%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM739^1 : 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 09:24:29 AM UTC 2026
% Result : Theorem 1.49s 1.24s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 345 ( 104 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 413 ( 79 ~; 50 |; 1 &; 256 @)
% ( 0 <=>; 27 =>; 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 : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 75 ( 0 ^; 75 !; 0 ?; 75 :)
% 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_6,type,
eq: frac > frac > $o ).
thf(f139,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f138,f85]) ).
thf(f85,plain,
( ( moref @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( moref @ x @ y )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f73,f40]) ).
thf(f40,plain,
( ( eq @ y @ u )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( eq @ y @ u )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
eq @ y @ u,
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
eq @ y @ u,
file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',f) ).
thf(f73,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ u ) )
| ( $true
!= ( moref @ x @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ u ) )
| ( $true != $true )
| ( $true
!= ( moref @ x @ X0 ) ) ),
inference(superposition,[status(thm)],[f51,f43]) ).
thf(f43,plain,
( ( eq @ x @ z )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( eq @ x @ z )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
eq @ x @ z,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
eq @ x @ z,
file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',e) ).
thf(f51,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ z ) )
| ( $true
!= ( moref @ X0 @ X1 ) )
| ( ( eq @ X1 @ u )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( moref @ X0 @ X1 ) )
| ( $true != $true )
| ( $true
!= ( eq @ X0 @ z ) )
| ( ( eq @ X1 @ u )
!= $true ) ),
inference(superposition,[status(thm)],[f45,f42]) ).
thf(f42,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ X0 @ X3 )
= $true )
| ( ( moref @ X1 @ X2 )
!= $true )
| ( ( eq @ X2 @ X3 )
!= $true )
| ( $true
!= ( eq @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
!= ( eq @ X1 @ X0 ) )
| ( ( moref @ X0 @ X3 )
= $true )
| ( ( moref @ X1 @ X2 )
!= $true )
| ( ( eq @ X2 @ X3 )
!= $true ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
! [X3: frac,X0: frac,X2: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ X3 ) )
| ( $true
= ( moref @ X3 @ X1 ) )
| ( $true
!= ( moref @ X0 @ X2 ) )
| ( ( eq @ X2 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: frac,X2: frac,X3: frac,X0: frac] :
( ( $true
= ( moref @ X3 @ X1 ) )
| ( ( eq @ X2 @ X1 )
!= $true )
| ( $true
!= ( eq @ X0 @ X3 ) )
| ( $true
!= ( moref @ X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: frac,X2: frac,X3: frac,X0: frac] :
( ( $true
= ( moref @ X0 @ X2 ) )
=> ( ( $true
= ( eq @ X0 @ X3 ) )
=> ( ( ( eq @ X2 @ X1 )
= $true )
=> ( $true
= ( moref @ X3 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X2 )
=> ( ( eq @ X0 @ X3 )
=> ( ( eq @ X2 @ X1 )
=> ( moref @ X3 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X1: frac,X4: frac,X2: frac,X3: frac] :
( ( moref @ X1 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( ( eq @ X2 @ X4 )
=> ( moref @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',satz44) ).
thf(f45,plain,
( ( moref @ z @ u )
!= $true ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( eq @ z @ u )
!= $true )
& ( ( moref @ z @ u )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
~ ( ( ( moref @ z @ u )
!= $true )
=> ( ( eq @ z @ u )
= $true ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
~ ( ( ( moref @ z @ u )
!= $true )
=> ( ( eq @ z @ u )
= $true ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',satz46) ).
thf(f138,plain,
( ( moref @ x @ y )
= $true ),
inference(subsumption_resolution,[status(thm)],[f137,f40]) ).
thf(f137,plain,
( ( ( eq @ y @ u )
!= $true )
| ( ( moref @ x @ y )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
( ( ( eq @ y @ u )
!= $true )
| ( ( moref @ x @ y )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f127,f48]) ).
thf(f48,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( moref @ x @ y )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( moref @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',m) ).
thf(f127,plain,
! [X0: frac] :
( ( $true
!= ( eq @ x @ X0 ) )
| ( $true
!= ( eq @ X0 @ u ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ u ) )
| ( $true
!= ( eq @ x @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f78,f43]) ).
thf(f78,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ z ) )
| ( ( eq @ X1 @ u )
!= $true )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X0 @ X1 ) )
| ( $true != $true )
| ( $true
!= ( eq @ X0 @ z ) )
| ( ( eq @ X1 @ u )
!= $true ) ),
inference(superposition,[status(thm)],[f62,f47]) ).
thf(f47,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ X0 @ X1 ) )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( eq @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( eq @ X0 @ X1 ) )
| ( ( eq @ X2 @ X1 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ X0 @ X1 ) )
=> ( ( ( eq @ X1 @ X2 )
= $true )
=> ( ( eq @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: frac,X2: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',satz39) ).
thf(f62,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ u ) )
| ( $true
!= ( eq @ X0 @ z ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ u ) )
| ( $true
!= ( eq @ X0 @ z ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f55,f41]) ).
thf(f41,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( eq @ X1 @ X0 ) )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( eq @ X1 @ X0 ) )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: frac,X1: frac] :
( ( $true
= ( eq @ X0 @ X1 ) )
=> ( $true
= ( eq @ X1 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: frac,X2: frac] :
( ( eq @ X1 @ X2 )
=> ( eq @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',satz38) ).
thf(f55,plain,
! [X0: frac] :
( ( $true
!= ( eq @ z @ X0 ) )
| ( $true
!= ( eq @ X0 @ u ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true
!= ( eq @ X0 @ u ) )
| ( $true
!= ( eq @ z @ X0 ) ) ),
inference(superposition,[status(thm)],[f46,f47]) ).
thf(f46,plain,
( ( eq @ z @ u )
!= $true ),
inference(cnf_transformation,[status(thm)],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM739^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n011.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 11:12:17 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : NUM739^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.45 % Domain : Number Theory
% 0.31/0.45 % Problem : Landau theorem 46
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English : ~(moref z u) -> eq z u
% 0.31/0.45
% 0.31/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.31/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.31/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Bro09]
% 0.31/0.45 % Names : satz46 [Lan30]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % : Without extensionality : Theorem
% 0.31/0.45 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.31/0.45 % Syntax : Number of formulae : 15 ( 2 unt; 7 typ; 0 def)
% 0.31/0.45 % Number of atoms : 15 ( 0 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 4 ( 1 avg)
% 0.31/0.45 % Number of connectives : 43 ( 4 ~; 0 |; 0 &; 30 @)
% 0.31/0.45 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 10 ( 6 avg)
% 0.31/0.45 % Number of types : 2 ( 1 usr)
% 0.31/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 6 ( 6 usr; 4 con; 0-2 aty)
% 0.31/0.45 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.31/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.45
% 0.31/0.45 % Comments :
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf(frac_type,type,
% 0.31/0.45 frac: $tType ).
% 0.31/0.45
% 0.31/0.45 thf(x,type,
% 0.31/0.45 x: frac ).
% 0.31/0.45
% 0.31/0.45 thf(y,type,
% 0.31/0.45 y: frac ).
% 0.31/0.45
% 0.31/0.45 thf(z,type,
% 0.31/0.45 z: frac ).
% 0.31/0.45
% 0.31/0.45 thf(u,type,
% 0.31/0.45 u: frac ).
% 0.31/0.45
% 0.31/0.45 thf(moref,type,
% 0.31/0.45 moref: frac > frac > $o ).
% 0.31/0.45
% 0.31/0.45 thf(eq,type,
% 0.31/0.45 eq: frac > frac > $o ).
% 0.31/0.45
% 0.31/0.45 thf(m,axiom,
% 0.31/0.45 ( ~ ( moref @ x @ y )
% 0.31/0.45 => ( eq @ x @ y ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(e,axiom,
% 0.31/0.45 eq @ x @ z ).
% 0.31/0.45
% 0.31/0.45 thf(f,axiom,
% 0.31/0.45 eq @ y @ u ).
% 0.31/0.45
% 0.31/0.45 thf(et,axiom,
% 0.31/0.45 ! [Xa: $o] :
% 0.31/0.45 ( ~ ~ Xa
% 0.31/0.45 => Xa ) ).
% 0.31/0.45
% 0.31/0.45 thf(satz39,axiom,
% 0.31/0.45 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.31/0.45 ( ( eq @ Xx @ Xy )
% 0.31/0.45 => ( ( eq @ Xy @ Xz )
% 0.31/0.45 => ( eq @ Xx @ Xz ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(satz38,axiom,
% 0.31/0.45 ! [Xx: frac,Xy: frac] :
% 0.31/0.45 ( ( eq @ Xx @ Xy )
% 0.31/0.45 => ( eq @ Xy @ Xx ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(satz44,axiom,
% 0.31/0.45 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.31/0.45 ( ( moref @ Xx @ Xy )
% 0.31/0.45 => ( ( eq @ Xx @ Xz )
% 0.31/0.45 => ( ( eq @ Xy @ Xu )
% 0.31/0.45 => ( moref @ Xz @ Xu ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf(satz46,conjecture,
% 0.31/0.45 ( ~ ( moref @ z @ u )
% 0.31/0.45 => ( eq @ z @ u ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.49/1.20 ---- Embedded in THF ---
% 1.49/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.20 %%% Generated on Tue Feb 24 11:12:18 EST 2026
% 1.49/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.20 %%% Logic specification used:
% 1.49/1.20 %%% thf(spec, logic, $$dhol).
% 1.49/1.20
% 1.49/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2DTF12288.p
% See solution above
% 1.49/1.20 ------------------------
% 1.49/1.21 ---- Cleaned THF ---
% 1.49/1.22 thf(frac_type,type,
% 1.49/1.22 frac: $tType ).
% 1.49/1.22
% 1.49/1.22 thf(x,type,
% 1.49/1.22 x: frac ).
% 1.49/1.22
% 1.49/1.22 thf(y,type,
% 1.49/1.22 y: frac ).
% 1.49/1.22
% 1.49/1.22 thf(z,type,
% 1.49/1.22 z: frac ).
% 1.49/1.22
% 1.49/1.22 thf(u,type,
% 1.49/1.22 u: frac ).
% 1.49/1.22
% 1.49/1.22 thf(moref,type,
% 1.49/1.22 moref: frac > frac > $o ).
% 1.49/1.22
% 1.49/1.22 thf(eq,type,
% 1.49/1.22 eq: frac > frac > $o ).
% 1.49/1.22
% 1.49/1.22 thf(m,axiom,
% 1.49/1.22 ( ~ ( moref @ x @ y )
% 1.49/1.22 => ( eq @ x @ y ) ) ).
% 1.49/1.22
% 1.49/1.22 thf(e,axiom,
% 1.49/1.22 eq @ x @ z ).
% 1.49/1.22
% 1.49/1.22 thf(f,axiom,
% 1.49/1.22 eq @ y @ u ).
% 1.49/1.22
% 1.49/1.22 thf(et,axiom,
% 1.49/1.22 ! [Xa: $o] :
% 1.49/1.22 ( ~ ~ Xa
% 1.49/1.22 => Xa ) ).
% 1.49/1.22
% 1.49/1.22 thf(satz39,axiom,
% 1.49/1.22 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.49/1.22 ( ( eq @ Xx @ Xy )
% 1.49/1.22 => ( ( eq @ Xy @ Xz )
% 1.49/1.22 => ( eq @ Xx @ Xz ) ) ) ).
% 1.49/1.22
% 1.49/1.22 thf(satz38,axiom,
% 1.49/1.22 ! [Xx: frac,Xy: frac] :
% 1.49/1.22 ( ( eq @ Xx @ Xy )
% 1.49/1.22 => ( eq @ Xy @ Xx ) ) ).
% 1.49/1.22
% 1.49/1.22 thf(satz44,axiom,
% 1.49/1.22 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.49/1.22 ( ( moref @ Xx @ Xy )
% 1.49/1.22 => ( ( eq @ Xx @ Xz )
% 1.49/1.22 => ( ( eq @ Xy @ Xu )
% 1.49/1.22 => ( moref @ Xz @ Xu ) ) ) ) ).
% 1.49/1.22
% 1.49/1.22 thf(satz46,conjecture,
% 1.49/1.22 ( ~ ( moref @ z @ u )
% 1.49/1.22 => ( eq @ z @ u ) ) ).
% 1.49/1.22 ------------------------
% 1.49/1.23 % (12399)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_12288 for (2999ds/275Mi)
% 1.49/1.23 % (12398)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_12288 for (2999ds/2Mi)
% 1.49/1.23 % (12398)Instruction limit reached!
% 1.49/1.23 % (12398)------------------------------
% 1.49/1.23 % (12398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.23 % (12398)Termination reason: Unknown
% 1.49/1.23 % (12398)Termination phase: Saturation
% 1.49/1.23
% 1.49/1.23 % (12398)Memory used [KB]: 5500
% 1.49/1.23 % (12398)Time elapsed: 0.002 s
% 1.49/1.23 % (12398)Instructions burned: 3 (million)
% 1.49/1.23 % (12398)------------------------------
% 1.49/1.23 % (12398)------------------------------
% 1.49/1.24 % (12399)First to succeed.
% 1.49/1.24 % (12399)Refutation found. Thanks to Tanya!
% 1.49/1.24 % SZS status Theorem for DTF2THF_12288
% 1.49/1.24 % SZS output start Proof for DTF2THF_12288
% 1.49/1.24 thf(type_def_5, type, frac: $tType).
% 1.49/1.24 thf(func_def_0, type, frac: $tType).
% 1.49/1.24 thf(func_def_1, type, x: frac).
% 1.49/1.24 thf(func_def_2, type, y: frac).
% 1.49/1.24 thf(func_def_3, type, z: frac).
% 1.49/1.24 thf(func_def_4, type, u: frac).
% 1.49/1.24 thf(func_def_5, type, moref: frac > frac > $o).
% 1.49/1.24 thf(func_def_6, type, eq: frac > frac > $o).
% 1.49/1.24 thf(f139,plain,(
% 1.49/1.24 $false),
% 1.49/1.24 inference(subsumption_resolution,[status(thm)],[f138,f85])).
% 1.49/1.24 thf(f85,plain,(
% 1.49/1.24 ((moref @ x @ y) != $true)),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.49/1.24 thf(f80,plain,(
% 1.49/1.24 ((moref @ x @ y) != $true) | ($true != $true)),
% 1.49/1.24 inference(superposition,[status(thm)],[f73,f40])).
% 1.49/1.24 thf(f40,plain,(
% 1.49/1.24 ((eq @ y @ u) = $true)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.24 thf(f12,plain,(
% 1.49/1.24 ((eq @ y @ u) = $true)),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f11])).
% 1.49/1.24 thf(f11,plain,(
% 1.49/1.24 (eq @ y @ u)),
% 1.49/1.24 inference(rectify,[status(thm)],[f3])).
% 1.49/1.24 thf(f3,axiom,(
% 1.49/1.24 (eq @ y @ u)),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',f)).
% 1.49/1.24 thf(f73,plain,(
% 1.49/1.24 ( ! [X0 : frac] : (($true != (eq @ X0 @ u)) | ($true != (moref @ x @ X0))) )),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.49/1.24 thf(f70,plain,(
% 1.49/1.24 ( ! [X0 : frac] : (($true != (eq @ X0 @ u)) | ($true != $true) | ($true != (moref @ x @ X0))) )),
% 1.49/1.24 inference(superposition,[status(thm)],[f51,f43])).
% 1.49/1.24 thf(f43,plain,(
% 1.49/1.24 ((eq @ x @ z) = $true)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.24 thf(f14,plain,(
% 1.49/1.24 ((eq @ x @ z) = $true)),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f13])).
% 1.49/1.24 thf(f13,plain,(
% 1.49/1.24 (eq @ x @ z)),
% 1.49/1.24 inference(rectify,[status(thm)],[f2])).
% 1.49/1.24 thf(f2,axiom,(
% 1.49/1.24 (eq @ x @ z)),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',e)).
% 1.49/1.24 thf(f51,plain,(
% 1.49/1.24 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ X0 @ z)) | ($true != (moref @ X0 @ X1)) | ((eq @ X1 @ u) != $true)) )),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.49/1.24 thf(f50,plain,(
% 1.49/1.24 ( ! [X0 : frac,X1 : frac] : (($true != (moref @ X0 @ X1)) | ($true != $true) | ($true != (eq @ X0 @ z)) | ((eq @ X1 @ u) != $true)) )),
% 1.49/1.24 inference(superposition,[status(thm)],[f45,f42])).
% 1.49/1.24 thf(f42,plain,(
% 1.49/1.24 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((moref @ X0 @ X3) = $true) | ((moref @ X1 @ X2) != $true) | ((eq @ X2 @ X3) != $true) | ($true != (eq @ X1 @ X0))) )),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f38])).
% 1.49/1.24 thf(f38,plain,(
% 1.49/1.24 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true != (eq @ X1 @ X0)) | ((moref @ X0 @ X3) = $true) | ((moref @ X1 @ X2) != $true) | ((eq @ X2 @ X3) != $true))),
% 1.49/1.24 inference(rectify,[status(thm)],[f35])).
% 1.49/1.24 thf(f35,plain,(
% 1.49/1.24 ! [X3 : frac,X0 : frac,X2 : frac,X1 : frac] : (($true != (eq @ X0 @ X3)) | ($true = (moref @ X3 @ X1)) | ($true != (moref @ X0 @ X2)) | ((eq @ X2 @ X1) != $true))),
% 1.49/1.24 inference(flattening,[status(thm)],[f34])).
% 1.49/1.24 thf(f34,plain,(
% 1.49/1.24 ! [X1 : frac,X2 : frac,X3 : frac,X0 : frac] : (((($true = (moref @ X3 @ X1)) | ((eq @ X2 @ X1) != $true)) | ($true != (eq @ X0 @ X3))) | ($true != (moref @ X0 @ X2)))),
% 1.49/1.24 inference(ennf_transformation,[status(thm)],[f18])).
% 1.49/1.24 thf(f18,plain,(
% 1.49/1.24 ! [X1 : frac,X2 : frac,X3 : frac,X0 : frac] : (($true = (moref @ X0 @ X2)) => (($true = (eq @ X0 @ X3)) => (((eq @ X2 @ X1) = $true) => ($true = (moref @ X3 @ X1)))))),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f17])).
% 1.49/1.24 thf(f17,plain,(
% 1.49/1.24 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X2) => ((eq @ X0 @ X3) => ((eq @ X2 @ X1) => (moref @ X3 @ X1))))),
% 1.49/1.24 inference(rectify,[status(thm)],[f7])).
% 1.49/1.24 thf(f7,axiom,(
% 1.49/1.24 ! [X1 : frac,X4 : frac,X2 : frac,X3 : frac] : ((moref @ X1 @ X2) => ((eq @ X1 @ X3) => ((eq @ X2 @ X4) => (moref @ X3 @ X4))))),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',satz44)).
% 1.49/1.24 thf(f45,plain,(
% 1.49/1.24 ((moref @ z @ u) != $true)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f37])).
% 1.49/1.24 thf(f37,plain,(
% 1.49/1.24 ((eq @ z @ u) != $true) & ((moref @ z @ u) != $true)),
% 1.49/1.24 inference(ennf_transformation,[status(thm)],[f27])).
% 1.49/1.24 thf(f27,plain,(
% 1.49/1.24 ~(((moref @ z @ u) != $true) => ((eq @ z @ u) = $true))),
% 1.49/1.24 inference(flattening,[status(thm)],[f22])).
% 1.49/1.24 thf(f22,plain,(
% 1.49/1.24 ~(~((moref @ z @ u) = $true) => ((eq @ z @ u) = $true))),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f21])).
% 1.49/1.24 thf(f21,plain,(
% 1.49/1.24 ~(~(moref @ z @ u) => (eq @ z @ u))),
% 1.49/1.24 inference(rectify,[status(thm)],[f9])).
% 1.49/1.24 thf(f9,negated_conjecture,(
% 1.49/1.24 ~(~(moref @ z @ u) => (eq @ z @ u))),
% 1.49/1.24 inference(negated_conjecture,[status(cth)],[f8])).
% 1.49/1.24 thf(f8,conjecture,(
% 1.49/1.24 ~(moref @ z @ u) => (eq @ z @ u)),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',satz46)).
% 1.49/1.24 thf(f138,plain,(
% 1.49/1.24 ((moref @ x @ y) = $true)),
% 1.49/1.24 inference(subsumption_resolution,[status(thm)],[f137,f40])).
% 1.49/1.24 thf(f137,plain,(
% 1.49/1.24 ((eq @ y @ u) != $true) | ((moref @ x @ y) = $true)),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 1.49/1.24 thf(f130,plain,(
% 1.49/1.24 ((eq @ y @ u) != $true) | ((moref @ x @ y) = $true) | ($true != $true)),
% 1.49/1.24 inference(superposition,[status(thm)],[f127,f48])).
% 1.49/1.24 thf(f48,plain,(
% 1.49/1.24 ((eq @ x @ y) = $true) | ((moref @ x @ y) = $true)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f31])).
% 1.49/1.24 thf(f31,plain,(
% 1.49/1.24 ((moref @ x @ y) = $true) | ((eq @ x @ y) = $true)),
% 1.49/1.24 inference(ennf_transformation,[status(thm)],[f29])).
% 1.49/1.24 thf(f29,plain,(
% 1.49/1.24 ((moref @ x @ y) != $true) => ((eq @ x @ y) = $true)),
% 1.49/1.24 inference(flattening,[status(thm)],[f26])).
% 1.49/1.24 thf(f26,plain,(
% 1.49/1.24 ~((moref @ x @ y) = $true) => ((eq @ x @ y) = $true)),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f25])).
% 1.49/1.24 thf(f25,plain,(
% 1.49/1.24 ~(moref @ x @ y) => (eq @ x @ y)),
% 1.49/1.24 inference(rectify,[status(thm)],[f1])).
% 1.49/1.24 thf(f1,axiom,(
% 1.49/1.24 ~(moref @ x @ y) => (eq @ x @ y)),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',m)).
% 1.49/1.24 thf(f127,plain,(
% 1.49/1.24 ( ! [X0 : frac] : (($true != (eq @ x @ X0)) | ($true != (eq @ X0 @ u))) )),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.49/1.24 thf(f126,plain,(
% 1.49/1.24 ( ! [X0 : frac] : (($true != (eq @ X0 @ u)) | ($true != (eq @ x @ X0)) | ($true != $true)) )),
% 1.49/1.24 inference(superposition,[status(thm)],[f78,f43])).
% 1.49/1.24 thf(f78,plain,(
% 1.49/1.24 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ X0 @ z)) | ((eq @ X1 @ u) != $true) | ($true != (eq @ X0 @ X1))) )),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.49/1.24 thf(f76,plain,(
% 1.49/1.24 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ X0 @ X1)) | ($true != $true) | ($true != (eq @ X0 @ z)) | ((eq @ X1 @ u) != $true)) )),
% 1.49/1.24 inference(superposition,[status(thm)],[f62,f47])).
% 1.49/1.24 thf(f47,plain,(
% 1.49/1.24 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (eq @ X0 @ X1)) | ((eq @ X0 @ X2) != $true) | ((eq @ X2 @ X1) != $true)) )),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f39])).
% 1.49/1.24 thf(f39,plain,(
% 1.49/1.24 ! [X0 : frac,X1 : frac,X2 : frac] : (($true = (eq @ X0 @ X1)) | ((eq @ X2 @ X1) != $true) | ((eq @ X0 @ X2) != $true))),
% 1.49/1.24 inference(rectify,[status(thm)],[f33])).
% 1.49/1.24 thf(f33,plain,(
% 1.49/1.24 ! [X0 : frac,X2 : frac,X1 : frac] : (((eq @ X0 @ X2) = $true) | ((eq @ X1 @ X2) != $true) | ($true != (eq @ X0 @ X1)))),
% 1.49/1.24 inference(flattening,[status(thm)],[f32])).
% 1.49/1.24 thf(f32,plain,(
% 1.49/1.24 ! [X2 : frac,X0 : frac,X1 : frac] : ((((eq @ X0 @ X2) = $true) | ((eq @ X1 @ X2) != $true)) | ($true != (eq @ X0 @ X1)))),
% 1.49/1.24 inference(ennf_transformation,[status(thm)],[f16])).
% 1.49/1.24 thf(f16,plain,(
% 1.49/1.24 ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (eq @ X0 @ X1)) => (((eq @ X1 @ X2) = $true) => ((eq @ X0 @ X2) = $true)))),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f15])).
% 1.49/1.24 thf(f15,plain,(
% 1.49/1.24 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X1) => ((eq @ X1 @ X2) => (eq @ X0 @ X2)))),
% 1.49/1.24 inference(rectify,[status(thm)],[f5])).
% 1.49/1.24 thf(f5,axiom,(
% 1.49/1.24 ! [X1 : frac,X2 : frac,X3 : frac] : ((eq @ X1 @ X2) => ((eq @ X2 @ X3) => (eq @ X1 @ X3)))),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',satz39)).
% 1.49/1.24 thf(f62,plain,(
% 1.49/1.24 ( ! [X0 : frac] : (($true != (eq @ X0 @ u)) | ($true != (eq @ X0 @ z))) )),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.49/1.24 thf(f60,plain,(
% 1.49/1.24 ( ! [X0 : frac] : (($true != (eq @ X0 @ u)) | ($true != (eq @ X0 @ z)) | ($true != $true)) )),
% 1.49/1.24 inference(superposition,[status(thm)],[f55,f41])).
% 1.49/1.24 thf(f41,plain,(
% 1.49/1.24 ( ! [X0 : frac,X1 : frac] : (($true = (eq @ X1 @ X0)) | ($true != (eq @ X0 @ X1))) )),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f30])).
% 1.49/1.24 thf(f30,plain,(
% 1.49/1.24 ! [X0 : frac,X1 : frac] : (($true = (eq @ X1 @ X0)) | ($true != (eq @ X0 @ X1)))),
% 1.49/1.24 inference(ennf_transformation,[status(thm)],[f20])).
% 1.49/1.24 thf(f20,plain,(
% 1.49/1.24 ! [X0 : frac,X1 : frac] : (($true = (eq @ X0 @ X1)) => ($true = (eq @ X1 @ X0)))),
% 1.49/1.24 inference(fool_elimination,[status(thm)],[f19])).
% 1.49/1.24 thf(f19,plain,(
% 1.49/1.24 ! [X0 : frac,X1 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 1.49/1.24 inference(rectify,[status(thm)],[f6])).
% 1.49/1.24 thf(f6,axiom,(
% 1.49/1.24 ! [X1 : frac,X2 : frac] : ((eq @ X1 @ X2) => (eq @ X2 @ X1))),
% 1.49/1.24 file('/export/starexec/sandbox/tmp/tmp.nAVPoTT9U4/DTF2THF_12288.p',satz38)).
% 1.49/1.24 thf(f55,plain,(
% 1.49/1.24 ( ! [X0 : frac] : (($true != (eq @ z @ X0)) | ($true != (eq @ X0 @ u))) )),
% 1.49/1.24 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.49/1.24 thf(f53,plain,(
% 1.49/1.24 ( ! [X0 : frac] : (($true != $true) | ($true != (eq @ X0 @ u)) | ($true != (eq @ z @ X0))) )),
% 1.49/1.24 inference(superposition,[status(thm)],[f46,f47])).
% 1.49/1.24 thf(f46,plain,(
% 1.49/1.24 ((eq @ z @ u) != $true)),
% 1.49/1.24 inference(cnf_transformation,[status(thm)],[f37])).
% 1.49/1.24 % SZS output end Proof for DTF2THF_12288
% 1.49/1.24 % (12399)------------------------------
% 1.49/1.24 % (12399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.24 % (12399)Termination reason: Refutation
% 1.49/1.24
% 1.49/1.24 % (12399)Memory used [KB]: 5500
% 1.49/1.24 % (12399)Time elapsed: 0.008 s
% 1.49/1.24 % (12399)Instructions burned: 18 (million)
% 1.49/1.24 % (12399)------------------------------
% 1.49/1.24 % (12399)------------------------------
% 1.49/1.24 % (12393)Success in time 0.009 s
%------------------------------------------------------------------------------