%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM755^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 09:24:34 AM UTC 2026
% Result : Theorem 1.58s 1.31s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 296 ( 88 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 456 ( 81 ~; 31 |; 6 &; 304 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 71 ( 0 ^; 71 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $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,
z: frac ).
thf(func_def_4,type,
moref: frac > frac > $o ).
thf(func_def_5,type,
pf: frac > frac > frac ).
thf(func_def_7,type,
eq: frac > frac > $o ).
thf(func_def_8,type,
lessf: frac > frac > $o ).
thf(f62,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f61,f52]) ).
thf(f52,plain,
( $true
!= ( eq @ x @ y ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true != $true )
| ( $true
!= ( eq @ x @ y ) ) ),
inference(superposition,[status(thm)],[f48,f38]) ).
thf(f38,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) ) )
| ( ( eq @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) ) )
| ( ( eq @ X1 @ X2 )
!= $true ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( $true
= ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: frac,X2: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz62b) ).
thf(f48,plain,
( $true
!= ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true
!= ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f39,f42]) ).
thf(f42,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
moref @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
moref @ ( pf @ x @ z ) @ ( pf @ y @ z ),
file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',m) ).
thf(f39,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( moref @ X0 @ X1 ) )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: frac,X1: frac] :
( ( ( $true
!= ( lessf @ X0 @ X1 ) )
| ( $true
!= ( moref @ X0 @ X1 ) ) )
& ( ( ( eq @ X0 @ X1 )
!= $true )
| ( $true
!= ( lessf @ X0 @ X1 ) ) )
& ( ( $true
!= ( moref @ X0 @ X1 ) )
| ( ( eq @ X0 @ X1 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: frac,X0: frac] :
( ( ( $true
!= ( lessf @ X1 @ X0 ) )
| ( $true
!= ( moref @ X1 @ X0 ) ) )
& ( ( $true
!= ( eq @ X1 @ X0 ) )
| ( $true
!= ( lessf @ X1 @ X0 ) ) )
& ( ( $true
!= ( moref @ X1 @ X0 ) )
| ( $true
!= ( eq @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: frac,X1: frac] :
( ( ( $true
!= ( eq @ X1 @ X0 ) )
| ( $true
!= ( lessf @ X1 @ X0 ) ) )
& ( ( $true
!= ( lessf @ X1 @ X0 ) )
| ( $true
!= ( moref @ X1 @ X0 ) ) )
& ( ( $true
!= ( moref @ X1 @ X0 ) )
| ( $true
!= ( eq @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: frac,X1: frac] :
~ ( ( ( $true
= ( eq @ X1 @ X0 ) )
=> ( $true
!= ( moref @ X1 @ X0 ) ) )
=> ( ( ( $true
= ( moref @ X1 @ X0 ) )
=> ( $true
!= ( lessf @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( lessf @ X1 @ X0 ) )
=> ( $true
!= ( eq @ X1 @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: frac,X1: frac] :
~ ( ( ( $true
= ( eq @ X1 @ X0 ) )
=> ( $true
!= ( moref @ X1 @ X0 ) ) )
=> ~ ~ ( ( ( $true
= ( moref @ X1 @ X0 ) )
=> ( $true
!= ( lessf @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( lessf @ X1 @ X0 ) )
=> ( $true
!= ( eq @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: frac,X1: frac] :
~ ( ( ( eq @ X1 @ X0 )
=> ~ ( moref @ X1 @ X0 ) )
=> ~ ~ ( ( ( moref @ X1 @ X0 )
=> ~ ( lessf @ X1 @ X0 ) )
=> ~ ( ( lessf @ X1 @ X0 )
=> ~ ( eq @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: frac,X1: frac] :
~ ( ( ( eq @ X1 @ X2 )
=> ~ ( moref @ X1 @ X2 ) )
=> ~ ~ ( ( ( moref @ X1 @ X2 )
=> ~ ( lessf @ X1 @ X2 ) )
=> ~ ( ( lessf @ X1 @ X2 )
=> ~ ( eq @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz41b) ).
thf(f61,plain,
( $true
= ( eq @ x @ y ) ),
inference(subsumption_resolution,[status(thm)],[f60,f37]) ).
thf(f37,plain,
( ( moref @ x @ y )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( moref @ x @ y )
!= $true ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( moref @ x @ y )
!= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( moref @ x @ y ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( moref @ x @ y ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
moref @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz63a) ).
thf(f60,plain,
( ( ( moref @ x @ y )
= $true )
| ( $true
= ( eq @ x @ y ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true
= ( eq @ x @ y ) )
| ( ( moref @ x @ y )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f58,f43]) ).
thf(f43,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( lessf @ X1 @ X0 ) )
| ( $true
= ( eq @ X1 @ X0 ) )
| ( $true
= ( moref @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( eq @ X1 @ X0 ) )
| ( $true
= ( lessf @ X1 @ X0 ) )
| ( $true
= ( moref @ X1 @ X0 ) ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( lessf @ X1 @ X0 ) )
| ( $true
= ( moref @ X1 @ X0 ) )
| ( $true
= ( eq @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X1 @ X0 ) )
=> ( ( $true
!= ( moref @ X1 @ X0 ) )
=> ( $true
= ( lessf @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X1 @ X0 ) )
=> ( ( $true
!= ( moref @ X1 @ X0 ) )
=> ( $true
= ( lessf @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac] :
( ~ ( eq @ X1 @ X0 )
=> ( ~ ( moref @ X1 @ X0 )
=> ( lessf @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X2: frac,X1: frac] :
( ~ ( eq @ X1 @ X2 )
=> ( ~ ( moref @ X1 @ X2 )
=> ( lessf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz41a) ).
thf(f58,plain,
( ( lessf @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( lessf @ x @ y )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f55,f42]) ).
thf(f55,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) )
!= $true )
| ( $true
!= ( lessf @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) )
!= $true )
| ( $true
!= ( lessf @ X0 @ X2 ) ) ),
inference(superposition,[status(thm)],[f41,f45]) ).
thf(f45,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( lessf @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) ) )
| ( ( lessf @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X1 @ X2 )
!= $true )
| ( $true
= ( lessf @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: frac,X1: frac,X0: frac] :
( ( ( lessf @ X1 @ X2 )
= $true )
=> ( $true
= ( lessf @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X1 @ X2 )
=> ( lessf @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X3: frac,X1: frac,X2: frac] :
( ( lessf @ X1 @ X2 )
=> ( lessf @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz62c) ).
thf(f41,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( lessf @ X0 @ X1 ) )
| ( $true
!= ( moref @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM755^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n011.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 11:13:32 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : NUM755^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Number Theory
% 0.18/0.38 % Problem : Landau theorem 63a
% 0.18/0.38 % Version : Especial.
% 0.18/0.38 % English : moref x y
% 0.18/0.38
% 0.18/0.38 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.18/0.38 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.18/0.38 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.38 % Source : [Bro09]
% 0.18/0.38 % Names : satz63a [Lan30]
% 0.18/0.38 % : satz73a [Lan30]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % : Without extensionality : Theorem
% 0.18/0.38 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 15 ( 2 unt; 8 typ; 0 def)
% 0.18/0.38 % Number of atoms : 15 ( 0 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 6 ( 2 avg)
% 0.18/0.38 % Number of connectives : 63 ( 11 ~; 0 |; 0 &; 42 @)
% 0.18/0.38 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 13 ( 7 avg)
% 0.18/0.38 % Number of types : 2 ( 1 usr)
% 0.18/0.38 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.18/0.38 % Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% 0.18/0.38 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.38
% 0.18/0.38 % Comments :
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(frac_type,type,
% 0.18/0.38 frac: $tType ).
% 0.18/0.38
% 0.18/0.38 thf(x,type,
% 0.18/0.38 x: frac ).
% 0.18/0.38
% 0.18/0.38 thf(y,type,
% 0.18/0.38 y: frac ).
% 0.18/0.38
% 0.18/0.38 thf(z,type,
% 0.18/0.38 z: frac ).
% 0.18/0.38
% 0.18/0.38 thf(moref,type,
% 0.18/0.38 moref: frac > frac > $o ).
% 0.18/0.38
% 0.18/0.38 thf(pf,type,
% 0.18/0.38 pf: frac > frac > frac ).
% 0.18/0.38
% 0.18/0.38 thf(m,axiom,
% 0.18/0.38 moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) ).
% 0.18/0.38
% 0.18/0.38 thf(et,axiom,
% 0.18/0.38 ! [Xa: $o] :
% 0.18/0.38 ( ~ ~ Xa
% 0.18/0.38 => Xa ) ).
% 0.18/0.38
% 0.18/0.38 thf(eq,type,
% 0.18/0.38 eq: frac > frac > $o ).
% 0.18/0.38
% 0.18/0.38 thf(lessf,type,
% 0.18/0.38 lessf: frac > frac > $o ).
% 0.18/0.38
% 0.18/0.38 thf(satz41b,axiom,
% 0.18/0.38 ! [Xx: frac,Xy: frac] :
% 0.18/0.38 ~ ( ( ( eq @ Xx @ Xy )
% 0.18/0.38 => ~ ( moref @ Xx @ Xy ) )
% 0.18/0.38 => ~ ~ ( ( ( moref @ Xx @ Xy )
% 0.18/0.38 => ~ ( lessf @ Xx @ Xy ) )
% 0.18/0.38 => ~ ( ( lessf @ Xx @ Xy )
% 0.18/0.38 => ~ ( eq @ Xx @ Xy ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(satz62b,axiom,
% 0.18/0.38 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.18/0.38 ( ( eq @ Xx @ Xy )
% 0.18/0.38 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(satz62c,axiom,
% 0.18/0.38 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.18/0.38 ( ( lessf @ Xx @ Xy )
% 0.18/0.38 => ( lessf @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(satz41a,axiom,
% 0.18/0.38 ! [Xx: frac,Xy: frac] :
% 0.18/0.38 ( ~ ( eq @ Xx @ Xy )
% 0.18/0.38 => ( ~ ( moref @ Xx @ Xy )
% 0.18/0.38 => ( lessf @ Xx @ Xy ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(satz63a,conjecture,
% 0.18/0.38 moref @ x @ y ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.42/1.28 ---- Embedded in THF ---
% 1.42/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.42/1.28 %%% Generated on Tue Feb 24 11:13:33 EST 2026
% 1.42/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.42/1.28 %%% Logic specification used:
% 1.42/1.28 %%% thf(spec, logic, $$dhol).
% 1.42/1.28
% 1.42/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2DTF16731.p
% See solution above
% 1.42/1.28 ------------------------
% 1.42/1.29 ---- Cleaned THF ---
% 1.42/1.29 thf(frac_type,type,
% 1.42/1.29 frac: $tType ).
% 1.42/1.29
% 1.42/1.29 thf(x,type,
% 1.42/1.29 x: frac ).
% 1.42/1.29
% 1.42/1.29 thf(y,type,
% 1.42/1.29 y: frac ).
% 1.42/1.29
% 1.42/1.29 thf(z,type,
% 1.42/1.29 z: frac ).
% 1.42/1.29
% 1.42/1.29 thf(moref,type,
% 1.42/1.29 moref: frac > frac > $o ).
% 1.42/1.29
% 1.42/1.29 thf(pf,type,
% 1.42/1.29 pf: frac > frac > frac ).
% 1.42/1.29
% 1.42/1.29 thf(m,axiom,
% 1.42/1.29 moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) ).
% 1.42/1.29
% 1.42/1.29 thf(et,axiom,
% 1.42/1.29 ! [Xa: $o] :
% 1.42/1.29 ( ~ ~ Xa
% 1.42/1.29 => Xa ) ).
% 1.42/1.29
% 1.42/1.29 thf(eq,type,
% 1.42/1.29 eq: frac > frac > $o ).
% 1.42/1.29
% 1.42/1.29 thf(lessf,type,
% 1.42/1.29 lessf: frac > frac > $o ).
% 1.42/1.29
% 1.42/1.29 thf(satz41b,axiom,
% 1.42/1.29 ! [Xx: frac,Xy: frac] :
% 1.42/1.29 ~ ( ( ( eq @ Xx @ Xy )
% 1.42/1.29 => ~ ( moref @ Xx @ Xy ) )
% 1.42/1.29 => ~ ~ ( ( ( moref @ Xx @ Xy )
% 1.42/1.29 => ~ ( lessf @ Xx @ Xy ) )
% 1.42/1.29 => ~ ( ( lessf @ Xx @ Xy )
% 1.42/1.29 => ~ ( eq @ Xx @ Xy ) ) ) ) ).
% 1.42/1.29
% 1.42/1.29 thf(satz62b,axiom,
% 1.42/1.29 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.42/1.29 ( ( eq @ Xx @ Xy )
% 1.42/1.29 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 1.42/1.29
% 1.42/1.29 thf(satz62c,axiom,
% 1.42/1.29 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.42/1.29 ( ( lessf @ Xx @ Xy )
% 1.42/1.29 => ( lessf @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 1.42/1.29
% 1.42/1.29 thf(satz41a,axiom,
% 1.42/1.29 ! [Xx: frac,Xy: frac] :
% 1.42/1.29 ( ~ ( eq @ Xx @ Xy )
% 1.42/1.29 => ( ~ ( moref @ Xx @ Xy )
% 1.42/1.29 => ( lessf @ Xx @ Xy ) ) ) ).
% 1.42/1.29
% 1.42/1.29 thf(satz63a,conjecture,
% 1.42/1.29 moref @ x @ y ).
% 1.42/1.29 ------------------------
% 1.58/1.31 % (16830)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_16731 for (2999ds/27Mi)
% 1.58/1.31 % (16829)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_16731 for (2999ds/4Mi)
% 1.58/1.31 % (16831)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16731 for (2999ds/2Mi)
% 1.58/1.31 % (16833)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_16731 for (2999ds/275Mi)
% 1.58/1.31 % (16832)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_16731 for (2999ds/2Mi)
% 1.58/1.31 % (16828)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16731 for (2999ds/183Mi)
% 1.58/1.31 % (16834)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16731 for (2999ds/18Mi)
% 1.58/1.31 % (16831)Instruction limit reached!
% 1.58/1.31 % (16831)------------------------------
% 1.58/1.31 % (16831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (16831)Termination reason: Unknown
% 1.58/1.31 % (16832)Instruction limit reached!
% 1.58/1.31 % (16832)------------------------------
% 1.58/1.31 % (16832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (16833)Refutation not found, incomplete strategy
% 1.58/1.31 % (16833)------------------------------
% 1.58/1.31 % (16833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (16831)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (16833)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.31
% 1.58/1.31
% 1.58/1.31 % (16831)Memory used [KB]: 5500
% 1.58/1.31 % (16833)Memory used [KB]: 5500
% 1.58/1.31 % (16831)Time elapsed: 0.003 s
% 1.58/1.31 % (16833)Time elapsed: 0.002 s
% 1.58/1.31 % (16831)Instructions burned: 2 (million)
% 1.58/1.31 % (16833)Instructions burned: 1 (million)
% 1.58/1.31 % (16831)------------------------------
% 1.58/1.31 % (16831)------------------------------
% 1.58/1.31 % (16833)------------------------------
% 1.58/1.31 % (16833)------------------------------
% 1.58/1.31 % (16832)Termination reason: Unknown
% 1.58/1.31 % (16832)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (16832)Memory used [KB]: 1023
% 1.58/1.31 % (16832)Time elapsed: 0.003 s
% 1.58/1.31 % (16832)Instructions burned: 3 (million)
% 1.58/1.31 % (16832)------------------------------
% 1.58/1.31 % (16832)------------------------------
% 1.58/1.31 % (16829)Instruction limit reached!
% 1.58/1.31 % (16829)------------------------------
% 1.58/1.31 % (16829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (16829)Termination reason: Unknown
% 1.58/1.31 % (16829)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (16829)Memory used [KB]: 5500
% 1.58/1.31 % (16829)Time elapsed: 0.004 s
% 1.58/1.31 % (16829)Instructions burned: 4 (million)
% 1.58/1.31 % (16829)------------------------------
% 1.58/1.31 % (16829)------------------------------
% 1.58/1.31 % (16828)First to succeed.
% 1.58/1.31 % (16830)Also succeeded, but the first one will report.
% 1.58/1.31 % (16828)Refutation found. Thanks to Tanya!
% 1.58/1.31 % SZS status Theorem for DTF2THF_16731
% 1.58/1.31 % SZS output start Proof for DTF2THF_16731
% 1.58/1.31 thf(type_def_5, type, frac: $tType).
% 1.58/1.31 thf(func_def_0, type, frac: $tType).
% 1.58/1.31 thf(func_def_1, type, x: frac).
% 1.58/1.31 thf(func_def_2, type, y: frac).
% 1.58/1.31 thf(func_def_3, type, z: frac).
% 1.58/1.31 thf(func_def_4, type, moref: frac > frac > $o).
% 1.58/1.31 thf(func_def_5, type, pf: frac > frac > frac).
% 1.58/1.31 thf(func_def_7, type, eq: frac > frac > $o).
% 1.58/1.31 thf(func_def_8, type, lessf: frac > frac > $o).
% 1.58/1.31 thf(f62,plain,(
% 1.58/1.31 $false),
% 1.58/1.31 inference(subsumption_resolution,[status(thm)],[f61,f52])).
% 1.58/1.31 thf(f52,plain,(
% 1.58/1.31 ($true != (eq @ x @ y))),
% 1.58/1.31 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.58/1.31 thf(f51,plain,(
% 1.58/1.31 ($true != $true) | ($true != (eq @ x @ y))),
% 1.58/1.31 inference(superposition,[status(thm)],[f48,f38])).
% 1.58/1.31 thf(f38,plain,(
% 1.58/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (eq @ (pf @ X1 @ X0) @ (pf @ X2 @ X0))) | ((eq @ X1 @ X2) != $true)) )),
% 1.58/1.31 inference(cnf_transformation,[status(thm)],[f35])).
% 1.58/1.31 thf(f35,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : (($true = (eq @ (pf @ X1 @ X0) @ (pf @ X2 @ X0))) | ((eq @ X1 @ X2) != $true))),
% 1.58/1.31 inference(rectify,[status(thm)],[f29])).
% 1.58/1.31 thf(f29,plain,(
% 1.58/1.31 ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) | ((eq @ X0 @ X1) != $true))),
% 1.58/1.31 inference(ennf_transformation,[status(thm)],[f21])).
% 1.58/1.31 thf(f21,plain,(
% 1.58/1.31 ! [X0 : frac,X2 : frac,X1 : frac] : (((eq @ X0 @ X1) = $true) => ($true = (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))))),
% 1.58/1.31 inference(fool_elimination,[status(thm)],[f20])).
% 1.58/1.31 thf(f20,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X1) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 1.58/1.31 inference(rectify,[status(thm)],[f4])).
% 1.58/1.31 thf(f4,axiom,(
% 1.58/1.31 ! [X1 : frac,X2 : frac,X3 : frac] : ((eq @ X1 @ X2) => (eq @ (pf @ X1 @ X3) @ (pf @ X2 @ X3)))),
% 1.58/1.31 file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz62b)).
% 1.58/1.31 thf(f48,plain,(
% 1.58/1.31 ($true != (eq @ (pf @ x @ z) @ (pf @ y @ z)))),
% 1.58/1.31 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.58/1.31 thf(f47,plain,(
% 1.58/1.31 ($true != (eq @ (pf @ x @ z) @ (pf @ y @ z))) | ($true != $true)),
% 1.58/1.31 inference(superposition,[status(thm)],[f39,f42])).
% 1.58/1.31 thf(f42,plain,(
% 1.58/1.31 ((moref @ (pf @ x @ z) @ (pf @ y @ z)) = $true)),
% 1.58/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.58/1.31 thf(f23,plain,(
% 1.58/1.31 ((moref @ (pf @ x @ z) @ (pf @ y @ z)) = $true)),
% 1.58/1.31 inference(fool_elimination,[status(thm)],[f22])).
% 1.58/1.31 thf(f22,plain,(
% 1.58/1.31 (moref @ (pf @ x @ z) @ (pf @ y @ z))),
% 1.58/1.31 inference(rectify,[status(thm)],[f1])).
% 1.58/1.31 thf(f1,axiom,(
% 1.58/1.31 (moref @ (pf @ x @ z) @ (pf @ y @ z))),
% 1.58/1.31 file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',m)).
% 1.58/1.31 thf(f39,plain,(
% 1.58/1.31 ( ! [X0 : frac,X1 : frac] : (($true != (moref @ X0 @ X1)) | ((eq @ X0 @ X1) != $true)) )),
% 1.58/1.31 inference(cnf_transformation,[status(thm)],[f36])).
% 1.58/1.31 thf(f36,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : ((($true != (lessf @ X0 @ X1)) | ($true != (moref @ X0 @ X1))) & (((eq @ X0 @ X1) != $true) | ($true != (lessf @ X0 @ X1))) & (($true != (moref @ X0 @ X1)) | ((eq @ X0 @ X1) != $true)))),
% 1.58/1.31 inference(rectify,[status(thm)],[f32])).
% 1.58/1.31 thf(f32,plain,(
% 1.58/1.31 ! [X1 : frac,X0 : frac] : ((($true != (lessf @ X1 @ X0)) | ($true != (moref @ X1 @ X0))) & (($true != (eq @ X1 @ X0)) | ($true != (lessf @ X1 @ X0))) & (($true != (moref @ X1 @ X0)) | ($true != (eq @ X1 @ X0))))),
% 1.58/1.31 inference(flattening,[status(thm)],[f31])).
% 1.58/1.31 thf(f31,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : (((($true != (eq @ X1 @ X0)) | ($true != (lessf @ X1 @ X0))) & (($true != (lessf @ X1 @ X0)) | ($true != (moref @ X1 @ X0)))) & (($true != (moref @ X1 @ X0)) | ($true != (eq @ X1 @ X0))))),
% 1.58/1.31 inference(ennf_transformation,[status(thm)],[f26])).
% 1.58/1.31 thf(f26,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : ~((($true = (eq @ X1 @ X0)) => ($true != (moref @ X1 @ X0))) => ((($true = (moref @ X1 @ X0)) => ($true != (lessf @ X1 @ X0))) => ~(($true = (lessf @ X1 @ X0)) => ($true != (eq @ X1 @ X0)))))),
% 1.58/1.31 inference(flattening,[status(thm)],[f17])).
% 1.58/1.31 thf(f17,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : ~((($true = (eq @ X1 @ X0)) => ~($true = (moref @ X1 @ X0))) => ~~((($true = (moref @ X1 @ X0)) => ~($true = (lessf @ X1 @ X0))) => ~(($true = (lessf @ X1 @ X0)) => ~($true = (eq @ X1 @ X0)))))),
% 1.58/1.31 inference(fool_elimination,[status(thm)],[f16])).
% 1.58/1.31 thf(f16,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : ~(((eq @ X1 @ X0) => ~(moref @ X1 @ X0)) => ~~(((moref @ X1 @ X0) => ~(lessf @ X1 @ X0)) => ~((lessf @ X1 @ X0) => ~(eq @ X1 @ X0))))),
% 1.58/1.31 inference(rectify,[status(thm)],[f3])).
% 1.58/1.31 thf(f3,axiom,(
% 1.58/1.31 ! [X2 : frac,X1 : frac] : ~(((eq @ X1 @ X2) => ~(moref @ X1 @ X2)) => ~~(((moref @ X1 @ X2) => ~(lessf @ X1 @ X2)) => ~((lessf @ X1 @ X2) => ~(eq @ X1 @ X2))))),
% 1.58/1.31 file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz41b)).
% 1.58/1.31 thf(f61,plain,(
% 1.58/1.31 ($true = (eq @ x @ y))),
% 1.58/1.31 inference(subsumption_resolution,[status(thm)],[f60,f37])).
% 1.58/1.31 thf(f37,plain,(
% 1.58/1.31 ((moref @ x @ y) != $true)),
% 1.58/1.31 inference(cnf_transformation,[status(thm)],[f24])).
% 1.58/1.31 thf(f24,plain,(
% 1.58/1.31 ((moref @ x @ y) != $true)),
% 1.58/1.31 inference(flattening,[status(thm)],[f11])).
% 1.58/1.31 thf(f11,plain,(
% 1.58/1.31 ~((moref @ x @ y) = $true)),
% 1.58/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.58/1.31 thf(f10,plain,(
% 1.58/1.31 ~(moref @ x @ y)),
% 1.58/1.31 inference(rectify,[status(thm)],[f8])).
% 1.58/1.31 thf(f8,negated_conjecture,(
% 1.58/1.31 ~(moref @ x @ y)),
% 1.58/1.31 inference(negated_conjecture,[status(cth)],[f7])).
% 1.58/1.31 thf(f7,conjecture,(
% 1.58/1.31 (moref @ x @ y)),
% 1.58/1.31 file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz63a)).
% 1.58/1.31 thf(f60,plain,(
% 1.58/1.31 ((moref @ x @ y) = $true) | ($true = (eq @ x @ y))),
% 1.58/1.31 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.58/1.31 thf(f59,plain,(
% 1.58/1.31 ($true = (eq @ x @ y)) | ((moref @ x @ y) = $true) | ($true != $true)),
% 1.58/1.31 inference(superposition,[status(thm)],[f58,f43])).
% 1.58/1.31 thf(f43,plain,(
% 1.58/1.31 ( ! [X0 : frac,X1 : frac] : (($true = (lessf @ X1 @ X0)) | ($true = (eq @ X1 @ X0)) | ($true = (moref @ X1 @ X0))) )),
% 1.58/1.31 inference(cnf_transformation,[status(thm)],[f34])).
% 1.58/1.31 thf(f34,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : (($true = (eq @ X1 @ X0)) | ($true = (lessf @ X1 @ X0)) | ($true = (moref @ X1 @ X0)))),
% 1.58/1.31 inference(flattening,[status(thm)],[f33])).
% 1.58/1.31 thf(f33,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : ((($true = (lessf @ X1 @ X0)) | ($true = (moref @ X1 @ X0))) | ($true = (eq @ X1 @ X0)))),
% 1.58/1.31 inference(ennf_transformation,[status(thm)],[f27])).
% 1.58/1.31 thf(f27,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : (($true != (eq @ X1 @ X0)) => (($true != (moref @ X1 @ X0)) => ($true = (lessf @ X1 @ X0))))),
% 1.58/1.31 inference(flattening,[status(thm)],[f19])).
% 1.58/1.31 thf(f19,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : (~($true = (eq @ X1 @ X0)) => (~($true = (moref @ X1 @ X0)) => ($true = (lessf @ X1 @ X0))))),
% 1.58/1.31 inference(fool_elimination,[status(thm)],[f18])).
% 1.58/1.31 thf(f18,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac] : (~(eq @ X1 @ X0) => (~(moref @ X1 @ X0) => (lessf @ X1 @ X0)))),
% 1.58/1.31 inference(rectify,[status(thm)],[f6])).
% 1.58/1.31 thf(f6,axiom,(
% 1.58/1.31 ! [X2 : frac,X1 : frac] : (~(eq @ X1 @ X2) => (~(moref @ X1 @ X2) => (lessf @ X1 @ X2)))),
% 1.58/1.31 file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz41a)).
% 1.58/1.31 thf(f58,plain,(
% 1.58/1.31 ((lessf @ x @ y) != $true)),
% 1.58/1.31 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.58/1.31 thf(f57,plain,(
% 1.58/1.31 ((lessf @ x @ y) != $true) | ($true != $true)),
% 1.58/1.31 inference(superposition,[status(thm)],[f55,f42])).
% 1.58/1.31 thf(f55,plain,(
% 1.58/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((moref @ (pf @ X0 @ X1) @ (pf @ X2 @ X1)) != $true) | ($true != (lessf @ X0 @ X2))) )),
% 1.58/1.31 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.58/1.31 thf(f53,plain,(
% 1.58/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ((moref @ (pf @ X0 @ X1) @ (pf @ X2 @ X1)) != $true) | ($true != (lessf @ X0 @ X2))) )),
% 1.58/1.31 inference(superposition,[status(thm)],[f41,f45])).
% 1.58/1.31 thf(f45,plain,(
% 1.58/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (lessf @ (pf @ X1 @ X0) @ (pf @ X2 @ X0))) | ((lessf @ X1 @ X2) != $true)) )),
% 1.58/1.31 inference(cnf_transformation,[status(thm)],[f30])).
% 1.58/1.31 thf(f30,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : (((lessf @ X1 @ X2) != $true) | ($true = (lessf @ (pf @ X1 @ X0) @ (pf @ X2 @ X0))))),
% 1.58/1.31 inference(ennf_transformation,[status(thm)],[f13])).
% 1.58/1.31 thf(f13,plain,(
% 1.58/1.31 ! [X2 : frac,X1 : frac,X0 : frac] : (((lessf @ X1 @ X2) = $true) => ($true = (lessf @ (pf @ X1 @ X0) @ (pf @ X2 @ X0))))),
% 1.58/1.31 inference(fool_elimination,[status(thm)],[f12])).
% 1.58/1.31 thf(f12,plain,(
% 1.58/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X1 @ X2) => (lessf @ (pf @ X1 @ X0) @ (pf @ X2 @ X0)))),
% 1.58/1.31 inference(rectify,[status(thm)],[f5])).
% 1.58/1.31 thf(f5,axiom,(
% 1.58/1.31 ! [X3 : frac,X1 : frac,X2 : frac] : ((lessf @ X1 @ X2) => (lessf @ (pf @ X1 @ X3) @ (pf @ X2 @ X3)))),
% 1.58/1.31 file('/export/starexec/sandbox/tmp/tmp.RukBcwaqMu/DTF2THF_16731.p',satz62c)).
% 1.58/1.31 thf(f41,plain,(
% 1.58/1.31 ( ! [X0 : frac,X1 : frac] : (($true != (lessf @ X0 @ X1)) | ($true != (moref @ X0 @ X1))) )),
% 1.58/1.31 inference(cnf_transformation,[status(thm)],[f36])).
% 1.58/1.31 % SZS output end Proof for DTF2THF_16731
% 1.58/1.31 % (16828)------------------------------
% 1.58/1.31 % (16828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (16828)Termination reason: Refutation
% 1.58/1.31
% 1.58/1.31 % (16828)Memory used [KB]: 5500
% 1.58/1.31 % (16828)Time elapsed: 0.007 s
% 1.58/1.31 % (16828)Instructions burned: 5 (million)
% 1.58/1.31 % (16828)------------------------------
% 1.58/1.31 % (16828)------------------------------
% 1.58/1.31 % (16827)Success in time 0.021 s
%------------------------------------------------------------------------------