%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM753^1 : 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 : n028.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 09:24:33 AM UTC 2026
% Result : Theorem 1.54s 1.26s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 277 ( 83 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 430 ( 59 ~; 43 |; 0 &; 310 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 91 ( 0 ^; 91 !; 0 ?; 91 :)
% 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,
u: frac ).
thf(func_def_5,type,
eq: frac > frac > $o ).
thf(func_def_7,type,
moref: frac > frac > $o ).
thf(func_def_8,type,
pf: frac > frac > frac ).
thf(f86,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f85,f38]) ).
thf(f38,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: frac] : ( eq @ X0 @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz37) ).
thf(f85,plain,
( ( eq @ u @ u )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $true != $true )
| ( ( eq @ u @ u )
!= $true ) ),
inference(superposition,[status(thm)],[f58,f34]) ).
thf(f34,plain,
( ( moref @ z @ u )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( moref @ z @ u )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
moref @ z @ u,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
moref @ z @ u,
file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',m) ).
thf(f58,plain,
! [X0: frac] :
( ( $true
!= ( moref @ z @ X0 ) )
| ( ( eq @ X0 @ u )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f56,f33]) ).
thf(f33,plain,
( ( eq @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( eq @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
eq @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
eq @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',e) ).
thf(f56,plain,
! [X0: frac] :
( ( ( eq @ x @ y )
!= $true )
| ( $true
!= ( moref @ z @ X0 ) )
| ( ( eq @ X0 @ u )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: frac] :
( ( $true
!= ( moref @ z @ X0 ) )
| ( ( eq @ X0 @ u )
!= $true )
| ( $true != $true )
| ( ( eq @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f48,f35]) ).
thf(f35,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ ( pf @ X2 @ X1 ) @ ( pf @ X2 @ X0 ) ) )
| ( ( moref @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( moref @ X1 @ X0 )
!= $true )
| ( $true
= ( moref @ ( pf @ X2 @ X1 ) @ ( pf @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( moref @ X0 @ X2 )
!= $true )
| ( $true
= ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( ( moref @ X0 @ X2 )
= $true )
=> ( $true
= ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X0 @ X2 )
=> ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: frac,X2: frac,X1: frac] :
( ( moref @ X0 @ X1 )
=> ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz62d) ).
thf(f48,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ ( pf @ x @ z ) @ ( pf @ X0 @ X1 ) )
!= $true )
| ( $true
!= ( eq @ X1 @ u ) )
| ( $true
!= ( eq @ X0 @ y ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X1 @ u ) )
| ( $true != $true )
| ( $true
!= ( eq @ X0 @ y ) )
| ( ( moref @ ( pf @ x @ z ) @ ( pf @ X0 @ X1 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f45,f39]) ).
thf(f39,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true )
| ( ( eq @ X2 @ X3 )
!= $true ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( eq @ X2 @ X3 )
!= $true )
| ( $true
= ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X3 @ X1 ) ) )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: frac,X3: frac,X1: frac,X2: frac] :
( ( $true
= ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X3 @ X1 ) ) )
| ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X2 @ X3 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: frac,X3: frac,X1: frac,X2: frac] :
( ( ( eq @ X2 @ X3 )
= $true )
=> ( ( ( eq @ X0 @ X1 )
= $true )
=> ( $true
= ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X3 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ X2 @ X3 )
=> ( ( eq @ X0 @ X1 )
=> ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X3 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz56) ).
thf(f45,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ ( pf @ y @ u ) ) )
| ( ( moref @ ( pf @ x @ z ) @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: frac] :
( ( $true != $true )
| ( ( moref @ ( pf @ x @ z ) @ X0 )
!= $true )
| ( $true
!= ( eq @ X0 @ ( pf @ y @ u ) ) ) ),
inference(superposition,[status(thm)],[f41,f38]) ).
thf(f41,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ ( pf @ x @ z ) ) )
| ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ ( pf @ y @ u ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ ( pf @ x @ z ) ) )
| ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ ( pf @ y @ u ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f37,f36]) ).
thf(f36,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ X1 @ X2 ) )
| ( $true
!= ( moref @ X3 @ X0 ) )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( $true
!= ( eq @ X3 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ X0 @ X2 )
!= $true )
| ( $true
= ( moref @ X1 @ X2 ) )
| ( $true
!= ( eq @ X3 @ X1 ) )
| ( $true
!= ( moref @ X3 @ X0 ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
! [X3: frac,X0: frac,X1: frac,X2: frac] :
( ( $true
!= ( eq @ X3 @ X1 ) )
| ( ( moref @ X0 @ X1 )
= $true )
| ( $true
!= ( eq @ X2 @ X0 ) )
| ( ( moref @ X2 @ X3 )
!= $true ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: frac,X1: frac,X0: frac,X3: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
| ( $true
!= ( eq @ X3 @ X1 ) )
| ( $true
!= ( eq @ X2 @ X0 ) )
| ( ( moref @ X2 @ X3 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: frac,X1: frac,X0: frac,X3: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
=> ( ( $true
= ( eq @ X2 @ X0 ) )
=> ( ( $true
= ( eq @ X3 @ X1 ) )
=> ( ( moref @ X0 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X2 @ X3 )
=> ( ( eq @ X2 @ X0 )
=> ( ( eq @ X3 @ X1 )
=> ( moref @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz44) ).
thf(f37,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz62g) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM753^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:13:42 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : NUM753^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Number Theory
% 0.29/0.46 % Problem : Landau theorem 62g
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : moref (pf x z) (pf y u)
% 0.29/0.46
% 0.29/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.29/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : satz62g [Lan30]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % : Without extensionality : Theorem
% 0.29/0.46 % Rating : 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.2.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 15 ( 4 unt; 8 typ; 0 def)
% 0.29/0.46 % Number of atoms : 13 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.29/0.46 % Number of connectives : 44 ( 0 ~; 0 |; 0 &; 38 @)
% 0.29/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 11 ( 6 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 7 ( 7 usr; 4 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(frac_type,type,
% 0.29/0.46 frac: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(x,type,
% 0.29/0.46 x: frac ).
% 0.29/0.46
% 0.29/0.46 thf(y,type,
% 0.29/0.46 y: frac ).
% 0.29/0.46
% 0.29/0.46 thf(z,type,
% 0.29/0.46 z: frac ).
% 0.29/0.46
% 0.29/0.46 thf(u,type,
% 0.29/0.46 u: frac ).
% 0.29/0.46
% 0.29/0.46 thf(eq,type,
% 0.29/0.46 eq: frac > frac > $o ).
% 0.29/0.46
% 0.29/0.46 thf(e,axiom,
% 0.29/0.46 eq @ x @ y ).
% 0.29/0.46
% 0.29/0.46 thf(moref,type,
% 0.29/0.46 moref: frac > frac > $o ).
% 0.29/0.46
% 0.29/0.46 thf(m,axiom,
% 0.29/0.46 moref @ z @ u ).
% 0.29/0.46
% 0.29/0.46 thf(pf,type,
% 0.29/0.46 pf: frac > frac > frac ).
% 0.29/0.46
% 0.29/0.46 thf(satz44,axiom,
% 0.29/0.46 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.29/0.46 ( ( moref @ Xx @ Xy )
% 0.29/0.46 => ( ( eq @ Xx @ Xz )
% 0.29/0.46 => ( ( eq @ Xy @ Xu )
% 0.29/0.46 => ( moref @ Xz @ Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz62d,axiom,
% 0.29/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.29/0.46 ( ( moref @ Xx @ Xy )
% 0.29/0.46 => ( moref @ ( pf @ Xz @ Xx ) @ ( pf @ Xz @ Xy ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz37,axiom,
% 0.29/0.46 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz56,axiom,
% 0.29/0.46 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.29/0.46 ( ( eq @ Xx @ Xy )
% 0.29/0.46 => ( ( eq @ Xz @ Xu )
% 0.29/0.46 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz62g,conjecture,
% 0.29/0.46 moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.54/1.23 ---- Embedded in THF ---
% 1.54/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.23 %%% Generated on Tue Feb 24 11:13:42 EST 2026
% 1.54/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.23 %%% Logic specification used:
% 1.54/1.23 %%% thf(spec, logic, $$dhol).
% 1.54/1.23
% 1.54/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2DTF14539.p
% See solution above
% 1.54/1.23 ------------------------
% 1.54/1.24 ---- Cleaned THF ---
% 1.54/1.24 thf(frac_type,type,
% 1.54/1.24 frac: $tType ).
% 1.54/1.24
% 1.54/1.24 thf(x,type,
% 1.54/1.24 x: frac ).
% 1.54/1.24
% 1.54/1.24 thf(y,type,
% 1.54/1.24 y: frac ).
% 1.54/1.24
% 1.54/1.24 thf(z,type,
% 1.54/1.24 z: frac ).
% 1.54/1.24
% 1.54/1.24 thf(u,type,
% 1.54/1.24 u: frac ).
% 1.54/1.24
% 1.54/1.24 thf(eq,type,
% 1.54/1.24 eq: frac > frac > $o ).
% 1.54/1.24
% 1.54/1.24 thf(e,axiom,
% 1.54/1.24 eq @ x @ y ).
% 1.54/1.24
% 1.54/1.24 thf(moref,type,
% 1.54/1.24 moref: frac > frac > $o ).
% 1.54/1.24
% 1.54/1.24 thf(m,axiom,
% 1.54/1.24 moref @ z @ u ).
% 1.54/1.24
% 1.54/1.24 thf(pf,type,
% 1.54/1.24 pf: frac > frac > frac ).
% 1.54/1.24
% 1.54/1.24 thf(satz44,axiom,
% 1.54/1.24 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.54/1.24 ( ( moref @ Xx @ Xy )
% 1.54/1.24 => ( ( eq @ Xx @ Xz )
% 1.54/1.24 => ( ( eq @ Xy @ Xu )
% 1.54/1.24 => ( moref @ Xz @ Xu ) ) ) ) ).
% 1.54/1.24
% 1.54/1.24 thf(satz62d,axiom,
% 1.54/1.24 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.54/1.24 ( ( moref @ Xx @ Xy )
% 1.54/1.24 => ( moref @ ( pf @ Xz @ Xx ) @ ( pf @ Xz @ Xy ) ) ) ).
% 1.54/1.24
% 1.54/1.24 thf(satz37,axiom,
% 1.54/1.24 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 1.54/1.24
% 1.54/1.24 thf(satz56,axiom,
% 1.54/1.24 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.54/1.24 ( ( eq @ Xx @ Xy )
% 1.54/1.24 => ( ( eq @ Xz @ Xu )
% 1.54/1.24 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 1.54/1.24
% 1.54/1.24 thf(satz62g,conjecture,
% 1.54/1.24 moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ).
% 1.54/1.24 ------------------------
% 1.54/1.25 % (14642)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14539 for (3000ds/18Mi)
% 1.54/1.25 % (14637)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_14539 for (3000ds/4Mi)
% 1.54/1.25 % (14641)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_14539 for (3000ds/275Mi)
% 1.54/1.25 % (14637)Instruction limit reached!
% 1.54/1.25 % (14637)------------------------------
% 1.54/1.25 % (14637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.25 % (14637)Termination reason: Unknown
% 1.54/1.25 % (14637)Termination phase: Saturation
% 1.54/1.25
% 1.54/1.25 % (14637)Memory used [KB]: 5500
% 1.54/1.25 % (14637)Time elapsed: 0.003 s
% 1.54/1.25 % (14637)Instructions burned: 6 (million)
% 1.54/1.25 % (14637)------------------------------
% 1.54/1.25 % (14637)------------------------------
% 1.54/1.26 % (14642)Instruction limit reached!
% 1.54/1.26 % (14642)------------------------------
% 1.54/1.26 % (14642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.26 % (14642)Termination reason: Unknown
% 1.54/1.26 % (14642)Termination phase: Saturation
% 1.54/1.26
% 1.54/1.26 % (14642)Memory used [KB]: 5628
% 1.54/1.26 % (14642)Time elapsed: 0.008 s
% 1.54/1.26 % (14642)Instructions burned: 18 (million)
% 1.54/1.26 % (14642)------------------------------
% 1.54/1.26 % (14642)------------------------------
% 1.54/1.26 % (14641)First to succeed.
% 1.54/1.26 % (14641)Refutation found. Thanks to Tanya!
% 1.54/1.26 % SZS status Theorem for DTF2THF_14539
% 1.54/1.26 % SZS output start Proof for DTF2THF_14539
% 1.54/1.26 thf(type_def_5, type, frac: $tType).
% 1.54/1.26 thf(func_def_0, type, frac: $tType).
% 1.54/1.26 thf(func_def_1, type, x: frac).
% 1.54/1.26 thf(func_def_2, type, y: frac).
% 1.54/1.26 thf(func_def_3, type, z: frac).
% 1.54/1.26 thf(func_def_4, type, u: frac).
% 1.54/1.26 thf(func_def_5, type, eq: frac > frac > $o).
% 1.54/1.26 thf(func_def_7, type, moref: frac > frac > $o).
% 1.54/1.26 thf(func_def_8, type, pf: frac > frac > frac).
% 1.54/1.26 thf(f86,plain,(
% 1.54/1.26 $false),
% 1.54/1.26 inference(subsumption_resolution,[status(thm)],[f85,f38])).
% 1.54/1.26 thf(f38,plain,(
% 1.54/1.26 ( ! [X0 : frac] : (((eq @ X0 @ X0) = $true)) )),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.54/1.26 thf(f13,plain,(
% 1.54/1.26 ! [X0 : frac] : ((eq @ X0 @ X0) = $true)),
% 1.54/1.26 inference(fool_elimination,[status(thm)],[f12])).
% 1.54/1.26 thf(f12,plain,(
% 1.54/1.26 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.54/1.26 inference(rectify,[status(thm)],[f5])).
% 1.54/1.26 thf(f5,axiom,(
% 1.54/1.26 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.54/1.26 file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz37)).
% 1.54/1.26 thf(f85,plain,(
% 1.54/1.26 ((eq @ u @ u) != $true)),
% 1.54/1.26 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.54/1.26 thf(f82,plain,(
% 1.54/1.26 ($true != $true) | ((eq @ u @ u) != $true)),
% 1.54/1.26 inference(superposition,[status(thm)],[f58,f34])).
% 1.54/1.26 thf(f34,plain,(
% 1.54/1.26 ((moref @ z @ u) = $true)),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f15])).
% 1.54/1.26 thf(f15,plain,(
% 1.54/1.26 ((moref @ z @ u) = $true)),
% 1.54/1.26 inference(fool_elimination,[status(thm)],[f14])).
% 1.54/1.26 thf(f14,plain,(
% 1.54/1.26 (moref @ z @ u)),
% 1.54/1.26 inference(rectify,[status(thm)],[f2])).
% 1.54/1.26 thf(f2,axiom,(
% 1.54/1.26 (moref @ z @ u)),
% 1.54/1.26 file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',m)).
% 1.54/1.26 thf(f58,plain,(
% 1.54/1.26 ( ! [X0 : frac] : (($true != (moref @ z @ X0)) | ((eq @ X0 @ u) != $true)) )),
% 1.54/1.26 inference(subsumption_resolution,[status(thm)],[f56,f33])).
% 1.54/1.26 thf(f33,plain,(
% 1.54/1.26 ((eq @ x @ y) = $true)),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f21])).
% 1.54/1.26 thf(f21,plain,(
% 1.54/1.26 ((eq @ x @ y) = $true)),
% 1.54/1.26 inference(fool_elimination,[status(thm)],[f20])).
% 1.54/1.26 thf(f20,plain,(
% 1.54/1.26 (eq @ x @ y)),
% 1.54/1.26 inference(rectify,[status(thm)],[f1])).
% 1.54/1.26 thf(f1,axiom,(
% 1.54/1.26 (eq @ x @ y)),
% 1.54/1.26 file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',e)).
% 1.54/1.26 thf(f56,plain,(
% 1.54/1.26 ( ! [X0 : frac] : (((eq @ x @ y) != $true) | ($true != (moref @ z @ X0)) | ((eq @ X0 @ u) != $true)) )),
% 1.54/1.26 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.54/1.26 thf(f54,plain,(
% 1.54/1.26 ( ! [X0 : frac] : (($true != (moref @ z @ X0)) | ((eq @ X0 @ u) != $true) | ($true != $true) | ((eq @ x @ y) != $true)) )),
% 1.54/1.26 inference(superposition,[status(thm)],[f48,f35])).
% 1.54/1.26 thf(f35,plain,(
% 1.54/1.26 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (moref @ (pf @ X2 @ X1) @ (pf @ X2 @ X0))) | ((moref @ X1 @ X0) != $true)) )),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f30])).
% 1.54/1.26 thf(f30,plain,(
% 1.54/1.26 ! [X0 : frac,X1 : frac,X2 : frac] : (((moref @ X1 @ X0) != $true) | ($true = (moref @ (pf @ X2 @ X1) @ (pf @ X2 @ X0))))),
% 1.54/1.26 inference(rectify,[status(thm)],[f27])).
% 1.54/1.26 thf(f27,plain,(
% 1.54/1.26 ! [X2 : frac,X0 : frac,X1 : frac] : (((moref @ X0 @ X2) != $true) | ($true = (moref @ (pf @ X1 @ X0) @ (pf @ X1 @ X2))))),
% 1.54/1.26 inference(ennf_transformation,[status(thm)],[f19])).
% 1.54/1.26 thf(f19,plain,(
% 1.54/1.26 ! [X0 : frac,X2 : frac,X1 : frac] : (((moref @ X0 @ X2) = $true) => ($true = (moref @ (pf @ X1 @ X0) @ (pf @ X1 @ X2))))),
% 1.54/1.26 inference(fool_elimination,[status(thm)],[f18])).
% 1.54/1.26 thf(f18,plain,(
% 1.54/1.26 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X0 @ X2) => (moref @ (pf @ X1 @ X0) @ (pf @ X1 @ X2)))),
% 1.54/1.26 inference(rectify,[status(thm)],[f4])).
% 1.54/1.26 thf(f4,axiom,(
% 1.54/1.26 ! [X0 : frac,X2 : frac,X1 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X2 @ X0) @ (pf @ X2 @ X1)))),
% 1.54/1.26 file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz62d)).
% 1.54/1.26 thf(f48,plain,(
% 1.54/1.26 ( ! [X0 : frac,X1 : frac] : (((moref @ (pf @ x @ z) @ (pf @ X0 @ X1)) != $true) | ($true != (eq @ X1 @ u)) | ($true != (eq @ X0 @ y))) )),
% 1.54/1.26 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.54/1.26 thf(f46,plain,(
% 1.54/1.26 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ X1 @ u)) | ($true != $true) | ($true != (eq @ X0 @ y)) | ((moref @ (pf @ x @ z) @ (pf @ X0 @ X1)) != $true)) )),
% 1.54/1.26 inference(superposition,[status(thm)],[f45,f39])).
% 1.54/1.26 thf(f39,plain,(
% 1.54/1.26 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3)) = $true) | ((eq @ X0 @ X1) != $true) | ((eq @ X2 @ X3) != $true)) )),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f32])).
% 1.54/1.26 thf(f32,plain,(
% 1.54/1.26 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((eq @ X0 @ X1) != $true) | ((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3)) = $true) | ((eq @ X2 @ X3) != $true))),
% 1.54/1.26 inference(rectify,[status(thm)],[f26])).
% 1.54/1.26 thf(f26,plain,(
% 1.54/1.26 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((eq @ X2 @ X3) != $true) | ($true = (eq @ (pf @ X2 @ X0) @ (pf @ X3 @ X1))) | ((eq @ X0 @ X1) != $true))),
% 1.54/1.26 inference(flattening,[status(thm)],[f25])).
% 1.54/1.26 thf(f25,plain,(
% 1.54/1.26 ! [X0 : frac,X3 : frac,X1 : frac,X2 : frac] : ((($true = (eq @ (pf @ X2 @ X0) @ (pf @ X3 @ X1))) | ((eq @ X0 @ X1) != $true)) | ((eq @ X2 @ X3) != $true))),
% 1.54/1.26 inference(ennf_transformation,[status(thm)],[f23])).
% 1.54/1.26 thf(f23,plain,(
% 1.54/1.26 ! [X0 : frac,X3 : frac,X1 : frac,X2 : frac] : (((eq @ X2 @ X3) = $true) => (((eq @ X0 @ X1) = $true) => ($true = (eq @ (pf @ X2 @ X0) @ (pf @ X3 @ X1)))))),
% 1.54/1.26 inference(fool_elimination,[status(thm)],[f22])).
% 1.54/1.26 thf(f22,plain,(
% 1.54/1.26 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X2 @ X3) => ((eq @ X0 @ X1) => (eq @ (pf @ X2 @ X0) @ (pf @ X3 @ X1))))),
% 1.54/1.26 inference(rectify,[status(thm)],[f6])).
% 1.54/1.26 thf(f6,axiom,(
% 1.54/1.26 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 1.54/1.26 file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz56)).
% 1.54/1.26 thf(f45,plain,(
% 1.54/1.26 ( ! [X0 : frac] : (($true != (eq @ X0 @ (pf @ y @ u))) | ((moref @ (pf @ x @ z) @ X0) != $true)) )),
% 1.54/1.26 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.54/1.26 thf(f43,plain,(
% 1.54/1.26 ( ! [X0 : frac] : (($true != $true) | ((moref @ (pf @ x @ z) @ X0) != $true) | ($true != (eq @ X0 @ (pf @ y @ u)))) )),
% 1.54/1.26 inference(superposition,[status(thm)],[f41,f38])).
% 1.54/1.26 thf(f41,plain,(
% 1.54/1.26 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ X0 @ (pf @ x @ z))) | ((moref @ X0 @ X1) != $true) | ((eq @ X1 @ (pf @ y @ u)) != $true)) )),
% 1.54/1.26 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.54/1.26 thf(f40,plain,(
% 1.54/1.26 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ X0 @ (pf @ x @ z))) | ((moref @ X0 @ X1) != $true) | ((eq @ X1 @ (pf @ y @ u)) != $true) | ($true != $true)) )),
% 1.54/1.26 inference(superposition,[status(thm)],[f37,f36])).
% 1.54/1.26 thf(f36,plain,(
% 1.54/1.26 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true = (moref @ X1 @ X2)) | ($true != (moref @ X3 @ X0)) | ((eq @ X0 @ X2) != $true) | ($true != (eq @ X3 @ X1))) )),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f31])).
% 1.54/1.26 thf(f31,plain,(
% 1.54/1.26 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((eq @ X0 @ X2) != $true) | ($true = (moref @ X1 @ X2)) | ($true != (eq @ X3 @ X1)) | ($true != (moref @ X3 @ X0)))),
% 1.54/1.26 inference(rectify,[status(thm)],[f29])).
% 1.54/1.26 thf(f29,plain,(
% 1.54/1.26 ! [X3 : frac,X0 : frac,X1 : frac,X2 : frac] : (($true != (eq @ X3 @ X1)) | ((moref @ X0 @ X1) = $true) | ($true != (eq @ X2 @ X0)) | ((moref @ X2 @ X3) != $true))),
% 1.54/1.26 inference(flattening,[status(thm)],[f28])).
% 1.54/1.26 thf(f28,plain,(
% 1.54/1.26 ! [X2 : frac,X1 : frac,X0 : frac,X3 : frac] : (((((moref @ X0 @ X1) = $true) | ($true != (eq @ X3 @ X1))) | ($true != (eq @ X2 @ X0))) | ((moref @ X2 @ X3) != $true))),
% 1.54/1.26 inference(ennf_transformation,[status(thm)],[f17])).
% 1.54/1.26 thf(f17,plain,(
% 1.54/1.26 ! [X2 : frac,X1 : frac,X0 : frac,X3 : frac] : (((moref @ X2 @ X3) = $true) => (($true = (eq @ X2 @ X0)) => (($true = (eq @ X3 @ X1)) => ((moref @ X0 @ X1) = $true))))),
% 1.54/1.26 inference(fool_elimination,[status(thm)],[f16])).
% 1.54/1.26 thf(f16,plain,(
% 1.54/1.26 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X2 @ X3) => ((eq @ X2 @ X0) => ((eq @ X3 @ X1) => (moref @ X0 @ X1))))),
% 1.54/1.26 inference(rectify,[status(thm)],[f3])).
% 1.54/1.26 thf(f3,axiom,(
% 1.54/1.26 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 1.54/1.26 file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz44)).
% 1.54/1.26 thf(f37,plain,(
% 1.54/1.26 ((moref @ (pf @ x @ z) @ (pf @ y @ u)) != $true)),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f24])).
% 1.54/1.26 thf(f24,plain,(
% 1.54/1.26 ((moref @ (pf @ x @ z) @ (pf @ y @ u)) != $true)),
% 1.54/1.26 inference(flattening,[status(thm)],[f11])).
% 1.54/1.26 thf(f11,plain,(
% 1.54/1.26 ~((moref @ (pf @ x @ z) @ (pf @ y @ u)) = $true)),
% 1.54/1.26 inference(fool_elimination,[status(thm)],[f10])).
% 1.54/1.26 thf(f10,plain,(
% 1.54/1.26 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 1.54/1.26 inference(rectify,[status(thm)],[f8])).
% 1.54/1.26 thf(f8,negated_conjecture,(
% 1.54/1.26 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 1.54/1.26 inference(negated_conjecture,[status(cth)],[f7])).
% 1.54/1.26 thf(f7,conjecture,(
% 1.54/1.26 (moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 1.54/1.26 file('/export/starexec/sandbox/tmp/tmp.ayfY2NNCjO/DTF2THF_14539.p',satz62g)).
% 1.54/1.26 % SZS output end Proof for DTF2THF_14539
% 1.54/1.26 % (14641)------------------------------
% 1.54/1.26 % (14641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.26 % (14641)Termination reason: Refutation
% 1.54/1.26
% 1.54/1.26 % (14641)Memory used [KB]: 5500
% 1.54/1.26 % (14641)Time elapsed: 0.008 s
% 1.54/1.26 % (14641)Instructions burned: 11 (million)
% 1.54/1.26 % (14641)------------------------------
% 1.54/1.26 % (14641)------------------------------
% 1.54/1.26 % (14635)Success in time 0.019 s
%------------------------------------------------------------------------------