%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM760^1 : 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 : n012.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 09:24:36 AM UTC 2026
% Result : Theorem 0.22s 1.35s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 70 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 396 ( 120 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 592 ( 86 ~; 62 |; 0 &; 420 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 121 ( 0 ^; 121 !; 0 ?; 121 :)
% 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,
moref: frac > frac > $o ).
thf(func_def_7,type,
pf: frac > frac > frac ).
thf(func_def_8,type,
lessf: frac > frac > $o ).
thf(func_def_9,type,
eq: frac > frac > $o ).
thf(f187,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f186,f50]) ).
thf(f50,plain,
( ( moref @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( moref @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
moref @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
moref @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',m) ).
thf(f186,plain,
( ( moref @ x @ y )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f183,f48]) ).
thf(f48,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/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',n) ).
thf(f183,plain,
( ( ( moref @ z @ u )
!= $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f180]) ).
thf(f180,plain,
( ( ( moref @ x @ y )
!= $true )
| ( $true != $true )
| ( ( moref @ z @ u )
!= $true ) ),
inference(superposition,[status(thm)],[f179,f46]) ).
thf(f46,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X2 ) )
= $true )
| ( ( moref @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( moref @ X1 @ X0 )
!= $true )
| ( ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X2 ) )
= $true ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: frac,X2: frac,X0: frac] :
( ( ( moref @ X2 @ X1 )
!= $true )
| ( ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( moref @ X2 @ X1 )
= $true )
=> ( ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X2 @ X1 )
=> ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X2: frac,X1: frac,X0: frac] :
( ( moref @ X0 @ X1 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz61) ).
thf(f179,plain,
! [X0: frac] :
( ( ( moref @ ( pf @ x @ X0 ) @ ( pf @ y @ u ) )
!= $true )
| ( ( moref @ z @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f178]) ).
thf(f178,plain,
! [X0: frac] :
( ( ( moref @ z @ X0 )
!= $true )
| ( ( moref @ ( pf @ x @ X0 ) @ ( pf @ y @ u ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f173,f47]) ).
thf(f47,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: frac,X1: frac] : ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X0: frac,X1: frac] : ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz58) ).
thf(f173,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X0 @ x ) @ X1 )
!= $true )
| ( ( moref @ X1 @ ( pf @ y @ u ) )
!= $true )
| ( ( moref @ z @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f168]) ).
thf(f168,plain,
! [X0: frac,X1: frac] :
( ( $true != $true )
| ( ( moref @ X1 @ ( pf @ y @ u ) )
!= $true )
| ( ( moref @ z @ X0 )
!= $true )
| ( ( eq @ ( pf @ X0 @ x ) @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f167,f46]) ).
thf(f167,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ ( pf @ z @ x ) @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
!= $true )
| ( ( moref @ X0 @ ( pf @ y @ u ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ ( pf @ y @ u ) )
!= $true )
| ( $true != $true )
| ( ( moref @ ( pf @ z @ x ) @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f71,f47]) ).
thf(f71,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X1 @ ( pf @ x @ z ) )
!= $true )
| ( ( moref @ X0 @ ( pf @ y @ u ) )
!= $true )
| ( ( moref @ X1 @ X2 )
!= $true )
| ( ( eq @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X1 @ ( pf @ x @ z ) )
!= $true )
| ( ( moref @ X0 @ ( pf @ y @ u ) )
!= $true )
| ( ( eq @ X2 @ X0 )
!= $true )
| ( $true != $true )
| ( ( moref @ X1 @ X2 )
!= $true ) ),
inference(superposition,[status(thm)],[f66,f43]) ).
thf(f43,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ X1 @ X0 )
= $true )
| ( ( moref @ X3 @ X2 )
!= $true )
| ( ( eq @ X2 @ X0 )
!= $true )
| ( ( eq @ X3 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X3 @ X2 )
!= $true )
| ( ( eq @ X2 @ X0 )
!= $true )
| ( ( moref @ X1 @ X0 )
= $true )
| ( ( eq @ X3 @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,plain,
! [X3: frac,X2: frac,X1: frac,X0: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X0 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: frac,X1: frac,X0: frac,X3: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: frac,X1: frac,X0: frac,X3: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( ( eq @ X0 @ X2 )
= $true )
=> ( ( ( eq @ X1 @ X3 )
= $true )
=> ( ( moref @ X2 @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz44) ).
thf(f66,plain,
! [X0: frac] :
( ( ( moref @ ( pf @ x @ z ) @ X0 )
!= $true )
| ( ( moref @ X0 @ ( pf @ y @ u ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X0: frac] :
( ( $true != $true )
| ( ( moref @ X0 @ ( pf @ y @ u ) )
!= $true )
| ( ( moref @ ( pf @ x @ z ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f62,f45]) ).
thf(f45,plain,
! [X0: frac,X1: frac] :
( ( ( lessf @ X1 @ X0 )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( lessf @ X1 @ X0 )
= $true ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: frac,X0: frac] :
( ( ( moref @ X1 @ X0 )
!= $true )
| ( ( lessf @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: frac,X0: frac] :
( ( ( moref @ X1 @ X0 )
= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac] :
( ( moref @ X1 @ X0 )
=> ( lessf @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: frac,X0: frac] :
( ( moref @ X0 @ X1 )
=> ( lessf @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz42) ).
thf(f62,plain,
! [X0: frac] :
( ( ( lessf @ X0 @ ( pf @ x @ z ) )
!= $true )
| ( ( moref @ X0 @ ( pf @ y @ u ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X0: frac] :
( ( $true != $true )
| ( ( lessf @ X0 @ ( pf @ x @ z ) )
!= $true )
| ( ( moref @ X0 @ ( pf @ y @ u ) )
!= $true ) ),
inference(superposition,[status(thm)],[f57,f45]) ).
thf(f57,plain,
! [X0: frac] :
( ( ( lessf @ ( pf @ y @ u ) @ X0 )
!= $true )
| ( ( lessf @ X0 @ ( pf @ x @ z ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: frac] :
( ( $true != $true )
| ( ( lessf @ X0 @ ( pf @ x @ z ) )
!= $true )
| ( ( lessf @ ( pf @ y @ u ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f53,f51]) ).
thf(f51,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( lessf @ X1 @ X2 )
= $true )
| ( ( lessf @ X0 @ X2 )
!= $true )
| ( ( lessf @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X1 @ X2 )
= $true )
| ( ( lessf @ X0 @ X2 )
!= $true )
| ( ( lessf @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: frac,X2: frac,X0: frac] :
( ( ( lessf @ X2 @ X0 )
= $true )
| ( ( lessf @ X1 @ X0 )
!= $true )
| ( ( lessf @ X2 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X2 @ X0 )
= $true )
| ( ( lessf @ X1 @ X0 )
!= $true )
| ( ( lessf @ X2 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X2 @ X1 )
= $true )
=> ( ( ( lessf @ X1 @ X0 )
= $true )
=> ( ( lessf @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X2 @ X1 )
=> ( ( lessf @ X1 @ X0 )
=> ( lessf @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: frac,X1: frac,X0: frac] :
( ( lessf @ X0 @ X1 )
=> ( ( lessf @ X1 @ X2 )
=> ( lessf @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz50) ).
thf(f53,plain,
( ( lessf @ ( pf @ y @ u ) @ ( pf @ x @ z ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( lessf @ ( pf @ y @ u ) @ ( pf @ x @ z ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f49,f44]) ).
thf(f44,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X1 @ X0 )
= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: frac,X1: frac] :
( ( ( lessf @ X0 @ X1 )
!= $true )
| ( ( moref @ X1 @ X0 )
= $true ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: frac,X0: frac] :
( ( ( lessf @ X1 @ X0 )
!= $true )
| ( ( moref @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: frac,X0: frac] :
( ( ( lessf @ X1 @ X0 )
= $true )
=> ( ( moref @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac] :
( ( lessf @ X1 @ X0 )
=> ( moref @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: frac,X0: frac] :
( ( lessf @ X0 @ X1 )
=> ( moref @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz43) ).
thf(f49,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f9,conjecture,
moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz64) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM760^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n012.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 11:13:15 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : NUM760^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Number Theory
% 0.16/0.39 % Problem : Landau theorem 64
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : moref (pf x z) (pf y u)
% 0.16/0.39
% 0.16/0.39 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.16/0.39 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.16/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : satz64 [Lan30]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % : Without extensionality : Theorem
% 0.16/0.39 % Rating : 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 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, 0.33 v6.2.0, 0.17 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, 0.33 v4.0.0, 0.67 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 18 ( 4 unt; 9 typ; 0 def)
% 0.16/0.39 % Number of atoms : 17 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 4 ( 1 avg)
% 0.16/0.39 % Number of connectives : 54 ( 0 ~; 0 |; 0 &; 46 @)
% 0.16/0.39 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 10 ( 6 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 8 ( 8 usr; 4 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments :
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(frac_type,type,
% 0.16/0.39 frac: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(x,type,
% 0.16/0.39 x: frac ).
% 0.16/0.39
% 0.16/0.39 thf(y,type,
% 0.16/0.39 y: frac ).
% 0.16/0.39
% 0.16/0.39 thf(z,type,
% 0.16/0.39 z: frac ).
% 0.16/0.39
% 0.16/0.39 thf(u,type,
% 0.16/0.39 u: frac ).
% 0.16/0.39
% 0.16/0.39 thf(moref,type,
% 0.16/0.39 moref: frac > frac > $o ).
% 0.16/0.39
% 0.16/0.39 thf(m,axiom,
% 0.16/0.39 moref @ x @ y ).
% 0.16/0.39
% 0.16/0.39 thf(n,axiom,
% 0.16/0.39 moref @ z @ u ).
% 0.16/0.39
% 0.16/0.39 thf(pf,type,
% 0.16/0.39 pf: frac > frac > frac ).
% 0.16/0.39
% 0.16/0.39 thf(lessf,type,
% 0.16/0.39 lessf: frac > frac > $o ).
% 0.16/0.39
% 0.16/0.39 thf(satz43,axiom,
% 0.16/0.39 ! [Xx: frac,Xy: frac] :
% 0.16/0.39 ( ( lessf @ Xx @ Xy )
% 0.16/0.39 => ( moref @ Xy @ Xx ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(satz50,axiom,
% 0.16/0.39 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.16/0.39 ( ( lessf @ Xx @ Xy )
% 0.16/0.39 => ( ( lessf @ Xy @ Xz )
% 0.16/0.39 => ( lessf @ Xx @ Xz ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(satz42,axiom,
% 0.16/0.39 ! [Xx: frac,Xy: frac] :
% 0.16/0.39 ( ( moref @ Xx @ Xy )
% 0.16/0.39 => ( lessf @ Xy @ Xx ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eq,type,
% 0.16/0.39 eq: frac > frac > $o ).
% 0.16/0.39
% 0.16/0.39 thf(satz44,axiom,
% 0.16/0.39 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.16/0.39 ( ( moref @ Xx @ Xy )
% 0.16/0.39 => ( ( eq @ Xx @ Xz )
% 0.16/0.39 => ( ( eq @ Xy @ Xu )
% 0.16/0.39 => ( moref @ Xz @ Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(satz61,axiom,
% 0.16/0.39 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.16/0.39 ( ( moref @ Xx @ Xy )
% 0.16/0.39 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(satz58,axiom,
% 0.16/0.39 ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(satz64,conjecture,
% 0.16/0.39 moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 0.22/1.30 ---- Embedded in THF ---
% 0.22/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.22/1.30 %%% Generated on Tue Feb 24 11:13:16 EST 2026
% 0.22/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.22/1.30 %%% Logic specification used:
% 0.22/1.30 %%% thf(spec, logic, $$dhol).
% 0.22/1.30
% 0.22/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2DTF25067.p
% See solution above
% 0.22/1.30 ------------------------
% 0.22/1.31 ---- Cleaned THF ---
% 0.22/1.31 thf(frac_type,type,
% 0.22/1.31 frac: $tType ).
% 0.22/1.31
% 0.22/1.31 thf(x,type,
% 0.22/1.31 x: frac ).
% 0.22/1.31
% 0.22/1.31 thf(y,type,
% 0.22/1.31 y: frac ).
% 0.22/1.31
% 0.22/1.31 thf(z,type,
% 0.22/1.31 z: frac ).
% 0.22/1.31
% 0.22/1.31 thf(u,type,
% 0.22/1.31 u: frac ).
% 0.22/1.31
% 0.22/1.31 thf(moref,type,
% 0.22/1.31 moref: frac > frac > $o ).
% 0.22/1.31
% 0.22/1.31 thf(m,axiom,
% 0.22/1.31 moref @ x @ y ).
% 0.22/1.31
% 0.22/1.31 thf(n,axiom,
% 0.22/1.31 moref @ z @ u ).
% 0.22/1.31
% 0.22/1.31 thf(pf,type,
% 0.22/1.31 pf: frac > frac > frac ).
% 0.22/1.31
% 0.22/1.31 thf(lessf,type,
% 0.22/1.31 lessf: frac > frac > $o ).
% 0.22/1.31
% 0.22/1.31 thf(satz43,axiom,
% 0.22/1.31 ! [Xx: frac,Xy: frac] :
% 0.22/1.31 ( ( lessf @ Xx @ Xy )
% 0.22/1.31 => ( moref @ Xy @ Xx ) ) ).
% 0.22/1.31
% 0.22/1.31 thf(satz50,axiom,
% 0.22/1.31 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.22/1.31 ( ( lessf @ Xx @ Xy )
% 0.22/1.31 => ( ( lessf @ Xy @ Xz )
% 0.22/1.31 => ( lessf @ Xx @ Xz ) ) ) ).
% 0.22/1.31
% 0.22/1.31 thf(satz42,axiom,
% 0.22/1.31 ! [Xx: frac,Xy: frac] :
% 0.22/1.31 ( ( moref @ Xx @ Xy )
% 0.22/1.31 => ( lessf @ Xy @ Xx ) ) ).
% 0.22/1.31
% 0.22/1.31 thf(eq,type,
% 0.22/1.31 eq: frac > frac > $o ).
% 0.22/1.31
% 0.22/1.31 thf(satz44,axiom,
% 0.22/1.31 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.22/1.31 ( ( moref @ Xx @ Xy )
% 0.22/1.31 => ( ( eq @ Xx @ Xz )
% 0.22/1.31 => ( ( eq @ Xy @ Xu )
% 0.22/1.31 => ( moref @ Xz @ Xu ) ) ) ) ).
% 0.22/1.31
% 0.22/1.31 thf(satz61,axiom,
% 0.22/1.31 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.22/1.31 ( ( moref @ Xx @ Xy )
% 0.22/1.31 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 0.22/1.31
% 0.22/1.31 thf(satz58,axiom,
% 0.22/1.31 ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) ).
% 0.22/1.31
% 0.22/1.31 thf(satz64,conjecture,
% 0.22/1.31 moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ).
% 0.22/1.31 ------------------------
% 0.22/1.33 % (25164)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25067 for (2999ds/183Mi)
% 0.22/1.33 % (25166)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_25067 for (2999ds/27Mi)
% 0.22/1.33 % (25165)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_25067 for (2999ds/4Mi)
% 0.22/1.33 % (25167)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25067 for (2999ds/2Mi)
% 0.22/1.33 % (25168)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_25067 for (2999ds/2Mi)
% 0.22/1.33 % (25169)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_25067 for (2999ds/275Mi)
% 0.22/1.33 % (25170)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25067 for (2999ds/18Mi)
% 0.22/1.33 % (25167)Instruction limit reached!
% 0.22/1.33 % (25167)------------------------------
% 0.22/1.33 % (25167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (25167)Termination reason: Unknown
% 0.22/1.33 % (25168)Instruction limit reached!
% 0.22/1.33 % (25168)------------------------------
% 0.22/1.33 % (25168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (25167)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (25167)Memory used [KB]: 5500
% 0.22/1.33 % (25167)Time elapsed: 0.003 s
% 0.22/1.33 % (25167)Instructions burned: 2 (million)
% 0.22/1.33 % (25167)------------------------------
% 0.22/1.33 % (25167)------------------------------
% 0.22/1.33 % (25168)Termination reason: Unknown
% 0.22/1.33 % (25168)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (25168)Memory used [KB]: 1023
% 0.22/1.33 % (25168)Time elapsed: 0.003 s
% 0.22/1.33 % (25168)Instructions burned: 3 (million)
% 0.22/1.33 % (25168)------------------------------
% 0.22/1.33 % (25168)------------------------------
% 0.22/1.33 % (25169)Refutation not found, incomplete strategy
% 0.22/1.33 % (25169)------------------------------
% 0.22/1.33 % (25169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (25169)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.33
% 0.22/1.33
% 0.22/1.33 % (25169)Memory used [KB]: 5500
% 0.22/1.33 % (25169)Time elapsed: 0.003 s
% 0.22/1.33 % (25169)Instructions burned: 2 (million)
% 0.22/1.33 % (25169)------------------------------
% 0.22/1.33 % (25169)------------------------------
% 0.22/1.33 % (25165)Instruction limit reached!
% 0.22/1.33 % (25165)------------------------------
% 0.22/1.33 % (25165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (25165)Termination reason: Unknown
% 0.22/1.33 % (25165)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (25165)Memory used [KB]: 5500
% 0.22/1.33 % (25165)Time elapsed: 0.004 s
% 0.22/1.33 % (25165)Instructions burned: 4 (million)
% 0.22/1.33 % (25165)------------------------------
% 0.22/1.33 % (25165)------------------------------
% 0.22/1.34 % (25170)Instruction limit reached!
% 0.22/1.34 % (25170)------------------------------
% 0.22/1.34 % (25170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.34 % (25170)Termination reason: Unknown
% 0.22/1.34 % (25170)Termination phase: Saturation
% 0.22/1.34
% 0.22/1.34 % (25170)Memory used [KB]: 5628
% 0.22/1.34 % (25170)Time elapsed: 0.012 s
% 0.22/1.34 % (25170)Instructions burned: 19 (million)
% 0.22/1.34 % (25170)------------------------------
% 0.22/1.34 % (25170)------------------------------
% 0.22/1.34 % (25166)Instruction limit reached!
% 0.22/1.34 % (25166)------------------------------
% 0.22/1.34 % (25166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.34 % (25166)Termination reason: Unknown
% 0.22/1.34 % (25166)Termination phase: Saturation
% 0.22/1.34
% 0.22/1.34 % (25166)Memory used [KB]: 5628
% 0.22/1.34 % (25166)Time elapsed: 0.017 s
% 0.22/1.34 % (25166)Instructions burned: 28 (million)
% 0.22/1.34 % (25166)------------------------------
% 0.22/1.34 % (25166)------------------------------
% 0.22/1.35 % (25171)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25067 for (2999ds/3Mi)
% 0.22/1.35 % (25172)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_25067 for (2999ds/37Mi)
% 0.22/1.35 % (25173)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_25067 for (2999ds/15Mi)
% 0.22/1.35 % (25174)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_25067 for (2999ds/3Mi)
% 0.22/1.35 % (25171)Instruction limit reached!
% 0.22/1.35 % (25171)------------------------------
% 0.22/1.35 % (25171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.35 % (25171)Termination reason: Unknown
% 0.22/1.35 % (25171)Termination phase: Saturation
% 0.22/1.35
% 0.22/1.35 % (25171)Memory used [KB]: 5500
% 0.22/1.35 % (25171)Time elapsed: 0.003 s
% 0.22/1.35 % (25171)Instructions burned: 3 (million)
% 0.22/1.35 % (25171)------------------------------
% 0.22/1.35 % (25171)------------------------------
% 0.22/1.35 % (25174)Instruction limit reached!
% 0.22/1.35 % (25174)------------------------------
% 0.22/1.35 % (25174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.35 % (25174)Termination reason: Unknown
% 0.22/1.35 % (25174)Termination phase: Saturation
% 0.22/1.35
% 0.22/1.35 % (25174)Memory used [KB]: 5500
% 0.22/1.35 % (25174)Time elapsed: 0.003 s
% 0.22/1.35 % (25164)First to succeed.
% 0.22/1.35 % (25174)Instructions burned: 3 (million)
% 0.22/1.35 % (25174)------------------------------
% 0.22/1.35 % (25174)------------------------------
% 0.22/1.35 % (25164)Refutation found. Thanks to Tanya!
% 0.22/1.35 % SZS status Theorem for DTF2THF_25067
% 0.22/1.35 % SZS output start Proof for DTF2THF_25067
% 0.22/1.35 thf(type_def_5, type, frac: $tType).
% 0.22/1.35 thf(func_def_0, type, frac: $tType).
% 0.22/1.35 thf(func_def_1, type, x: frac).
% 0.22/1.35 thf(func_def_2, type, y: frac).
% 0.22/1.35 thf(func_def_3, type, z: frac).
% 0.22/1.35 thf(func_def_4, type, u: frac).
% 0.22/1.35 thf(func_def_5, type, moref: frac > frac > $o).
% 0.22/1.35 thf(func_def_7, type, pf: frac > frac > frac).
% 0.22/1.35 thf(func_def_8, type, lessf: frac > frac > $o).
% 0.22/1.35 thf(func_def_9, type, eq: frac > frac > $o).
% 0.22/1.35 thf(f187,plain,(
% 0.22/1.35 $false),
% 0.22/1.35 inference(subsumption_resolution,[status(thm)],[f186,f50])).
% 0.22/1.35 thf(f50,plain,(
% 0.22/1.35 ((moref @ x @ y) = $true)),
% 0.22/1.35 inference(cnf_transformation,[status(thm)],[f21])).
% 0.22/1.35 thf(f21,plain,(
% 0.22/1.35 ((moref @ x @ y) = $true)),
% 0.22/1.35 inference(fool_elimination,[status(thm)],[f20])).
% 0.22/1.35 thf(f20,plain,(
% 0.22/1.35 (moref @ x @ y)),
% 0.22/1.35 inference(rectify,[status(thm)],[f1])).
% 0.22/1.35 thf(f1,axiom,(
% 0.22/1.35 (moref @ x @ y)),
% 0.22/1.35 file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',m)).
% 0.22/1.35 thf(f186,plain,(
% 0.22/1.35 ((moref @ x @ y) != $true)),
% 0.22/1.35 inference(subsumption_resolution,[status(thm)],[f183,f48])).
% 0.22/1.35 thf(f48,plain,(
% 0.22/1.35 ((moref @ z @ u) = $true)),
% 0.22/1.35 inference(cnf_transformation,[status(thm)],[f15])).
% 0.22/1.35 thf(f15,plain,(
% 0.22/1.35 ((moref @ z @ u) = $true)),
% 0.22/1.35 inference(fool_elimination,[status(thm)],[f14])).
% 0.22/1.35 thf(f14,plain,(
% 0.22/1.35 (moref @ z @ u)),
% 0.22/1.35 inference(rectify,[status(thm)],[f2])).
% 0.22/1.35 thf(f2,axiom,(
% 0.22/1.35 (moref @ z @ u)),
% 0.22/1.35 file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',n)).
% 0.22/1.35 thf(f183,plain,(
% 0.22/1.35 ((moref @ z @ u) != $true) | ((moref @ x @ y) != $true)),
% 0.22/1.35 inference(trivial_inequality_removal,[status(thm)],[f180])).
% 0.22/1.35 thf(f180,plain,(
% 0.22/1.35 ((moref @ x @ y) != $true) | ($true != $true) | ((moref @ z @ u) != $true)),
% 0.22/1.35 inference(superposition,[status(thm)],[f179,f46])).
% 0.22/1.35 thf(f46,plain,(
% 0.22/1.35 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((moref @ (pf @ X1 @ X2) @ (pf @ X0 @ X2)) = $true) | ((moref @ X1 @ X0) != $true)) )),
% 0.22/1.35 inference(cnf_transformation,[status(thm)],[f41])).
% 0.22/1.35 thf(f41,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac] : (((moref @ X1 @ X0) != $true) | ((moref @ (pf @ X1 @ X2) @ (pf @ X0 @ X2)) = $true))),
% 0.22/1.35 inference(rectify,[status(thm)],[f35])).
% 0.22/1.35 thf(f35,plain,(
% 0.22/1.35 ! [X1 : frac,X2 : frac,X0 : frac] : (((moref @ X2 @ X1) != $true) | ((moref @ (pf @ X2 @ X0) @ (pf @ X1 @ X0)) = $true))),
% 0.22/1.35 inference(ennf_transformation,[status(thm)],[f13])).
% 0.22/1.35 thf(f13,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac] : (((moref @ X2 @ X1) = $true) => ((moref @ (pf @ X2 @ X0) @ (pf @ X1 @ X0)) = $true))),
% 0.22/1.35 inference(fool_elimination,[status(thm)],[f12])).
% 0.22/1.35 thf(f12,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X2 @ X1) => (moref @ (pf @ X2 @ X0) @ (pf @ X1 @ X0)))),
% 0.22/1.35 inference(rectify,[status(thm)],[f7])).
% 0.22/1.35 thf(f7,axiom,(
% 0.22/1.35 ! [X2 : frac,X1 : frac,X0 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.22/1.35 file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz61)).
% 0.22/1.35 thf(f179,plain,(
% 0.22/1.35 ( ! [X0 : frac] : (((moref @ (pf @ x @ X0) @ (pf @ y @ u)) != $true) | ((moref @ z @ X0) != $true)) )),
% 0.22/1.35 inference(trivial_inequality_removal,[status(thm)],[f178])).
% 0.22/1.35 thf(f178,plain,(
% 0.22/1.35 ( ! [X0 : frac] : (((moref @ z @ X0) != $true) | ((moref @ (pf @ x @ X0) @ (pf @ y @ u)) != $true) | ($true != $true)) )),
% 0.22/1.35 inference(superposition,[status(thm)],[f173,f47])).
% 0.22/1.35 thf(f47,plain,(
% 0.22/1.35 ( ! [X0 : frac,X1 : frac] : (((eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0)) = $true)) )),
% 0.22/1.35 inference(cnf_transformation,[status(thm)],[f25])).
% 0.22/1.35 thf(f25,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac] : ((eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0)) = $true)),
% 0.22/1.35 inference(fool_elimination,[status(thm)],[f24])).
% 0.22/1.35 thf(f24,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac] : (eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))),
% 0.22/1.35 inference(rectify,[status(thm)],[f8])).
% 0.22/1.35 thf(f8,axiom,(
% 0.22/1.35 ! [X0 : frac,X1 : frac] : (eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))),
% 0.22/1.35 file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz58)).
% 0.22/1.35 thf(f173,plain,(
% 0.22/1.35 ( ! [X0 : frac,X1 : frac] : (((eq @ (pf @ X0 @ x) @ X1) != $true) | ((moref @ X1 @ (pf @ y @ u)) != $true) | ((moref @ z @ X0) != $true)) )),
% 0.22/1.35 inference(trivial_inequality_removal,[status(thm)],[f168])).
% 0.22/1.35 thf(f168,plain,(
% 0.22/1.35 ( ! [X0 : frac,X1 : frac] : (($true != $true) | ((moref @ X1 @ (pf @ y @ u)) != $true) | ((moref @ z @ X0) != $true) | ((eq @ (pf @ X0 @ x) @ X1) != $true)) )),
% 0.22/1.35 inference(superposition,[status(thm)],[f167,f46])).
% 0.22/1.35 thf(f167,plain,(
% 0.22/1.35 ( ! [X0 : frac,X1 : frac] : (((moref @ (pf @ z @ x) @ X1) != $true) | ((eq @ X1 @ X0) != $true) | ((moref @ X0 @ (pf @ y @ u)) != $true)) )),
% 0.22/1.35 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 0.22/1.35 thf(f166,plain,(
% 0.22/1.35 ( ! [X0 : frac,X1 : frac] : (((moref @ X0 @ (pf @ y @ u)) != $true) | ($true != $true) | ((moref @ (pf @ z @ x) @ X1) != $true) | ((eq @ X1 @ X0) != $true)) )),
% 0.22/1.35 inference(superposition,[status(thm)],[f71,f47])).
% 0.22/1.35 thf(f71,plain,(
% 0.22/1.35 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X1 @ (pf @ x @ z)) != $true) | ((moref @ X0 @ (pf @ y @ u)) != $true) | ((moref @ X1 @ X2) != $true) | ((eq @ X2 @ X0) != $true)) )),
% 0.22/1.35 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 0.22/1.35 thf(f69,plain,(
% 0.22/1.35 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X1 @ (pf @ x @ z)) != $true) | ((moref @ X0 @ (pf @ y @ u)) != $true) | ((eq @ X2 @ X0) != $true) | ($true != $true) | ((moref @ X1 @ X2) != $true)) )),
% 0.22/1.35 inference(superposition,[status(thm)],[f66,f43])).
% 0.22/1.35 thf(f43,plain,(
% 0.22/1.35 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((moref @ X1 @ X0) = $true) | ((moref @ X3 @ X2) != $true) | ((eq @ X2 @ X0) != $true) | ((eq @ X3 @ X1) != $true)) )),
% 0.22/1.35 inference(cnf_transformation,[status(thm)],[f38])).
% 0.22/1.35 thf(f38,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((moref @ X3 @ X2) != $true) | ((eq @ X2 @ X0) != $true) | ((moref @ X1 @ X0) = $true) | ((eq @ X3 @ X1) != $true))),
% 0.22/1.35 inference(rectify,[status(thm)],[f34])).
% 0.22/1.35 thf(f34,plain,(
% 0.22/1.35 ! [X3 : frac,X2 : frac,X1 : frac,X0 : frac] : (((moref @ X0 @ X1) != $true) | ((eq @ X1 @ X3) != $true) | ((moref @ X2 @ X3) = $true) | ((eq @ X0 @ X2) != $true))),
% 0.22/1.35 inference(flattening,[status(thm)],[f33])).
% 0.22/1.35 thf(f33,plain,(
% 0.22/1.35 ! [X2 : frac,X1 : frac,X0 : frac,X3 : frac] : (((((moref @ X2 @ X3) = $true) | ((eq @ X1 @ X3) != $true)) | ((eq @ X0 @ X2) != $true)) | ((moref @ X0 @ X1) != $true))),
% 0.22/1.35 inference(ennf_transformation,[status(thm)],[f29])).
% 0.22/1.35 thf(f29,plain,(
% 0.22/1.35 ! [X2 : frac,X1 : frac,X0 : frac,X3 : frac] : (((moref @ X0 @ X1) = $true) => (((eq @ X0 @ X2) = $true) => (((eq @ X1 @ X3) = $true) => ((moref @ X2 @ X3) = $true))))),
% 0.22/1.35 inference(fool_elimination,[status(thm)],[f28])).
% 0.22/1.35 thf(f28,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.22/1.35 inference(rectify,[status(thm)],[f6])).
% 0.22/1.35 thf(f6,axiom,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.22/1.35 file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz44)).
% 0.22/1.35 thf(f66,plain,(
% 0.22/1.35 ( ! [X0 : frac] : (((moref @ (pf @ x @ z) @ X0) != $true) | ((moref @ X0 @ (pf @ y @ u)) != $true)) )),
% 0.22/1.35 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 0.22/1.35 thf(f65,plain,(
% 0.22/1.35 ( ! [X0 : frac] : (($true != $true) | ((moref @ X0 @ (pf @ y @ u)) != $true) | ((moref @ (pf @ x @ z) @ X0) != $true)) )),
% 0.22/1.35 inference(superposition,[status(thm)],[f62,f45])).
% 0.22/1.35 thf(f45,plain,(
% 0.22/1.35 ( ! [X0 : frac,X1 : frac] : (((lessf @ X1 @ X0) = $true) | ((moref @ X0 @ X1) != $true)) )),
% 0.22/1.35 inference(cnf_transformation,[status(thm)],[f40])).
% 0.22/1.35 thf(f40,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac] : (((moref @ X0 @ X1) != $true) | ((lessf @ X1 @ X0) = $true))),
% 0.22/1.35 inference(rectify,[status(thm)],[f31])).
% 0.22/1.35 thf(f31,plain,(
% 0.22/1.35 ! [X1 : frac,X0 : frac] : (((moref @ X1 @ X0) != $true) | ((lessf @ X0 @ X1) = $true))),
% 0.22/1.35 inference(ennf_transformation,[status(thm)],[f19])).
% 0.22/1.35 thf(f19,plain,(
% 0.22/1.35 ! [X1 : frac,X0 : frac] : (((moref @ X1 @ X0) = $true) => ((lessf @ X0 @ X1) = $true))),
% 0.22/1.35 inference(fool_elimination,[status(thm)],[f18])).
% 0.22/1.35 thf(f18,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac] : ((moref @ X1 @ X0) => (lessf @ X0 @ X1))),
% 0.22/1.35 inference(rectify,[status(thm)],[f5])).
% 0.22/1.35 thf(f5,axiom,(
% 0.22/1.35 ! [X1 : frac,X0 : frac] : ((moref @ X0 @ X1) => (lessf @ X1 @ X0))),
% 0.22/1.35 file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz42)).
% 0.22/1.35 thf(f62,plain,(
% 0.22/1.35 ( ! [X0 : frac] : (((lessf @ X0 @ (pf @ x @ z)) != $true) | ((moref @ X0 @ (pf @ y @ u)) != $true)) )),
% 0.22/1.35 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 0.22/1.35 thf(f61,plain,(
% 0.22/1.35 ( ! [X0 : frac] : (($true != $true) | ((lessf @ X0 @ (pf @ x @ z)) != $true) | ((moref @ X0 @ (pf @ y @ u)) != $true)) )),
% 0.22/1.35 inference(superposition,[status(thm)],[f57,f45])).
% 0.22/1.35 thf(f57,plain,(
% 0.22/1.35 ( ! [X0 : frac] : (((lessf @ (pf @ y @ u) @ X0) != $true) | ((lessf @ X0 @ (pf @ x @ z)) != $true)) )),
% 0.22/1.35 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 0.22/1.35 thf(f56,plain,(
% 0.22/1.35 ( ! [X0 : frac] : (($true != $true) | ((lessf @ X0 @ (pf @ x @ z)) != $true) | ((lessf @ (pf @ y @ u) @ X0) != $true)) )),
% 0.22/1.35 inference(superposition,[status(thm)],[f53,f51])).
% 0.22/1.35 thf(f51,plain,(
% 0.22/1.35 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((lessf @ X1 @ X2) = $true) | ((lessf @ X0 @ X2) != $true) | ((lessf @ X1 @ X0) != $true)) )),
% 0.22/1.35 inference(cnf_transformation,[status(thm)],[f42])).
% 0.22/1.35 thf(f42,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac] : (((lessf @ X1 @ X2) = $true) | ((lessf @ X0 @ X2) != $true) | ((lessf @ X1 @ X0) != $true))),
% 0.22/1.35 inference(rectify,[status(thm)],[f37])).
% 0.22/1.35 thf(f37,plain,(
% 0.22/1.35 ! [X1 : frac,X2 : frac,X0 : frac] : (((lessf @ X2 @ X0) = $true) | ((lessf @ X1 @ X0) != $true) | ((lessf @ X2 @ X1) != $true))),
% 0.22/1.35 inference(flattening,[status(thm)],[f36])).
% 0.22/1.35 thf(f36,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac] : ((((lessf @ X2 @ X0) = $true) | ((lessf @ X1 @ X0) != $true)) | ((lessf @ X2 @ X1) != $true))),
% 0.22/1.35 inference(ennf_transformation,[status(thm)],[f27])).
% 0.22/1.35 thf(f27,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac] : (((lessf @ X2 @ X1) = $true) => (((lessf @ X1 @ X0) = $true) => ((lessf @ X2 @ X0) = $true)))),
% 0.22/1.35 inference(fool_elimination,[status(thm)],[f26])).
% 0.22/1.35 thf(f26,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac,X2 : frac] : ((lessf @ X2 @ X1) => ((lessf @ X1 @ X0) => (lessf @ X2 @ X0)))),
% 0.22/1.35 inference(rectify,[status(thm)],[f4])).
% 0.22/1.35 thf(f4,axiom,(
% 0.22/1.35 ! [X2 : frac,X1 : frac,X0 : frac] : ((lessf @ X0 @ X1) => ((lessf @ X1 @ X2) => (lessf @ X0 @ X2)))),
% 0.22/1.35 file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz50)).
% 0.22/1.35 thf(f53,plain,(
% 0.22/1.35 ((lessf @ (pf @ y @ u) @ (pf @ x @ z)) != $true)),
% 0.22/1.35 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 0.22/1.35 thf(f52,plain,(
% 0.22/1.35 ((lessf @ (pf @ y @ u) @ (pf @ x @ z)) != $true) | ($true != $true)),
% 0.22/1.35 inference(superposition,[status(thm)],[f49,f44])).
% 0.22/1.35 thf(f44,plain,(
% 0.22/1.35 ( ! [X0 : frac,X1 : frac] : (((moref @ X1 @ X0) = $true) | ((lessf @ X0 @ X1) != $true)) )),
% 0.22/1.35 inference(cnf_transformation,[status(thm)],[f39])).
% 0.22/1.35 thf(f39,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac] : (((lessf @ X0 @ X1) != $true) | ((moref @ X1 @ X0) = $true))),
% 0.22/1.35 inference(rectify,[status(thm)],[f32])).
% 0.22/1.35 thf(f32,plain,(
% 0.22/1.35 ! [X1 : frac,X0 : frac] : (((lessf @ X1 @ X0) != $true) | ((moref @ X0 @ X1) = $true))),
% 0.22/1.35 inference(ennf_transformation,[status(thm)],[f23])).
% 0.22/1.35 thf(f23,plain,(
% 0.22/1.35 ! [X1 : frac,X0 : frac] : (((lessf @ X1 @ X0) = $true) => ((moref @ X0 @ X1) = $true))),
% 0.22/1.35 inference(fool_elimination,[status(thm)],[f22])).
% 0.22/1.35 thf(f22,plain,(
% 0.22/1.35 ! [X0 : frac,X1 : frac] : ((lessf @ X1 @ X0) => (moref @ X0 @ X1))),
% 0.22/1.35 inference(rectify,[status(thm)],[f3])).
% 0.22/1.35 thf(f3,axiom,(
% 0.22/1.35 ! [X1 : frac,X0 : frac] : ((lessf @ X0 @ X1) => (moref @ X1 @ X0))),
% 0.22/1.35 file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz43)).
% 0.22/1.35 thf(f49,plain,(
% 0.22/1.35 ((moref @ (pf @ x @ z) @ (pf @ y @ u)) != $true)),
% 0.22/1.35 inference(cnf_transformation,[status(thm)],[f30])).
% 0.22/1.35 thf(f30,plain,(
% 0.22/1.35 ((moref @ (pf @ x @ z) @ (pf @ y @ u)) != $true)),
% 0.22/1.35 inference(flattening,[status(thm)],[f17])).
% 0.22/1.35 thf(f17,plain,(
% 0.22/1.35 ~((moref @ (pf @ x @ z) @ (pf @ y @ u)) = $true)),
% 0.22/1.35 inference(fool_elimination,[status(thm)],[f16])).
% 0.22/1.35 thf(f16,plain,(
% 0.22/1.35 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.22/1.35 inference(rectify,[status(thm)],[f10])).
% 0.22/1.35 thf(f10,negated_conjecture,(
% 0.22/1.35 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.22/1.35 inference(negated_conjecture,[status(cth)],[f9])).
% 0.22/1.35 thf(f9,conjecture,(
% 0.22/1.35 (moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.22/1.35 file('/export/starexec/sandbox2/tmp/tmp.oI8UYxVsKv/DTF2THF_25067.p',satz64)).
% 0.22/1.35 % SZS output end Proof for DTF2THF_25067
% 0.22/1.35 % (25164)------------------------------
% 0.22/1.35 % (25164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.35 % (25164)Termination reason: Refutation
% 0.22/1.35
% 0.22/1.35 % (25164)Memory used [KB]: 5628
% 0.22/1.35 % (25164)Time elapsed: 0.023 s
% 0.22/1.35 % (25164)Instructions burned: 37 (million)
% 0.22/1.35 % (25164)------------------------------
% 0.22/1.35 % (25164)------------------------------
% 0.22/1.35 % (25163)Success in time 0.035 s
%------------------------------------------------------------------------------