21/0.45
% 0.21/0.45 thf(satz67a,conjecture,
% 0.21/0.45 ~ ! [Xx_0: frac] :
% 0.21/0.45 ~ ( eq @ ( pf @ y @ Xx_0 ) @ x ) ).
% 0.21/0.45
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 ------------------------
% 1.78/1.41 ---- Embedded in THF ---
% 1.78/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.78/1.41 %%% Generated on Tue Feb 24 11:13:34 EST 2026
% 1.78/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.78/1.41 %%% Logic specification used:
% 1.78/1.41 %%% thf(spec, logic, $$dhol).
% 1.78/1.41
% 1.78/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2DTF32047.p
% See solution above
% 1.78/1.41 ------------------------
% 1.78/1.42 ---- Cleaned THF ---
% 1.78/1.42 thf(frac_type,type,
% 1.78/1.42 frac: $tType ).
% 1.78/1.42
% 1.78/1.42 thf(x,type,
% 1.78/1.42 x: frac ).
% 1.78/1.42
% 1.78/1.42 thf(y,type,
% 1.78/1.42 y: frac ).
% 1.78/1.42
% 1.78/1.42 thf(nat_type,type,
% 1.78/1.42 nat: $tType ).
% 1.78/1.42
% 1.78/1.42 thf(ts,type,
% 1.78/1.42 ts: nat > nat > nat ).
% 1.78/1.42
% 1.78/1.42 thf(num,type,
% 1.78/1.42 num: frac > nat ).
% 1.78/1.42
% 1.78/1.42 thf(den,type,
% 1.78/1.42 den: frac > nat ).
% 1.78/1.42
% 1.78/1.42 thf(pl,type,
% 1.78/1.42 pl: nat > nat > nat ).
% 1.78/1.42
% 1.78/1.42 thf(m,axiom,
% 1.78/1.42 ~ ! [Xx_0: nat] :
% 1.78/1.42 ( ( ts @ ( num @ x ) @ ( den @ y ) )
% 1.78/1.42 != ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xx_0 ) ) ).
% 1.78/1.42
% 1.78/1.42 thf(eq,type,
% 1.78/1.42 eq: frac > frac > $o ).
% 1.78/1.42
% 1.78/1.42 thf(pf,type,
% 1.78/1.42 pf: frac > frac > frac ).
% 1.78/1.42
% 1.78/1.42 thf(fr,type,
% 1.78/1.42 fr: nat > nat > frac ).
% 1.78/1.42
% 1.78/1.42 thf(ind,type,
% 1.78/1.42 ind: ( nat > $o ) > nat ).
% 1.78/1.42
% 1.78/1.42 thf(amone,type,
% 1.78/1.42 amone: ( nat > $o ) > $o ).
% 1.78/1.42
% 1.78/1.42 thf(satz8b,axiom,
% 1.78/1.42 ! [Xx: nat,Xy: nat] :
% 1.78/1.42 ( amone
% 1.78/1.42 @ ^ [Xz: nat] :
% 1.78/1.42 ( Xx
% 1.78/1.42 = ( pl @ Xy @ Xz ) ) ) ).
% 1.78/1.42
% 1.78/1.42 thf(satz39,axiom,
% 1.78/1.42 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.78/1.42 ( ( eq @ Xx @ Xy )
% 1.78/1.42 => ( ( eq @ Xy @ Xz )
% 1.78/1.42 => ( eq @ Xx @ Xz ) ) ) ).
% 1.78/1.42
% 1.78/1.42 thf(satz56,axiom,
% 1.78/1.42 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.78/1.42 ( ( eq @ Xx @ Xy )
% 1.78/1.43 => ( ( eq @ Xz @ Xu )
% 1.78/1.43 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 1.78/1.43
% 1.78/1.43 thf(satz40,axiom,
% 1.78/1.43 ! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) ) ).
% 1.78/1.43
% 1.78/1.43 thf(satz37,axiom,
% 1.78/1.43 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 1.78/1.43
% 1.78/1.43 thf(satz29,axiom,
% 1.78/1.43 ! [Xx: nat,Xy: nat] :
% 1.78/1.43 ( ( ts @ Xx @ Xy )
% 1.78/1.43 = ( ts @ Xy @ Xx ) ) ).
% 1.78/1.43
% 1.78/1.43 thf(satz57,axiom,
% 1.78/1.43 ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) ).
% 1.78/1.43
% 1.78/1.43 thf(oneax,axiom,
% 1.78/1.43 ! [Xp: nat > $o] :
% 1.78/1.43 ( ~ ( ( amone @ Xp )
% 1.78/1.43 => ~ ~ ! [Xx: nat] :
% 1.78/1.43 ~ ( Xp @ Xx ) )
% 1.78/1.43 => ( Xp @ ( ind @ Xp ) ) ) ).
% 1.78/1.43
% 1.78/1.43 thf(satz40a,axiom,
% 1.78/1.43 ! [Xx: frac,Xn: nat] : ( eq @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) @ Xx ) ).
% 1.78/1.43
% 1.78/1.43 thf(satz67a,conjecture,
% 1.78/1.43 ~ ! [Xx_0: frac] :
% 1.78/1.43 ~ ( eq @ ( pf @ y @ Xx_0 ) @ x ) ).
% 1.78/1.43 ------------------------
% 1.78/1.44 % (32148)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_32047 for (2999ds/2Mi)
% 1.78/1.44 % (32145)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_32047 for (2999ds/4Mi)
% 1.78/1.44 % (32144)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/183Mi)
% 1.78/1.44 % (32146)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_32047 for (2999ds/27Mi)
% 1.78/1.44 % (32147)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/2Mi)
% 1.78/1.44 % (32150)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/18Mi)
% 1.78/1.45 % (32149)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_32047 for (2999ds/275Mi)
% 1.78/1.45 % (32147)Instruction limit reached!
% 1.78/1.45 % (32147)------------------------------
% 1.78/1.45 % (32147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.45 % (32147)Termination reason: Unknown
% 1.78/1.45 % (32148)Instruction limit reached!
% 1.78/1.45 % (32148)------------------------------
% 1.78/1.45 % (32148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.45 % (32147)Termination phase: shuffling
% 1.78/1.45
% 1.78/1.45 % (32147)Memory used [KB]: 1023
% 1.78/1.45 % (32147)Time elapsed: 0.003 s
% 1.78/1.45 % (32147)Instructions burned: 3 (million)
% 1.78/1.45 % (32147)------------------------------
% 1.78/1.45 % (32147)------------------------------
% 1.78/1.45 % (32148)Termination reason: Unknown
% 1.78/1.45 % (32148)Termination phase: shuffling
% 1.78/1.45
% 1.78/1.45 % (32148)Memory used [KB]: 1023
% 1.78/1.45 % (32148)Time elapsed: 0.003 s
% 1.78/1.45 % (32148)Instructions burned: 3 (million)
% 1.78/1.45 % (32148)------------------------------
% 1.78/1.45 % (32148)------------------------------
% 1.78/1.45 % (32145)Instruction limit reached!
% 1.78/1.45 % (32145)------------------------------
% 1.78/1.45 % (32145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.45 % (32145)Termination reason: Unknown
% 1.78/1.45 % (32145)Termination phase: Saturation
% 1.78/1.45
% 1.78/1.45 % (32145)Memory used [KB]: 5500
% 1.78/1.45 % (32145)Time elapsed: 0.004 s
% 1.78/1.45 % (32145)Instructions burned: 5 (million)
% 1.78/1.45 % (32145)------------------------------
% 1.78/1.45 % (32145)------------------------------
% 1.78/1.45 % (32150)Instruction limit reached!
% 1.78/1.45 % (32150)------------------------------
% 1.78/1.45 % (32150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.45 % (32150)Termination reason: Unknown
% 1.78/1.45 % (32150)Termination phase: Saturation
% 1.78/1.45
% 1.78/1.45 % (32150)Memory used [KB]: 5628
% 1.78/1.45 % (32150)Time elapsed: 0.011 s
% 1.78/1.45 % (32150)Instructions burned: 18 (million)
% 1.78/1.45 % (32150)------------------------------
% 1.78/1.45 % (32150)------------------------------
% 1.78/1.46 % (32146)Instruction limit reached!
% 1.78/1.46 % (32146)------------------------------
% 1.78/1.46 % (32146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.46 % (32146)Termination reason: Unknown
% 1.78/1.46 % (32146)Termination phase: Saturation
% 1.78/1.46
% 1.78/1.46 % (32146)Memory used [KB]: 5628
% 1.78/1.46 % (32146)Time elapsed: 0.016 s
% 1.78/1.46 % (32146)Instructions burned: 28 (million)
% 1.78/1.46 % (32146)------------------------------
% 1.78/1.46 % (32146)------------------------------
% 1.78/1.46 % (32151)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/3Mi)
% 1.78/1.46 % (32152)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/37Mi)
% 1.78/1.46 % (32153)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/15Mi)
% 1.78/1.46 % (32151)Instruction limit reached!
% 1.78/1.46 % (32151)------------------------------
% 1.78/1.46 % (32151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.46 % (32151)Termination reason: Unknown
% 1.78/1.46 % (32151)Termination phase: Saturation
% 1.78/1.46
% 1.78/1.46 % (32151)Memory used [KB]: 1023
% 1.78/1.46 % (32151)Time elapsed: 0.003 s
% 1.78/1.46 % (32151)Instructions burned: 3 (million)
% 1.78/1.46 % (32151)------------------------------
% 1.78/1.46 % (32151)------------------------------
% 1.78/1.47 % (32153)Instruction limit reached!
% 1.78/1.47 % (32153)------------------------------
% 1.78/1.47 % (32153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.47 % (32154)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/3Mi)
% 1.78/1.47 % (32153)Termination reason: Unknown
% 1.78/1.47 % (32153)Termination phase: Saturation
% 1.78/1.47
% 1.78/1.47 % (32153)Memory used [KB]: 5628
% 1.78/1.47 % (32153)Time elapsed: 0.032 s
% 1.78/1.47 % (32153)Instructions burned: 15 (million)
% 1.78/1.47 % (32153)------------------------------
% 1.78/1.47 % (32153)------------------------------
% 1.78/1.47 % (32154)Instruction limit reached!
% 1.78/1.47 % (32154)------------------------------
% 1.78/1.47 % (32154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.47 % (32154)Termination reason: Unknown
% 1.78/1.47 % (32154)Termination phase: Saturation
% 1.78/1.47
% 1.78/1.47 % (32154)Memory used [KB]: 5500
% 1.78/1.47 % (32154)Time elapsed: 0.003 s
% 1.78/1.47 % (32154)Instructions burned: 3 (million)
% 1.78/1.47 % (32154)------------------------------
% 1.78/1.47 % (32154)------------------------------
% 1.78/1.48 % (32155)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/1041Mi)
% 1.78/1.48 % (32156)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/7Mi)
% 1.78/1.48 % (32152)Instruction limit reached!
% 1.78/1.48 % (32152)------------------------------
% 1.78/1.48 % (32152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.48 % (32152)Termination reason: Unknown
% 1.78/1.48 % (32152)Termination phase: Saturation
% 1.78/1.48
% 1.78/1.48 % (32152)Memory used [KB]: 5884
% 1.78/1.48 % (32152)Time elapsed: 0.042 s
% 1.78/1.48 % (32152)Instructions burned: 37 (million)
% 1.78/1.48 % (32152)------------------------------
% 1.78/1.48 % (32152)------------------------------
% 1.78/1.48 % (32156)Instruction limit reached!
% 1.78/1.48 % (32156)------------------------------
% 1.78/1.48 % (32156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.48 % (32156)Termination reason: Unknown
% 1.78/1.48 % (32156)Termination phase: Saturation
% 1.78/1.48
% 1.78/1.48 % (32156)Memory used [KB]: 1151
% 1.78/1.48 % (32156)Time elapsed: 0.005 s
% 1.78/1.48 % (32156)Instructions burned: 7 (million)
% 1.78/1.48 % (32156)------------------------------
% 1.78/1.48 % (32156)------------------------------
% 1.78/1.49 % (32157)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/16Mi)
% 1.78/1.49 % (32158)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/3Mi)
% 1.78/1.49 % (32158)Instruction limit reached!
% 1.78/1.49 % (32158)------------------------------
% 1.78/1.49 % (32158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.49 % (32158)Termination reason: Unknown
% 1.78/1.49 % (32158)Termination phase: Twee Goal Transformation
% 1.78/1.49
% 1.78/1.49 % (32158)Memory used [KB]: 1023
% 1.78/1.49 % (32158)Time elapsed: 0.003 s
% 1.78/1.49 % (32158)Instructions burned: 3 (million)
% 1.78/1.49 % (32158)------------------------------
% 1.78/1.49 % (32158)------------------------------
% 1.78/1.50 % (32149)First to succeed.
% 1.78/1.50 % (32157)Instruction limit reached!
% 1.78/1.50 % (32157)------------------------------
% 1.78/1.50 % (32157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.50 % (32157)Termination reason: Unknown
% 1.78/1.50 % (32157)Termination phase: Saturation
% 1.78/1.50
% 1.78/1.50 % (32157)Memory used [KB]: 5628
% 1.78/1.50 % (32157)Time elapsed: 0.011 s
% 1.78/1.50 % (32157)Instructions burned: 17 (million)
% 1.78/1.50 % (32157)------------------------------
% 1.78/1.50 % (32157)------------------------------
% 1.81/1.50 % (32159)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32047 for (2999ds/3Mi)
% 1.81/1.50 % (32149)Refutation found. Thanks to Tanya!
% 1.81/1.50 % SZS status Theorem for DTF2THF_32047
% 1.81/1.50 % SZS output start Proof for DTF2THF_32047
% 1.81/1.50 thf(type_def_5, type, frac: $tType).
% 1.81/1.50 thf(type_def_6, type, nat: $tType).
% 1.81/1.50 thf(func_def_0, type, frac: $tType).
% 1.81/1.50 thf(func_def_1, type, x: frac).
% 1.81/1.50 thf(func_def_2, type, y: frac).
% 1.81/1.50 thf(func_def_3, type, nat: $tType).
% 1.81/1.50 thf(func_def_4, type, ts: nat > nat > nat).
% 1.81/1.50 thf(func_def_5, type, num: frac > nat).
% 1.81/1.50 thf(func_def_6, type, den: frac > nat).
% 1.81/1.50 thf(func_def_7, type, pl: nat > nat > nat).
% 1.81/1.50 thf(func_def_9, type, eq: frac > frac > $o).
% 1.81/1.50 thf(func_def_10, type, pf: frac > frac > frac).
% 1.81/1.50 thf(func_def_11, type, fr: nat > nat > frac).
% 1.81/1.50 thf(func_def_12, type, ind: (nat > $o) > nat).
% 1.81/1.50 thf(func_def_13, type, amone: (nat > $o) > $o).
% 1.81/1.50 thf(func_def_19, type, sK0: nat).
% 1.81/1.50 thf(f290,plain,(
% 1.81/1.50 $false),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f287])).
% 1.81/1.50 thf(f287,plain,(
% 1.81/1.50 ($true != $true)),
% 1.81/1.50 inference(superposition,[status(thm)],[f286,f42])).
% 1.81/1.50 thf(f42,plain,(
% 1.81/1.50 ( ! [X0 : nat,X1 : frac] : (($true = (eq @ (fr @ (ts @ (num @ X1) @ X0) @ (ts @ (den @ X1) @ X0)) @ X1))) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f23])).
% 1.81/1.50 thf(f23,plain,(
% 1.81/1.50 ! [X0 : nat,X1 : frac] : ($true = (eq @ (fr @ (ts @ (num @ X1) @ X0) @ (ts @ (den @ X1) @ X0)) @ X1))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f22])).
% 1.81/1.50 thf(f22,plain,(
% 1.81/1.50 ! [X0 : nat,X1 : frac] : (eq @ (fr @ (ts @ (num @ X1) @ X0) @ (ts @ (den @ X1) @ X0)) @ X1)),
% 1.81/1.50 inference(rectify,[status(thm)],[f10])).
% 1.81/1.50 thf(f10,axiom,(
% 1.81/1.50 ! [X5 : nat,X1 : frac] : (eq @ (fr @ (ts @ (num @ X1) @ X5) @ (ts @ (den @ X1) @ X5)) @ X1)),
% 1.81/1.50 file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz40a)).
% 1.81/1.50 thf(f286,plain,(
% 1.81/1.50 ( ! [X0 : frac] : (($true != (eq @ X0 @ (fr @ sK0 @ (ts @ (den @ x) @ (den @ y)))))) )),
% 1.81/1.50 inference(subsumption_resolution,[status(thm)],[f285,f42])).
% 1.81/1.50 thf(f285,plain,(
% 1.81/1.50 ( ! [X0 : frac] : (($true != (eq @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ x) @ (den @ y))) @ x)) | ($true != (eq @ X0 @ (fr @ sK0 @ (ts @ (den @ x) @ (den @ y)))))) )),
% 1.81/1.50 inference(forward_demodulation,[status(thm)],[f284,f43])).
% 1.81/1.50 thf(f43,plain,(
% 1.81/1.50 ( ! [X0 : nat,X1 : nat] : (((ts @ X1 @ X0) = (ts @ X0 @ X1))) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f33])).
% 1.81/1.50 thf(f33,plain,(
% 1.81/1.50 ! [X0 : nat,X1 : nat] : ((ts @ X1 @ X0) = (ts @ X0 @ X1))),
% 1.81/1.50 inference(rectify,[status(thm)],[f7])).
% 1.81/1.50 thf(f7,axiom,(
% 1.81/1.50 ! [X1 : nat,X2 : nat] : ((ts @ X1 @ X2) = (ts @ X2 @ X1))),
% 1.81/1.50 file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz29)).
% 1.81/1.50 thf(f284,plain,(
% 1.81/1.50 ( ! [X0 : frac] : (($true != (eq @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ y) @ (den @ x))) @ x)) | ($true != (eq @ X0 @ (fr @ sK0 @ (ts @ (den @ x) @ (den @ y)))))) )),
% 1.81/1.50 inference(forward_demodulation,[status(thm)],[f283,f43])).
% 1.81/1.50 thf(f283,plain,(
% 1.81/1.50 ( ! [X0 : frac] : (($true != (eq @ X0 @ (fr @ sK0 @ (ts @ (den @ y) @ (den @ x))))) | ($true != (eq @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ y) @ (den @ x))) @ x))) )),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f280])).
% 1.81/1.50 thf(f280,plain,(
% 1.81/1.50 ( ! [X0 : frac] : (($true != (eq @ (fr @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (den @ y) @ (den @ x))) @ x)) | ($true != $true) | ($true != (eq @ X0 @ (fr @ sK0 @ (ts @ (den @ y) @ (den @ x)))))) )),
% 1.81/1.50 inference(superposition,[status(thm)],[f144,f46])).
% 1.81/1.50 thf(f46,plain,(
% 1.81/1.50 ( ! [X0 : frac,X1 : nat] : (($true = (eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1))))) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f25])).
% 1.81/1.50 thf(f25,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : nat] : ($true = (eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1))))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f24])).
% 1.81/1.50 thf(f24,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : nat] : (eq @ X0 @ (fr @ (ts @ (num @ X0) @ X1) @ (ts @ (den @ X0) @ X1)))),
% 1.81/1.50 inference(rectify,[status(thm)],[f5])).
% 1.81/1.50 thf(f5,axiom,(
% 1.81/1.50 ! [X1 : frac,X5 : nat] : (eq @ X1 @ (fr @ (ts @ (num @ X1) @ X5) @ (ts @ (den @ X1) @ X5)))),
% 1.81/1.50 file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz40)).
% 1.81/1.50 thf(f144,plain,(
% 1.81/1.50 ( ! [X0 : nat,X1 : frac] : (($true != (eq @ y @ (fr @ (ts @ (num @ y) @ (den @ x)) @ X0))) | ((eq @ (fr @ (ts @ (num @ x) @ (den @ y)) @ X0) @ x) != $true) | ($true != (eq @ X1 @ (fr @ sK0 @ X0)))) )),
% 1.81/1.50 inference(superposition,[status(thm)],[f75,f44])).
% 1.81/1.50 thf(f44,plain,(
% 1.81/1.50 ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK0))),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f40])).
% 1.81/1.50 thf(f40,plain,(
% 1.81/1.50 ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK0))),
% 1.81/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f36,f39])).
% 1.81/1.50 thf(f39,plain,(
% 1.81/1.50 ? [X0 : nat] : ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ X0)) => ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ sK0))),
% 1.81/1.50 introduced(definition,[],[choice_axiom])).
% 1.81/1.50 thf(f36,plain,(
% 1.81/1.50 ? [X0 : nat] : ((ts @ (num @ x) @ (den @ y)) = (pl @ (ts @ (num @ y) @ (den @ x)) @ X0))),
% 1.81/1.50 inference(ennf_transformation,[status(thm)],[f1])).
% 1.81/1.50 thf(f1,axiom,(
% 1.81/1.50 ~! [X0 : nat] : ((ts @ (num @ x) @ (den @ y)) != (pl @ (ts @ (num @ y) @ (den @ x)) @ X0))),
% 1.81/1.50 file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',m)).
% 1.81/1.50 thf(f75,plain,(
% 1.81/1.50 ( ! [X2 : nat,X3 : frac,X0 : nat,X1 : nat] : (($true != (eq @ (fr @ (pl @ X0 @ X2) @ X1) @ x)) | ($true != (eq @ y @ (fr @ X0 @ X1))) | ($true != (eq @ X3 @ (fr @ X2 @ X1)))) )),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.81/1.50 thf(f71,plain,(
% 1.81/1.50 ( ! [X2 : nat,X3 : frac,X0 : nat,X1 : nat] : (($true != (eq @ y @ (fr @ X0 @ X1))) | ($true != $true) | ($true != (eq @ (fr @ (pl @ X0 @ X2) @ X1) @ x)) | ($true != (eq @ X3 @ (fr @ X2 @ X1)))) )),
% 1.81/1.50 inference(superposition,[status(thm)],[f61,f49])).
% 1.81/1.50 thf(f49,plain,(
% 1.81/1.50 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (eq @ (pf @ (fr @ X2 @ X1) @ (fr @ X0 @ X1)) @ (fr @ (pl @ X2 @ X0) @ X1)))) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f29])).
% 1.81/1.50 thf(f29,plain,(
% 1.81/1.50 ! [X0 : nat,X1 : nat,X2 : nat] : ($true = (eq @ (pf @ (fr @ X2 @ X1) @ (fr @ X0 @ X1)) @ (fr @ (pl @ X2 @ X0) @ X1)))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f28])).
% 1.81/1.50 thf(f28,plain,(
% 1.81/1.50 ! [X0 : nat,X1 : nat,X2 : nat] : (eq @ (pf @ (fr @ X2 @ X1) @ (fr @ X0 @ X1)) @ (fr @ (pl @ X2 @ X0) @ X1))),
% 1.81/1.50 inference(rectify,[status(thm)],[f8])).
% 1.81/1.50 thf(f8,axiom,(
% 1.81/1.50 ! [X7 : nat,X5 : nat,X6 : nat] : (eq @ (pf @ (fr @ X6 @ X5) @ (fr @ X7 @ X5)) @ (fr @ (pl @ X6 @ X7) @ X5))),
% 1.81/1.50 file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz57)).
% 1.81/1.50 thf(f61,plain,(
% 1.81/1.50 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != (eq @ (pf @ X0 @ X1) @ X3)) | ($true != (eq @ X2 @ X1)) | ($true != (eq @ y @ X0)) | ($true != (eq @ X3 @ x))) )),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.81/1.50 thf(f60,plain,(
% 1.81/1.50 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true != (eq @ X2 @ X1)) | ($true != (eq @ (pf @ X0 @ X1) @ X3)) | ($true != (eq @ y @ X0)) | ($true != (eq @ X3 @ x))) )),
% 1.81/1.50 inference(superposition,[status(thm)],[f56,f41])).
% 1.81/1.50 thf(f41,plain,(
% 1.81/1.50 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X1 @ X2) = $true) | ($true != (eq @ X0 @ X2)) | ($true != (eq @ X1 @ X0))) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.81/1.50 thf(f38,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : frac,X2 : frac] : (($true != (eq @ X0 @ X2)) | ((eq @ X1 @ X2) = $true) | ($true != (eq @ X1 @ X0)))),
% 1.81/1.50 inference(flattening,[status(thm)],[f37])).
% 1.81/1.50 thf(f37,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : frac,X2 : frac] : ((((eq @ X1 @ X2) = $true) | ($true != (eq @ X0 @ X2))) | ($true != (eq @ X1 @ X0)))),
% 1.81/1.50 inference(ennf_transformation,[status(thm)],[f21])).
% 1.81/1.50 thf(f21,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : frac,X2 : frac] : (($true = (eq @ X1 @ X0)) => (($true = (eq @ X0 @ X2)) => ((eq @ X1 @ X2) = $true)))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f20])).
% 1.81/1.50 thf(f20,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X1 @ X0) => ((eq @ X0 @ X2) => (eq @ X1 @ X2)))),
% 1.81/1.50 inference(rectify,[status(thm)],[f3])).
% 1.81/1.50 thf(f3,axiom,(
% 1.81/1.50 ! [X2 : frac,X1 : frac,X3 : frac] : ((eq @ X1 @ X2) => ((eq @ X2 @ X3) => (eq @ X1 @ X3)))),
% 1.81/1.50 file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz39)).
% 1.81/1.50 thf(f56,plain,(
% 1.81/1.50 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (eq @ (pf @ X1 @ X2) @ x)) | ($true != (eq @ X0 @ X2)) | ($true != (eq @ y @ X1))) )),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.81/1.50 thf(f52,plain,(
% 1.81/1.50 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (eq @ y @ X1)) | ($true != (eq @ X0 @ X2)) | ($true != $true) | ($true != (eq @ (pf @ X1 @ X2) @ x))) )),
% 1.81/1.50 inference(superposition,[status(thm)],[f51,f47])).
% 1.81/1.50 thf(f47,plain,(
% 1.81/1.50 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true = (eq @ (pf @ X0 @ X3) @ (pf @ X2 @ X1))) | ($true != (eq @ X0 @ X2)) | ($true != (eq @ X3 @ X1))) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f35])).
% 1.81/1.50 thf(f35,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true != (eq @ X0 @ X2)) | ($true = (eq @ (pf @ X0 @ X3) @ (pf @ X2 @ X1))) | ($true != (eq @ X3 @ X1)))),
% 1.81/1.50 inference(flattening,[status(thm)],[f34])).
% 1.81/1.50 thf(f34,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((($true = (eq @ (pf @ X0 @ X3) @ (pf @ X2 @ X1))) | ($true != (eq @ X3 @ X1))) | ($true != (eq @ X0 @ X2)))),
% 1.81/1.50 inference(ennf_transformation,[status(thm)],[f31])).
% 1.81/1.50 thf(f31,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true = (eq @ X0 @ X2)) => (($true = (eq @ X3 @ X1)) => ($true = (eq @ (pf @ X0 @ X3) @ (pf @ X2 @ X1)))))),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f30])).
% 1.81/1.50 thf(f30,plain,(
% 1.81/1.50 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X2) => ((eq @ X3 @ X1) => (eq @ (pf @ X0 @ X3) @ (pf @ X2 @ X1))))),
% 1.81/1.50 inference(rectify,[status(thm)],[f4])).
% 1.81/1.50 thf(f4,axiom,(
% 1.81/1.50 ! [X1 : frac,X4 : frac,X2 : frac,X3 : frac] : ((eq @ X1 @ X2) => ((eq @ X3 @ X4) => (eq @ (pf @ X1 @ X3) @ (pf @ X2 @ X4))))),
% 1.81/1.50 file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz56)).
% 1.81/1.50 thf(f51,plain,(
% 1.81/1.50 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ (pf @ y @ X0) @ X1)) | ($true != (eq @ X1 @ x))) )),
% 1.81/1.50 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.81/1.50 thf(f50,plain,(
% 1.81/1.50 ( ! [X0 : frac,X1 : frac] : (($true != $true) | ($true != (eq @ X1 @ x)) | ($true != (eq @ (pf @ y @ X0) @ X1))) )),
% 1.81/1.50 inference(superposition,[status(thm)],[f45,f41])).
% 1.81/1.50 thf(f45,plain,(
% 1.81/1.50 ( ! [X0 : frac] : (((eq @ (pf @ y @ X0) @ x) != $true)) )),
% 1.81/1.50 inference(cnf_transformation,[status(thm)],[f32])).
% 1.81/1.50 thf(f32,plain,(
% 1.81/1.50 ! [X0 : frac] : ((eq @ (pf @ y @ X0) @ x) != $true)),
% 1.81/1.50 inference(flattening,[status(thm)],[f19])).
% 1.81/1.50 thf(f19,plain,(
% 1.81/1.50 ~~! [X0 : frac] : ~((eq @ (pf @ y @ X0) @ x) = $true)),
% 1.81/1.50 inference(fool_elimination,[status(thm)],[f18])).
% 1.81/1.50 thf(f18,plain,(
% 1.81/1.50 ~~! [X0 : frac] : ~(eq @ (pf @ y @ X0) @ x)),
% 1.81/1.50 inference(rectify,[status(thm)],[f12])).
% 1.81/1.50 thf(f12,negated_conjecture,(
% 1.81/1.50 ~~! [X0 : frac] : ~(eq @ (pf @ y @ X0) @ x)),
% 1.81/1.50 inference(negated_conjecture,[status(cth)],[f11])).
% 1.81/1.50 thf(f11,conjecture,(
% 1.81/1.50 ~! [X0 : frac] : ~(eq @ (pf @ y @ X0) @ x)),
% 1.81/1.50 file('/export/starexec/sandbox2/tmp/tmp.US142uytIM/DTF2THF_32047.p',satz67a)).
% 1.81/1.50 % SZS output end Proof for DTF2THF_32047
% 1.81/1.50 % (32149)------------------------------
% 1.81/1.50 % (32149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.50 % (32149)Termination reason: Refutation
% 1.81/1.50
% 1.81/1.50 % (32149)Memory used [KB]: 5756
% 1.81/1.50 % (32149)Time elapsed: 0.053 s
% 1.81/1.50 % (32149)Instructions burned: 103 (million)
% 1.81/1.50 % (32149)------------------------------
% 1.81/1.50 % (32149)------------------------------
% 1.81/1.50 % (32143)Success in time 0.073 s
%------------------------------------------------------------------------------