%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM765^1 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:24:38 AM UTC 2026
% Result : Theorem 1.71s 1.44s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 3 unt; 0 typ; 4 def)
% Number of atoms : 426 ( 121 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 661 ( 94 ~; 59 |; 7 &; 454 @)
% ( 4 <=>; 43 =>; 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 : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 96 ( 0 ^; 96 !; 0 ?; 96 :)
% 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(func_def_8,type,
pf: frac > frac > frac ).
thf(f94,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f64,f82,f83,f87,f92,f93]) ).
thf(f93,plain,
( ~ spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f72,f57,f74]) ).
thf(f74,definition,
( spl0_3
<=> ( ( moref @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f57,definition,
( spl0_1
<=> ( ( eq @ z @ u )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f72,plain,
( ( ( moref @ x @ y )
!= $true )
| ( ( eq @ z @ u )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true != $true )
| ( ( eq @ z @ u )
!= $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f48,f50]) ).
thf(f50,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ ( pf @ X2 @ X3 ) @ ( pf @ X1 @ X0 ) ) )
| ( ( moref @ X2 @ X1 )
!= $true )
| ( ( eq @ X3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
= ( moref @ ( pf @ X2 @ X3 ) @ ( pf @ X1 @ X0 ) ) )
| ( ( moref @ X2 @ X1 )
!= $true )
| ( ( $true
!= ( moref @ X3 @ X0 ) )
& ( ( eq @ X3 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) )
= $true )
| ( ( moref @ X0 @ X3 )
!= $true )
| ( ( ( moref @ X1 @ X2 )
!= $true )
& ( ( eq @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f34]) ).
thf(f34,plain,
! [X3: frac,X0: frac,X2: frac,X1: frac] :
( ( ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) )
= $true )
| ( ( ( moref @ X1 @ X2 )
!= $true )
& ( ( eq @ X1 @ X2 )
!= $true ) )
| ( ( moref @ X0 @ X3 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X3: frac,X0: frac,X2: frac,X1: frac] :
( ( ( moref @ X0 @ X3 )
= $true )
=> ( ( ( ( moref @ X1 @ X2 )
!= $true )
=> ( ( eq @ X1 @ X2 )
= $true ) )
=> ( ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X0 @ X3 )
= $true )
=> ( ( ( ( moref @ X1 @ X2 )
!= $true )
=> ( ( eq @ X1 @ X2 )
= $true ) )
=> ( ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X3 )
=> ( ( ~ ( moref @ X1 @ X2 )
=> ( eq @ X1 @ X2 ) )
=> ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X1: frac,X3: frac,X4: frac,X2: frac] :
( ( moref @ X1 @ X2 )
=> ( ( ~ ( moref @ X3 @ X4 )
=> ( eq @ X3 @ X4 ) )
=> ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',satz65b) ).
thf(f48,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true )
& ( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
~ ( ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true )
=> ( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
= $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
~ ( ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true )
=> ( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
~ ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',satz66) ).
thf(f92,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f89,f61,f74]) ).
thf(f61,definition,
( spl0_2
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f89,plain,
( ( ( moref @ x @ y )
= $true )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true != $true )
| ( ( moref @ x @ y )
= $true )
| spl0_2 ),
inference(superposition,[status(thm)],[f63,f43]) ).
thf(f43,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( moref @ x @ y )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( moref @ x @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,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.yRyfa6yOOC/DTF2THF_9455.p',m) ).
thf(f63,plain,
( ( ( eq @ x @ y )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f87,plain,
( spl0_1
| spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f86]) ).
thf(f86,plain,
( $false
| spl0_1
| spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f85,f80]) ).
thf(f80,plain,
( ( ( moref @ z @ u )
!= $true )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f78,definition,
( spl0_4
<=> ( ( moref @ z @ u )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f85,plain,
( ( ( moref @ z @ u )
= $true )
| spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ( moref @ z @ u )
= $true )
| ( $true != $true )
| spl0_1 ),
inference(superposition,[status(thm)],[f59,f49]) ).
thf(f49,plain,
( ( ( eq @ z @ u )
= $true )
| ( ( moref @ z @ u )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,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)],[f13]) ).
thf(f13,plain,
( ( ( moref @ z @ u )
!= $true )
=> ( ( eq @ z @ u )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',n) ).
thf(f59,plain,
( ( ( eq @ z @ u )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f83,plain,
( ~ spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f69,f74,f78]) ).
thf(f69,plain,
( ( ( moref @ z @ u )
!= $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( moref @ z @ u )
!= $true )
| ( $true != $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f48,f44]) ).
thf(f44,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X0 ) )
= $true )
| ( ( moref @ X1 @ X2 )
!= $true )
| ( $true
!= ( moref @ X3 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( ( eq @ X1 @ X2 )
!= $true )
& ( ( moref @ X1 @ X2 )
!= $true ) )
| ( $true
!= ( moref @ X3 @ X0 ) )
| ( ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X0 ) )
= $true ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,plain,
! [X3: frac,X0: frac,X1: frac,X2: frac] :
( ( ( ( eq @ X0 @ X1 )
!= $true )
& ( ( moref @ X0 @ X1 )
!= $true ) )
| ( ( moref @ X2 @ X3 )
!= $true )
| ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true ) ),
inference(flattening,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true )
| ( ( moref @ X2 @ X3 )
!= $true )
| ( ( ( eq @ X0 @ X1 )
!= $true )
& ( ( moref @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( ( moref @ X0 @ X1 )
!= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) )
=> ( ( ( moref @ X2 @ X3 )
= $true )
=> ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( ( moref @ X0 @ X1 )
!= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) )
=> ( ( ( moref @ X2 @ X3 )
= $true )
=> ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ~ ( moref @ X0 @ X1 )
=> ( eq @ X0 @ X1 ) )
=> ( ( moref @ X2 @ X3 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( ~ ( moref @ X1 @ X2 )
=> ( eq @ X1 @ X2 ) )
=> ( ( moref @ X3 @ X4 )
=> ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',satz65a) ).
thf(f82,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f70,f78,f61]) ).
thf(f70,plain,
( ( ( eq @ x @ y )
!= $true )
| ( ( moref @ z @ u )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( moref @ z @ u )
!= $true )
| ( $true != $true )
| ( ( eq @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f48,f45]) ).
thf(f45,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X0 ) )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( $true
!= ( moref @ X3 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f64,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f55,f61,f57]) ).
thf(f55,plain,
( ( ( eq @ z @ u )
!= $true )
| ( ( eq @ x @ y )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( eq @ x @ y )
!= $true )
| ( ( eq @ z @ u )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f47,f46]) ).
thf(f46,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X3 ) ) )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( $true
!= ( eq @ X1 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X3 ) ) )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( $true
!= ( eq @ X1 @ X3 ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
! [X3: frac,X2: frac,X1: frac,X0: frac] :
( ( ( eq @ ( pf @ X3 @ X2 ) @ ( pf @ X1 @ X0 ) )
= $true )
| ( ( eq @ X3 @ X1 )
!= $true )
| ( $true
!= ( eq @ X2 @ X0 ) ) ),
inference(flattening,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: frac,X1: frac,X0: frac,X3: frac] :
( ( ( eq @ ( pf @ X3 @ X2 ) @ ( pf @ X1 @ X0 ) )
= $true )
| ( $true
!= ( eq @ X2 @ X0 ) )
| ( ( eq @ X3 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: frac,X1: frac,X0: frac,X3: frac] :
( ( ( eq @ X3 @ X1 )
= $true )
=> ( ( $true
= ( eq @ X2 @ X0 ) )
=> ( ( eq @ ( pf @ X3 @ X2 ) @ ( pf @ X1 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ X3 @ X1 )
=> ( ( eq @ X2 @ X0 )
=> ( eq @ ( pf @ X3 @ X2 ) @ ( pf @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X4: frac,X2: frac,X3: frac,X1: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X3 @ X4 )
=> ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',satz56) ).
thf(f47,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM765^1 : 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
% 0.15/0.34 % Computer : n009.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:13:25 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : NUM765^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.47 % Domain : Number Theory
% 0.20/0.47 % Problem : Landau theorem 66
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : ~(moref (pf x z) (pf y u)) -> eq (pf x z) (pf y u)
% 0.20/0.47
% 0.20/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : satz66 [Lan30]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % : Without extensionality : Theorem
% 0.20/0.47 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.20/0.47 % Syntax : Number of formulae : 15 ( 0 unt; 8 typ; 0 def)
% 0.20/0.47 % Number of atoms : 17 ( 0 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 4 ( 2 avg)
% 0.20/0.47 % Number of connectives : 73 ( 7 ~; 0 |; 0 &; 54 @)
% 0.20/0.47 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 11 ( 8 avg)
% 0.20/0.47 % Number of types : 2 ( 1 usr)
% 0.20/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 7 ( 7 usr; 4 con; 0-2 aty)
% 0.20/0.47 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.20/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.47
% 0.20/0.47 % Comments :
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(frac_type,type,
% 0.20/0.47 frac: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(x,type,
% 0.20/0.47 x: frac ).
% 0.20/0.47
% 0.20/0.47 thf(y,type,
% 0.20/0.47 y: frac ).
% 0.20/0.47
% 0.20/0.47 thf(z,type,
% 0.20/0.47 z: frac ).
% 0.20/0.47
% 0.20/0.47 thf(u,type,
% 0.20/0.47 u: frac ).
% 0.20/0.47
% 0.20/0.47 thf(moref,type,
% 0.20/0.47 moref: frac > frac > $o ).
% 0.20/0.47
% 0.20/0.47 thf(eq,type,
% 0.20/0.47 eq: frac > frac > $o ).
% 0.20/0.47
% 0.20/0.47 thf(m,axiom,
% 0.20/0.47 ( ~ ( moref @ x @ y )
% 0.20/0.47 => ( eq @ x @ y ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(n,axiom,
% 0.20/0.47 ( ~ ( moref @ z @ u )
% 0.20/0.47 => ( eq @ z @ u ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(pf,type,
% 0.20/0.47 pf: frac > frac > frac ).
% 0.20/0.47
% 0.20/0.47 thf(et,axiom,
% 0.20/0.47 ! [Xa: $o] :
% 0.20/0.47 ( ~ ~ Xa
% 0.20/0.47 => Xa ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz56,axiom,
% 0.20/0.47 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.20/0.47 ( ( eq @ Xx @ Xy )
% 0.20/0.47 => ( ( eq @ Xz @ Xu )
% 0.20/0.47 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz65b,axiom,
% 0.20/0.47 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.20/0.47 ( ( moref @ Xx @ Xy )
% 0.20/0.47 => ( ( ~ ( moref @ Xz @ Xu )
% 0.20/0.47 => ( eq @ Xz @ Xu ) )
% 0.20/0.47 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz65a,axiom,
% 0.20/0.47 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.20/0.47 ( ( ~ ( moref @ Xx @ Xy )
% 0.20/0.47 => ( eq @ Xx @ Xy ) )
% 0.20/0.47 => ( ( moref @ Xz @ Xu )
% 0.20/0.47 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz66,conjecture,
% 0.20/0.47 ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
% 0.20/0.47 => ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.71/1.40 ---- Embedded in THF ---
% 1.71/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.41 %%% Generated on Tue Feb 24 11:13:26 EST 2026
% 1.71/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.41 %%% Logic specification used:
% 1.71/1.41 %%% thf(spec, logic, $$dhol).
% 1.71/1.41
% 1.71/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2DTF9455.p
% See solution above
% 1.71/1.41 ------------------------
% 1.71/1.41 ---- Cleaned THF ---
% 1.71/1.41 thf(frac_type,type,
% 1.71/1.41 frac: $tType ).
% 1.71/1.41
% 1.71/1.41 thf(x,type,
% 1.71/1.41 x: frac ).
% 1.71/1.41
% 1.71/1.41 thf(y,type,
% 1.71/1.41 y: frac ).
% 1.71/1.41
% 1.71/1.41 thf(z,type,
% 1.71/1.41 z: frac ).
% 1.71/1.41
% 1.71/1.41 thf(u,type,
% 1.71/1.41 u: frac ).
% 1.71/1.41
% 1.71/1.41 thf(moref,type,
% 1.71/1.41 moref: frac > frac > $o ).
% 1.71/1.41
% 1.71/1.41 thf(eq,type,
% 1.71/1.41 eq: frac > frac > $o ).
% 1.71/1.41
% 1.71/1.41 thf(m,axiom,
% 1.71/1.41 ( ~ ( moref @ x @ y )
% 1.71/1.41 => ( eq @ x @ y ) ) ).
% 1.71/1.41
% 1.71/1.41 thf(n,axiom,
% 1.71/1.41 ( ~ ( moref @ z @ u )
% 1.71/1.41 => ( eq @ z @ u ) ) ).
% 1.71/1.41
% 1.71/1.41 thf(pf,type,
% 1.71/1.41 pf: frac > frac > frac ).
% 1.71/1.41
% 1.71/1.41 thf(et,axiom,
% 1.71/1.41 ! [Xa: $o] :
% 1.71/1.41 ( ~ ~ Xa
% 1.71/1.41 => Xa ) ).
% 1.71/1.41
% 1.71/1.41 thf(satz56,axiom,
% 1.71/1.41 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.71/1.41 ( ( eq @ Xx @ Xy )
% 1.71/1.41 => ( ( eq @ Xz @ Xu )
% 1.71/1.41 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 1.71/1.41
% 1.71/1.41 thf(satz65b,axiom,
% 1.71/1.41 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.71/1.41 ( ( moref @ Xx @ Xy )
% 1.71/1.41 => ( ( ~ ( moref @ Xz @ Xu )
% 1.71/1.41 => ( eq @ Xz @ Xu ) )
% 1.71/1.41 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 1.71/1.41
% 1.71/1.41 thf(satz65a,axiom,
% 1.71/1.41 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.71/1.41 ( ( ~ ( moref @ Xx @ Xy )
% 1.71/1.41 => ( eq @ Xx @ Xy ) )
% 1.71/1.41 => ( ( moref @ Xz @ Xu )
% 1.71/1.41 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 1.71/1.41
% 1.71/1.41 thf(satz66,conjecture,
% 1.71/1.41 ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
% 1.71/1.41 => ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ).
% 1.71/1.41 ------------------------
% 1.71/1.43 % (9553)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_9455 for (2999ds/4Mi)
% 1.71/1.43 % (9552)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9455 for (2999ds/183Mi)
% 1.71/1.43 % (9554)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_9455 for (2999ds/27Mi)
% 1.71/1.43 % (9555)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9455 for (2999ds/2Mi)
% 1.71/1.43 % (9556)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_9455 for (2999ds/2Mi)
% 1.71/1.43 % (9557)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_9455 for (2999ds/275Mi)
% 1.71/1.43 % (9558)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9455 for (2999ds/18Mi)
% 1.71/1.44 % (9555)Instruction limit reached!
% 1.71/1.44 % (9555)------------------------------
% 1.71/1.44 % (9555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.44 % (9555)Termination reason: Unknown
% 1.71/1.44 % (9556)Instruction limit reached!
% 1.71/1.44 % (9556)------------------------------
% 1.71/1.44 % (9556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.44 % (9555)Termination phase: Saturation
% 1.71/1.44
% 1.71/1.44 % (9555)Memory used [KB]: 1023
% 1.71/1.44 % (9555)Time elapsed: 0.003 s
% 1.71/1.44 % (9555)Instructions burned: 3 (million)
% 1.71/1.44 % (9555)------------------------------
% 1.71/1.44 % (9555)------------------------------
% 1.71/1.44 % (9556)Termination reason: Unknown
% 1.71/1.44 % (9556)Termination phase: Saturation
% 1.71/1.44
% 1.71/1.44 % (9556)Memory used [KB]: 1023
% 1.71/1.44 % (9556)Time elapsed: 0.003 s
% 1.71/1.44 % (9556)Instructions burned: 3 (million)
% 1.71/1.44 % (9556)------------------------------
% 1.71/1.44 % (9556)------------------------------
% 1.71/1.44 % (9553)Instruction limit reached!
% 1.71/1.44 % (9553)------------------------------
% 1.71/1.44 % (9553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.44 % (9553)Termination reason: Unknown
% 1.71/1.44 % (9553)Termination phase: Saturation
% 1.71/1.44
% 1.71/1.44 % (9553)Memory used [KB]: 5500
% 1.71/1.44 % (9553)Time elapsed: 0.004 s
% 1.71/1.44 % (9553)Instructions burned: 5 (million)
% 1.71/1.44 % (9553)------------------------------
% 1.71/1.44 % (9553)------------------------------
% 1.71/1.44 % (9557)First to succeed.
% 1.71/1.44 % (9552)Also succeeded, but the first one will report.
% 1.71/1.44 % (9557)Refutation found. Thanks to Tanya!
% 1.71/1.44 % SZS status Theorem for DTF2THF_9455
% 1.71/1.44 % SZS output start Proof for DTF2THF_9455
% 1.71/1.44 thf(type_def_5, type, frac: $tType).
% 1.71/1.44 thf(func_def_0, type, frac: $tType).
% 1.71/1.44 thf(func_def_1, type, x: frac).
% 1.71/1.44 thf(func_def_2, type, y: frac).
% 1.71/1.44 thf(func_def_3, type, z: frac).
% 1.71/1.44 thf(func_def_4, type, u: frac).
% 1.71/1.44 thf(func_def_5, type, moref: frac > frac > $o).
% 1.71/1.44 thf(func_def_6, type, eq: frac > frac > $o).
% 1.71/1.44 thf(func_def_8, type, pf: frac > frac > frac).
% 1.71/1.44 thf(f94,plain,(
% 1.71/1.44 $false),
% 1.71/1.44 inference(avatar_sat_refutation,[status(thm)],[f64,f82,f83,f87,f92,f93])).
% 1.71/1.44 thf(f93,plain,(
% 1.71/1.44 ~spl0_3 | ~spl0_1),
% 1.71/1.44 inference(avatar_split_clause,[status(thm)],[f72,f57,f74])).
% 1.71/1.44 thf(f74,definition,(
% 1.71/1.44 spl0_3 <=> ((moref @ x @ y) = $true)),
% 1.71/1.44 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.71/1.44 thf(f57,definition,(
% 1.71/1.44 spl0_1 <=> ((eq @ z @ u) = $true)),
% 1.71/1.44 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.71/1.44 thf(f72,plain,(
% 1.71/1.44 ((moref @ x @ y) != $true) | ((eq @ z @ u) != $true)),
% 1.71/1.44 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.71/1.44 thf(f66,plain,(
% 1.71/1.44 ($true != $true) | ((eq @ z @ u) != $true) | ((moref @ x @ y) != $true)),
% 1.71/1.44 inference(superposition,[status(thm)],[f48,f50])).
% 1.71/1.44 thf(f50,plain,(
% 1.71/1.44 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true = (moref @ (pf @ X2 @ X3) @ (pf @ X1 @ X0))) | ((moref @ X2 @ X1) != $true) | ((eq @ X3 @ X0) != $true)) )),
% 1.71/1.44 inference(cnf_transformation,[status(thm)],[f42])).
% 1.71/1.44 thf(f42,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true = (moref @ (pf @ X2 @ X3) @ (pf @ X1 @ X0))) | ((moref @ X2 @ X1) != $true) | (($true != (moref @ X3 @ X0)) & ((eq @ X3 @ X0) != $true)))),
% 1.71/1.44 inference(rectify,[status(thm)],[f35])).
% 1.71/1.44 thf(f35,plain,(
% 1.71/1.44 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((moref @ (pf @ X0 @ X1) @ (pf @ X3 @ X2)) = $true) | ((moref @ X0 @ X3) != $true) | (((moref @ X1 @ X2) != $true) & ((eq @ X1 @ X2) != $true)))),
% 1.71/1.44 inference(flattening,[status(thm)],[f34])).
% 1.71/1.44 thf(f34,plain,(
% 1.71/1.44 ! [X3 : frac,X0 : frac,X2 : frac,X1 : frac] : ((((moref @ (pf @ X0 @ X1) @ (pf @ X3 @ X2)) = $true) | (((moref @ X1 @ X2) != $true) & ((eq @ X1 @ X2) != $true))) | ((moref @ X0 @ X3) != $true))),
% 1.71/1.44 inference(ennf_transformation,[status(thm)],[f29])).
% 1.71/1.44 thf(f29,plain,(
% 1.71/1.44 ! [X3 : frac,X0 : frac,X2 : frac,X1 : frac] : (((moref @ X0 @ X3) = $true) => ((((moref @ X1 @ X2) != $true) => ((eq @ X1 @ X2) = $true)) => ((moref @ (pf @ X0 @ X1) @ (pf @ X3 @ X2)) = $true)))),
% 1.71/1.44 inference(flattening,[status(thm)],[f15])).
% 1.71/1.44 thf(f15,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((moref @ X0 @ X3) = $true) => ((~((moref @ X1 @ X2) = $true) => ((eq @ X1 @ X2) = $true)) => ((moref @ (pf @ X0 @ X1) @ (pf @ X3 @ X2)) = $true)))),
% 1.71/1.44 inference(fool_elimination,[status(thm)],[f14])).
% 1.71/1.44 thf(f14,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X3) => ((~(moref @ X1 @ X2) => (eq @ X1 @ X2)) => (moref @ (pf @ X0 @ X1) @ (pf @ X3 @ X2))))),
% 1.71/1.44 inference(rectify,[status(thm)],[f5])).
% 1.71/1.44 thf(f5,axiom,(
% 1.71/1.44 ! [X1 : frac,X3 : frac,X4 : frac,X2 : frac] : ((moref @ X1 @ X2) => ((~(moref @ X3 @ X4) => (eq @ X3 @ X4)) => (moref @ (pf @ X1 @ X3) @ (pf @ X2 @ X4))))),
% 1.71/1.44 file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',satz65b)).
% 1.71/1.44 thf(f48,plain,(
% 1.71/1.44 ((moref @ (pf @ x @ z) @ (pf @ y @ u)) != $true)),
% 1.71/1.44 inference(cnf_transformation,[status(thm)],[f38])).
% 1.71/1.44 thf(f38,plain,(
% 1.71/1.44 ((moref @ (pf @ x @ z) @ (pf @ y @ u)) != $true) & ((eq @ (pf @ x @ z) @ (pf @ y @ u)) != $true)),
% 1.71/1.44 inference(ennf_transformation,[status(thm)],[f24])).
% 1.71/1.44 thf(f24,plain,(
% 1.71/1.44 ~(((moref @ (pf @ x @ z) @ (pf @ y @ u)) != $true) => ((eq @ (pf @ x @ z) @ (pf @ y @ u)) = $true))),
% 1.71/1.44 inference(flattening,[status(thm)],[f23])).
% 1.71/1.44 thf(f23,plain,(
% 1.71/1.44 ~(~((moref @ (pf @ x @ z) @ (pf @ y @ u)) = $true) => ((eq @ (pf @ x @ z) @ (pf @ y @ u)) = $true))),
% 1.71/1.44 inference(fool_elimination,[status(thm)],[f22])).
% 1.71/1.44 thf(f22,plain,(
% 1.71/1.44 ~(~(moref @ (pf @ x @ z) @ (pf @ y @ u)) => (eq @ (pf @ x @ z) @ (pf @ y @ u)))),
% 1.71/1.44 inference(rectify,[status(thm)],[f8])).
% 1.71/1.44 thf(f8,negated_conjecture,(
% 1.71/1.44 ~(~(moref @ (pf @ x @ z) @ (pf @ y @ u)) => (eq @ (pf @ x @ z) @ (pf @ y @ u)))),
% 1.71/1.44 inference(negated_conjecture,[status(cth)],[f7])).
% 1.71/1.44 thf(f7,conjecture,(
% 1.71/1.44 ~(moref @ (pf @ x @ z) @ (pf @ y @ u)) => (eq @ (pf @ x @ z) @ (pf @ y @ u))),
% 1.71/1.44 file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',satz66)).
% 1.71/1.44 thf(f92,plain,(
% 1.71/1.44 spl0_3 | spl0_2),
% 1.71/1.44 inference(avatar_split_clause,[status(thm)],[f89,f61,f74])).
% 1.71/1.44 thf(f61,definition,(
% 1.71/1.44 spl0_2 <=> ((eq @ x @ y) = $true)),
% 1.71/1.44 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.71/1.44 thf(f89,plain,(
% 1.71/1.44 ((moref @ x @ y) = $true) | spl0_2),
% 1.71/1.44 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.71/1.44 thf(f88,plain,(
% 1.71/1.44 ($true != $true) | ((moref @ x @ y) = $true) | spl0_2),
% 1.71/1.44 inference(superposition,[status(thm)],[f63,f43])).
% 1.71/1.44 thf(f43,plain,(
% 1.71/1.44 ((eq @ x @ y) = $true) | ((moref @ x @ y) = $true)),
% 1.71/1.44 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.44 thf(f33,plain,(
% 1.71/1.44 ((eq @ x @ y) = $true) | ((moref @ x @ y) = $true)),
% 1.71/1.44 inference(ennf_transformation,[status(thm)],[f26])).
% 1.71/1.44 thf(f26,plain,(
% 1.71/1.44 ((moref @ x @ y) != $true) => ((eq @ x @ y) = $true)),
% 1.71/1.44 inference(flattening,[status(thm)],[f21])).
% 1.71/1.44 thf(f21,plain,(
% 1.71/1.44 ~((moref @ x @ y) = $true) => ((eq @ x @ y) = $true)),
% 1.71/1.44 inference(fool_elimination,[status(thm)],[f20])).
% 1.71/1.44 thf(f20,plain,(
% 1.71/1.44 ~(moref @ x @ y) => (eq @ x @ y)),
% 1.71/1.44 inference(rectify,[status(thm)],[f1])).
% 1.71/1.44 thf(f1,axiom,(
% 1.71/1.44 ~(moref @ x @ y) => (eq @ x @ y)),
% 1.71/1.44 file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',m)).
% 1.71/1.44 thf(f63,plain,(
% 1.71/1.44 ((eq @ x @ y) != $true) | spl0_2),
% 1.71/1.44 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.71/1.44 thf(f87,plain,(
% 1.71/1.44 spl0_1 | spl0_4),
% 1.71/1.44 inference(avatar_contradiction_clause,[status(thm)],[f86])).
% 1.71/1.44 thf(f86,plain,(
% 1.71/1.44 $false | (spl0_1 | spl0_4)),
% 1.71/1.44 inference(subsumption_resolution,[status(thm)],[f85,f80])).
% 1.71/1.44 thf(f80,plain,(
% 1.71/1.44 ((moref @ z @ u) != $true) | spl0_4),
% 1.71/1.44 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.71/1.44 thf(f78,definition,(
% 1.71/1.44 spl0_4 <=> ((moref @ z @ u) = $true)),
% 1.71/1.44 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.71/1.44 thf(f85,plain,(
% 1.71/1.44 ((moref @ z @ u) = $true) | spl0_1),
% 1.71/1.44 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.71/1.44 thf(f84,plain,(
% 1.71/1.44 ((moref @ z @ u) = $true) | ($true != $true) | spl0_1),
% 1.71/1.44 inference(superposition,[status(thm)],[f59,f49])).
% 1.71/1.44 thf(f49,plain,(
% 1.71/1.44 ((eq @ z @ u) = $true) | ((moref @ z @ u) = $true)),
% 1.71/1.44 inference(cnf_transformation,[status(thm)],[f30])).
% 1.71/1.44 thf(f30,plain,(
% 1.71/1.44 ((eq @ z @ u) = $true) | ((moref @ z @ u) = $true)),
% 1.71/1.44 inference(ennf_transformation,[status(thm)],[f27])).
% 1.71/1.44 thf(f27,plain,(
% 1.71/1.44 ((moref @ z @ u) != $true) => ((eq @ z @ u) = $true)),
% 1.71/1.44 inference(flattening,[status(thm)],[f13])).
% 1.71/1.44 thf(f13,plain,(
% 1.71/1.44 ~((moref @ z @ u) = $true) => ((eq @ z @ u) = $true)),
% 1.71/1.44 inference(fool_elimination,[status(thm)],[f12])).
% 1.71/1.44 thf(f12,plain,(
% 1.71/1.44 ~(moref @ z @ u) => (eq @ z @ u)),
% 1.71/1.44 inference(rectify,[status(thm)],[f2])).
% 1.71/1.44 thf(f2,axiom,(
% 1.71/1.44 ~(moref @ z @ u) => (eq @ z @ u)),
% 1.71/1.44 file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',n)).
% 1.71/1.44 thf(f59,plain,(
% 1.71/1.44 ((eq @ z @ u) != $true) | spl0_1),
% 1.71/1.44 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.71/1.44 thf(f83,plain,(
% 1.71/1.44 ~spl0_4 | ~spl0_3),
% 1.71/1.44 inference(avatar_split_clause,[status(thm)],[f69,f74,f78])).
% 1.71/1.44 thf(f69,plain,(
% 1.71/1.44 ((moref @ z @ u) != $true) | ((moref @ x @ y) != $true)),
% 1.71/1.44 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.71/1.44 thf(f67,plain,(
% 1.71/1.44 ((moref @ z @ u) != $true) | ($true != $true) | ((moref @ x @ y) != $true)),
% 1.71/1.44 inference(superposition,[status(thm)],[f48,f44])).
% 1.71/1.44 thf(f44,plain,(
% 1.71/1.44 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((moref @ (pf @ X1 @ X3) @ (pf @ X2 @ X0)) = $true) | ((moref @ X1 @ X2) != $true) | ($true != (moref @ X3 @ X0))) )),
% 1.71/1.44 inference(cnf_transformation,[status(thm)],[f40])).
% 1.71/1.44 thf(f40,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ X1 @ X2) != $true) & ((moref @ X1 @ X2) != $true)) | ($true != (moref @ X3 @ X0)) | ((moref @ (pf @ X1 @ X3) @ (pf @ X2 @ X0)) = $true))),
% 1.71/1.44 inference(rectify,[status(thm)],[f37])).
% 1.71/1.44 thf(f37,plain,(
% 1.71/1.44 ! [X3 : frac,X0 : frac,X1 : frac,X2 : frac] : ((((eq @ X0 @ X1) != $true) & ((moref @ X0 @ X1) != $true)) | ((moref @ X2 @ X3) != $true) | ((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3)) = $true))),
% 1.71/1.44 inference(flattening,[status(thm)],[f36])).
% 1.71/1.44 thf(f36,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3)) = $true) | ((moref @ X2 @ X3) != $true)) | (((eq @ X0 @ X1) != $true) & ((moref @ X0 @ X1) != $true)))),
% 1.71/1.44 inference(ennf_transformation,[status(thm)],[f28])).
% 1.71/1.44 thf(f28,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ X0 @ X1) != $true) => ((eq @ X0 @ X1) = $true)) => (((moref @ X2 @ X3) = $true) => ((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3)) = $true)))),
% 1.71/1.44 inference(flattening,[status(thm)],[f19])).
% 1.71/1.44 thf(f19,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((~((moref @ X0 @ X1) = $true) => ((eq @ X0 @ X1) = $true)) => (((moref @ X2 @ X3) = $true) => ((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3)) = $true)))),
% 1.71/1.44 inference(fool_elimination,[status(thm)],[f18])).
% 1.71/1.44 thf(f18,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((~(moref @ X0 @ X1) => (eq @ X0 @ X1)) => ((moref @ X2 @ X3) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 1.71/1.44 inference(rectify,[status(thm)],[f6])).
% 1.71/1.44 thf(f6,axiom,(
% 1.71/1.44 ! [X1 : frac,X2 : frac,X3 : frac,X4 : frac] : ((~(moref @ X1 @ X2) => (eq @ X1 @ X2)) => ((moref @ X3 @ X4) => (moref @ (pf @ X1 @ X3) @ (pf @ X2 @ X4))))),
% 1.71/1.44 file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',satz65a)).
% 1.71/1.44 thf(f82,plain,(
% 1.71/1.44 ~spl0_2 | ~spl0_4),
% 1.71/1.44 inference(avatar_split_clause,[status(thm)],[f70,f78,f61])).
% 1.71/1.44 thf(f70,plain,(
% 1.71/1.44 ((eq @ x @ y) != $true) | ((moref @ z @ u) != $true)),
% 1.71/1.44 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.71/1.44 thf(f68,plain,(
% 1.71/1.44 ((moref @ z @ u) != $true) | ($true != $true) | ((eq @ x @ y) != $true)),
% 1.71/1.44 inference(superposition,[status(thm)],[f48,f45])).
% 1.71/1.44 thf(f45,plain,(
% 1.71/1.44 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((moref @ (pf @ X1 @ X3) @ (pf @ X2 @ X0)) = $true) | ((eq @ X1 @ X2) != $true) | ($true != (moref @ X3 @ X0))) )),
% 1.71/1.44 inference(cnf_transformation,[status(thm)],[f40])).
% 1.71/1.44 thf(f64,plain,(
% 1.71/1.44 ~spl0_1 | ~spl0_2),
% 1.71/1.44 inference(avatar_split_clause,[status(thm)],[f55,f61,f57])).
% 1.71/1.44 thf(f55,plain,(
% 1.71/1.44 ((eq @ z @ u) != $true) | ((eq @ x @ y) != $true)),
% 1.71/1.44 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.71/1.44 thf(f54,plain,(
% 1.71/1.44 ((eq @ x @ y) != $true) | ((eq @ z @ u) != $true) | ($true != $true)),
% 1.71/1.44 inference(superposition,[status(thm)],[f47,f46])).
% 1.71/1.44 thf(f46,plain,(
% 1.71/1.44 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true = (eq @ (pf @ X0 @ X1) @ (pf @ X2 @ X3))) | ((eq @ X0 @ X2) != $true) | ($true != (eq @ X1 @ X3))) )),
% 1.71/1.44 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.44 thf(f41,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true = (eq @ (pf @ X0 @ X1) @ (pf @ X2 @ X3))) | ((eq @ X0 @ X2) != $true) | ($true != (eq @ X1 @ X3)))),
% 1.71/1.44 inference(rectify,[status(thm)],[f32])).
% 1.71/1.44 thf(f32,plain,(
% 1.71/1.44 ! [X3 : frac,X2 : frac,X1 : frac,X0 : frac] : (((eq @ (pf @ X3 @ X2) @ (pf @ X1 @ X0)) = $true) | ((eq @ X3 @ X1) != $true) | ($true != (eq @ X2 @ X0)))),
% 1.71/1.44 inference(flattening,[status(thm)],[f31])).
% 1.71/1.44 thf(f31,plain,(
% 1.71/1.44 ! [X2 : frac,X1 : frac,X0 : frac,X3 : frac] : ((((eq @ (pf @ X3 @ X2) @ (pf @ X1 @ X0)) = $true) | ($true != (eq @ X2 @ X0))) | ((eq @ X3 @ X1) != $true))),
% 1.71/1.44 inference(ennf_transformation,[status(thm)],[f11])).
% 1.71/1.44 thf(f11,plain,(
% 1.71/1.44 ! [X2 : frac,X1 : frac,X0 : frac,X3 : frac] : (((eq @ X3 @ X1) = $true) => (($true = (eq @ X2 @ X0)) => ((eq @ (pf @ X3 @ X2) @ (pf @ X1 @ X0)) = $true)))),
% 1.71/1.44 inference(fool_elimination,[status(thm)],[f10])).
% 1.71/1.44 thf(f10,plain,(
% 1.71/1.44 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X3 @ X1) => ((eq @ X2 @ X0) => (eq @ (pf @ X3 @ X2) @ (pf @ X1 @ X0))))),
% 1.71/1.44 inference(rectify,[status(thm)],[f4])).
% 1.71/1.44 thf(f4,axiom,(
% 1.71/1.44 ! [X4 : frac,X2 : frac,X3 : frac,X1 : frac] : ((eq @ X1 @ X2) => ((eq @ X3 @ X4) => (eq @ (pf @ X1 @ X3) @ (pf @ X2 @ X4))))),
% 1.71/1.44 file('/export/starexec/sandbox/tmp/tmp.yRyfa6yOOC/DTF2THF_9455.p',satz56)).
% 1.71/1.44 thf(f47,plain,(
% 1.71/1.44 ((eq @ (pf @ x @ z) @ (pf @ y @ u)) != $true)),
% 1.71/1.44 inference(cnf_transformation,[status(thm)],[f38])).
% 1.71/1.44 % SZS output end Proof for DTF2THF_9455
% 1.71/1.44 % (9557)------------------------------
% 1.71/1.44 % (9557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.44 % (9557)Termination reason: Refutation
% 1.71/1.44
% 1.71/1.44 % (9557)Memory used [KB]: 5500
% 1.71/1.44 % (9557)Time elapsed: 0.006 s
% 1.71/1.44 % (9557)Instructions burned: 4 (million)
% 1.71/1.44 % (9557)------------------------------
% 1.71/1.44 % (9557)------------------------------
% 1.71/1.44 % (9551)Success in time 0.021 s
%------------------------------------------------------------------------------