%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM762^1 : 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 : n013.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 09:24:37 AM UTC 2026
% Result : Theorem 1.71s 1.35s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 72 ( 18 unt; 0 typ; 2 def)
% Number of atoms : 421 ( 123 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 626 ( 93 ~; 73 |; 0 &; 430 @)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 126 ( 0 ^; 126 !; 0 ?; 126 :)
% 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,
eq: frac > frac > $o ).
thf(func_def_8,type,
pf: frac > frac > frac ).
thf(f141,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f113,f124,f140]) ).
thf(f140,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f139]) ).
thf(f139,plain,
( $false
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f138,f49]) ).
thf(f49,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: frac] : ( eq @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz37) ).
thf(f138,plain,
( ( ( eq @ y @ y )
!= $true )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $true != $true )
| ( ( eq @ y @ y )
!= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f108,f54]) ).
thf(f54,plain,
( ( moref @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( moref @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
moref @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
moref @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',m) ).
thf(f108,plain,
( ! [X0: frac] :
( ( $true
!= ( moref @ x @ X0 ) )
| ( ( eq @ X0 @ y )
!= $true ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl0_3
<=> ! [X0: frac] :
( ( $true
!= ( moref @ x @ X0 ) )
| ( ( eq @ X0 @ y )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f124,plain,
spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f123]) ).
thf(f123,plain,
( $false
| spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f122,f60]) ).
thf(f60,plain,
( ( moref @ z @ u )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f58,f54]) ).
thf(f58,plain,
( ( ( moref @ x @ y )
!= $true )
| ( ( moref @ z @ u )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( moref @ z @ u )
!= $true )
| ( $true != $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f47,f51]) ).
thf(f51,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X3 @ X1 ) @ ( pf @ X0 @ X2 ) )
= $true )
| ( ( moref @ X1 @ X2 )
!= $true )
| ( ( moref @ X3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X3 @ X0 )
!= $true )
| ( ( moref @ X1 @ X2 )
!= $true )
| ( ( moref @ ( pf @ X3 @ X1 ) @ ( pf @ X0 @ X2 ) )
= $true ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: frac,X3: frac,X2: frac,X0: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( moref @ X3 @ X2 )
!= $true )
| ( ( moref @ ( pf @ X0 @ X3 ) @ ( pf @ X1 @ X2 ) )
= $true ) ),
inference(flattening,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: frac,X0: frac,X3: frac,X1: frac] :
( ( ( moref @ ( pf @ X0 @ X3 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( moref @ X3 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: frac,X0: frac,X3: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( ( moref @ X3 @ X2 )
= $true )
=> ( ( moref @ ( pf @ X0 @ X3 ) @ ( pf @ X1 @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( moref @ X3 @ X2 )
=> ( moref @ ( pf @ X0 @ X3 ) @ ( pf @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X1: frac,X2: frac,X4: frac,X3: frac] :
( ( moref @ X1 @ X2 )
=> ( ( moref @ X3 @ X4 )
=> ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz64) ).
thf(f47,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)],[f15]) ).
thf(f15,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,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/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz65b) ).
thf(f122,plain,
( ( ( moref @ z @ u )
= $true )
| spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $true != $true )
| ( ( moref @ z @ u )
= $true )
| spl0_4 ),
inference(superposition,[status(thm)],[f112,f48]) ).
thf(f48,plain,
( ( ( eq @ z @ u )
= $true )
| ( ( moref @ z @ u )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( moref @ z @ u )
= $true )
| ( ( eq @ z @ u )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( moref @ z @ u )
!= $true )
=> ( ( eq @ z @ u )
= $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( moref @ z @ u )
!= $true )
=> ( ( eq @ z @ u )
= $true ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,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.kdjnnQlqPn/DTF2THF_22314.p',n) ).
thf(f112,plain,
( ( ( eq @ z @ u )
!= $true )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f110]) ).
thf(f110,definition,
( spl0_4
<=> ( ( eq @ z @ u )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f113,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f105,f110,f107]) ).
thf(f105,plain,
! [X0: frac] :
( ( $true
!= ( moref @ x @ X0 ) )
| ( ( eq @ z @ u )
!= $true )
| ( ( eq @ X0 @ y )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f103]) ).
thf(f103,plain,
! [X0: frac] :
( ( ( eq @ X0 @ y )
!= $true )
| ( ( eq @ z @ u )
!= $true )
| ( $true != $true )
| ( $true
!= ( moref @ x @ X0 ) ) ),
inference(superposition,[status(thm)],[f85,f49]) ).
thf(f85,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ x @ z ) )
!= $true )
| ( ( eq @ X1 @ u )
!= $true )
| ( ( moref @ X0 @ X2 )
!= $true )
| ( ( eq @ X2 @ y )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ x @ z ) )
!= $true )
| ( $true != $true )
| ( ( eq @ X1 @ u )
!= $true )
| ( ( moref @ X0 @ X2 )
!= $true )
| ( ( eq @ X2 @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f70,f50]) ).
thf(f50,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) )
= $true )
| ( ( moref @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( moref @ X1 @ X2 )
!= $true )
| ( ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X2 @ X0 ) )
= $true ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: frac,X2: frac,X0: frac] :
( ( $true
!= ( moref @ X2 @ X0 ) )
| ( $true
= ( moref @ ( pf @ X2 @ X1 ) @ ( pf @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( $true
= ( moref @ X2 @ X0 ) )
=> ( $true
= ( moref @ ( pf @ X2 @ X1 ) @ ( pf @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X2 @ X0 )
=> ( moref @ ( pf @ X2 @ X1 ) @ ( pf @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: frac,X3: frac,X1: frac] :
( ( moref @ X1 @ X2 )
=> ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz61) ).
thf(f70,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( moref @ X2 @ ( pf @ X0 @ X1 ) ) )
| ( ( eq @ X2 @ ( pf @ x @ z ) )
!= $true )
| ( ( eq @ X1 @ u )
!= $true )
| ( ( eq @ X0 @ y )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X2 @ ( pf @ x @ z ) )
!= $true )
| ( ( eq @ X1 @ u )
!= $true )
| ( $true
!= ( moref @ X2 @ ( pf @ X0 @ X1 ) ) )
| ( $true != $true )
| ( ( eq @ X0 @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f59,f46]) ).
thf(f46,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X3 @ X2 ) @ ( pf @ X1 @ X0 ) )
= $true )
| ( $true
!= ( eq @ X2 @ X0 ) )
| ( ( eq @ X3 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
!= ( eq @ X2 @ X0 ) )
| ( ( eq @ ( pf @ X3 @ X2 ) @ ( pf @ X1 @ X0 ) )
= $true )
| ( ( eq @ X3 @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: frac,X2: frac,X3: frac,X0: frac] :
( ( ( eq @ X3 @ X1 )
!= $true )
| ( ( eq @ ( pf @ X0 @ X3 ) @ ( pf @ X2 @ X1 ) )
= $true )
| ( $true
!= ( eq @ X0 @ X2 ) ) ),
inference(flattening,[status(thm)],[f34]) ).
thf(f34,plain,
! [X3: frac,X1: frac,X2: frac,X0: frac] :
( ( ( eq @ ( pf @ X0 @ X3 ) @ ( pf @ X2 @ X1 ) )
= $true )
| ( ( eq @ X3 @ X1 )
!= $true )
| ( $true
!= ( eq @ X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X3: frac,X1: frac,X2: frac,X0: frac] :
( ( $true
= ( eq @ X0 @ X2 ) )
=> ( ( ( eq @ X3 @ X1 )
= $true )
=> ( ( eq @ ( pf @ X0 @ X3 ) @ ( pf @ X2 @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ X0 @ X2 )
=> ( ( eq @ X3 @ X1 )
=> ( eq @ ( pf @ X0 @ X3 ) @ ( pf @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X1: frac,X4: frac,X2: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X3 @ X4 )
=> ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz56) ).
thf(f59,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ ( pf @ y @ u ) )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X0 @ ( pf @ x @ z ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ ( pf @ x @ z ) )
!= $true )
| ( ( eq @ X1 @ ( pf @ y @ u ) )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f47,f52]) ).
thf(f52,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( moref @ X1 @ X0 )
!= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ X0 @ X3 )
!= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( moref @ X2 @ X3 )
= $true )
| ( ( moref @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: frac,X3: frac,X2: frac,X0: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X3 @ X2 )
!= $true )
| ( $true
= ( moref @ X2 @ X0 ) )
| ( ( moref @ X3 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ X2 @ X0 ) )
| ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X3 @ X2 )
!= $true )
| ( ( moref @ X3 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ X3 @ X1 )
= $true )
=> ( ( ( eq @ X3 @ X2 )
= $true )
=> ( ( ( eq @ X1 @ X0 )
= $true )
=> ( $true
= ( moref @ X2 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X3 @ X1 )
=> ( ( eq @ X3 @ X2 )
=> ( ( eq @ X1 @ X0 )
=> ( moref @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X4: frac,X2: frac,X3: frac,X1: frac] :
( ( moref @ X1 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( ( eq @ X2 @ X4 )
=> ( moref @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz44) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM762^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:13:08 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : NUM762^1 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.46 % Domain : Number Theory
% 0.21/0.46 % Problem : Landau theorem 65b
% 0.21/0.46 % Version : Especial.
% 0.21/0.46 % English : moref (pf x z) (pf y u)
% 0.21/0.46
% 0.21/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.21/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.21/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.46 % Source : [Bro09]
% 0.21/0.46 % Names : satz65b [Lan30]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % : Without extensionality : Theorem
% 0.21/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.33 v8.2.0, 0.36 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.50 v6.2.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.33 v4.0.1, 1.00 v4.0.0, 0.67 v3.7.0
% 0.21/0.46 % Syntax : Number of formulae : 17 ( 3 unt; 8 typ; 0 def)
% 0.21/0.46 % Number of atoms : 17 ( 0 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.21/0.46 % Number of connectives : 63 ( 3 ~; 0 |; 0 &; 50 @)
% 0.21/0.46 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 11 ( 7 avg)
% 0.21/0.46 % Number of types : 2 ( 1 usr)
% 0.21/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 7 ( 7 usr; 4 con; 0-2 aty)
% 0.21/0.46 % Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 0.21/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.46
% 0.21/0.46 % Comments :
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(frac_type,type,
% 0.21/0.46 frac: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(x,type,
% 0.21/0.46 x: frac ).
% 0.21/0.46
% 0.21/0.46 thf(y,type,
% 0.21/0.46 y: frac ).
% 0.21/0.46
% 0.21/0.46 thf(z,type,
% 0.21/0.46 z: frac ).
% 0.21/0.46
% 0.21/0.46 thf(u,type,
% 0.21/0.46 u: frac ).
% 0.21/0.46
% 0.21/0.46 thf(moref,type,
% 0.21/0.46 moref: frac > frac > $o ).
% 0.21/0.46
% 0.21/0.46 thf(m,axiom,
% 0.21/0.46 moref @ x @ y ).
% 0.21/0.46
% 0.21/0.46 thf(eq,type,
% 0.21/0.46 eq: frac > frac > $o ).
% 0.21/0.46
% 0.21/0.46 thf(n,axiom,
% 0.21/0.46 ( ~ ( moref @ z @ u )
% 0.21/0.46 => ( eq @ z @ u ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(pf,type,
% 0.21/0.46 pf: frac > frac > frac ).
% 0.21/0.46
% 0.21/0.46 thf(et,axiom,
% 0.21/0.46 ! [Xa: $o] :
% 0.21/0.46 ( ~ ~ Xa
% 0.21/0.46 => Xa ) ).
% 0.21/0.46
% 0.21/0.46 thf(satz44,axiom,
% 0.21/0.46 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.21/0.46 ( ( moref @ Xx @ Xy )
% 0.21/0.46 => ( ( eq @ Xx @ Xz )
% 0.21/0.46 => ( ( eq @ Xy @ Xu )
% 0.21/0.46 => ( moref @ Xz @ Xu ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(satz61,axiom,
% 0.21/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.21/0.46 ( ( moref @ Xx @ Xy )
% 0.21/0.46 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(satz37,axiom,
% 0.21/0.46 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.21/0.46
% 0.21/0.46 thf(satz56,axiom,
% 0.21/0.46 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.21/0.46 ( ( eq @ Xx @ Xy )
% 0.21/0.46 => ( ( eq @ Xz @ Xu )
% 0.21/0.46 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(satz64,axiom,
% 0.21/0.46 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.21/0.46 ( ( moref @ Xx @ Xy )
% 0.21/0.46 => ( ( moref @ Xz @ Xu )
% 0.21/0.46 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(satz65b,conjecture,
% 0.21/0.46 moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ).
% 0.21/0.46
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 ------------------------
% 1.71/1.31 ---- Embedded in THF ---
% 1.71/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.31 %%% Generated on Tue Feb 24 11:13:09 EST 2026
% 1.71/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.31 %%% Logic specification used:
% 1.71/1.31 %%% thf(spec, logic, $$dhol).
% 1.71/1.31
% 1.71/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2DTF22314.p
% See solution above
% 1.71/1.31 ------------------------
% 1.71/1.32 ---- Cleaned THF ---
% 1.71/1.32 thf(frac_type,type,
% 1.71/1.32 frac: $tType ).
% 1.71/1.32
% 1.71/1.32 thf(x,type,
% 1.71/1.32 x: frac ).
% 1.71/1.32
% 1.71/1.32 thf(y,type,
% 1.71/1.32 y: frac ).
% 1.71/1.32
% 1.71/1.32 thf(z,type,
% 1.71/1.32 z: frac ).
% 1.71/1.32
% 1.71/1.32 thf(u,type,
% 1.71/1.32 u: frac ).
% 1.71/1.32
% 1.71/1.32 thf(moref,type,
% 1.71/1.32 moref: frac > frac > $o ).
% 1.71/1.32
% 1.71/1.32 thf(m,axiom,
% 1.71/1.32 moref @ x @ y ).
% 1.71/1.32
% 1.71/1.32 thf(eq,type,
% 1.71/1.32 eq: frac > frac > $o ).
% 1.71/1.32
% 1.71/1.32 thf(n,axiom,
% 1.71/1.32 ( ~ ( moref @ z @ u )
% 1.71/1.32 => ( eq @ z @ u ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(pf,type,
% 1.71/1.32 pf: frac > frac > frac ).
% 1.71/1.32
% 1.71/1.32 thf(et,axiom,
% 1.71/1.32 ! [Xa: $o] :
% 1.71/1.32 ( ~ ~ Xa
% 1.71/1.32 => Xa ) ).
% 1.71/1.32
% 1.71/1.32 thf(satz44,axiom,
% 1.71/1.32 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.71/1.32 ( ( moref @ Xx @ Xy )
% 1.71/1.32 => ( ( eq @ Xx @ Xz )
% 1.71/1.32 => ( ( eq @ Xy @ Xu )
% 1.71/1.32 => ( moref @ Xz @ Xu ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(satz61,axiom,
% 1.71/1.32 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.71/1.32 ( ( moref @ Xx @ Xy )
% 1.71/1.32 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(satz37,axiom,
% 1.71/1.32 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 1.71/1.32
% 1.71/1.32 thf(satz56,axiom,
% 1.71/1.32 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.71/1.32 ( ( eq @ Xx @ Xy )
% 1.71/1.32 => ( ( eq @ Xz @ Xu )
% 1.71/1.32 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(satz64,axiom,
% 1.71/1.32 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.71/1.32 ( ( moref @ Xx @ Xy )
% 1.71/1.32 => ( ( moref @ Xz @ Xu )
% 1.71/1.32 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(satz65b,conjecture,
% 1.71/1.32 moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ).
% 1.71/1.32 ------------------------
% 1.71/1.34 % (22505)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_22314 for (2999ds/4Mi)
% 1.71/1.34 % (22505)Instruction limit reached!
% 1.71/1.34 % (22505)------------------------------
% 1.71/1.34 % (22505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (22505)Termination reason: Unknown
% 1.71/1.34 % (22505)Termination phase: Saturation
% 1.71/1.34
% 1.71/1.34 % (22505)Memory used [KB]: 5500
% 1.71/1.34 % (22505)Time elapsed: 0.003 s
% 1.71/1.34 % (22505)Instructions burned: 5 (million)
% 1.71/1.34 % (22505)------------------------------
% 1.71/1.34 % (22505)------------------------------
% 1.71/1.34 % (22509)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_22314 for (2999ds/275Mi)
% 1.71/1.34 % (22508)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_22314 for (2999ds/2Mi)
% 1.71/1.34 % (22508)Instruction limit reached!
% 1.71/1.34 % (22508)------------------------------
% 1.71/1.34 % (22508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.34 % (22508)Termination reason: Unknown
% 1.71/1.34 % (22508)Termination phase: shuffling
% 1.71/1.34
% 1.71/1.34 % (22508)Memory used [KB]: 1023
% 1.71/1.34 % (22508)Time elapsed: 0.003 s
% 1.71/1.34 % (22508)Instructions burned: 2 (million)
% 1.71/1.34 % (22508)------------------------------
% 1.71/1.34 % (22508)------------------------------
% 1.71/1.35 % (22506)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_22314 for (2999ds/27Mi)
% 1.71/1.35 % (22511)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22314 for (2999ds/3Mi)
% 1.71/1.35 % (22511)Instruction limit reached!
% 1.71/1.35 % (22511)------------------------------
% 1.71/1.35 % (22511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.35 % (22511)Termination reason: Unknown
% 1.71/1.35 % (22511)Termination phase: Saturation
% 1.71/1.35
% 1.71/1.35 % (22511)Memory used [KB]: 5500
% 1.71/1.35 % (22511)Time elapsed: 0.003 s
% 1.71/1.35 % (22511)Instructions burned: 3 (million)
% 1.71/1.35 % (22511)------------------------------
% 1.71/1.35 % (22511)------------------------------
% 1.71/1.35 % (22509)First to succeed.
% 1.71/1.35 % (22509)Refutation found. Thanks to Tanya!
% 1.71/1.35 % SZS status Theorem for DTF2THF_22314
% 1.71/1.35 % SZS output start Proof for DTF2THF_22314
% 1.71/1.35 thf(type_def_5, type, frac: $tType).
% 1.71/1.35 thf(func_def_0, type, frac: $tType).
% 1.71/1.35 thf(func_def_1, type, x: frac).
% 1.71/1.35 thf(func_def_2, type, y: frac).
% 1.71/1.35 thf(func_def_3, type, z: frac).
% 1.71/1.35 thf(func_def_4, type, u: frac).
% 1.71/1.35 thf(func_def_5, type, moref: frac > frac > $o).
% 1.71/1.35 thf(func_def_7, type, eq: frac > frac > $o).
% 1.71/1.35 thf(func_def_8, type, pf: frac > frac > frac).
% 1.71/1.35 thf(f141,plain,(
% 1.71/1.35 $false),
% 1.71/1.35 inference(avatar_sat_refutation,[status(thm)],[f113,f124,f140])).
% 1.71/1.35 thf(f140,plain,(
% 1.71/1.35 ~spl0_3),
% 1.71/1.35 inference(avatar_contradiction_clause,[status(thm)],[f139])).
% 1.71/1.35 thf(f139,plain,(
% 1.71/1.35 $false | ~spl0_3),
% 1.71/1.35 inference(subsumption_resolution,[status(thm)],[f138,f49])).
% 1.71/1.35 thf(f49,plain,(
% 1.71/1.35 ( ! [X0 : frac] : (((eq @ X0 @ X0) = $true)) )),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.71/1.35 thf(f29,plain,(
% 1.71/1.35 ! [X0 : frac] : ((eq @ X0 @ X0) = $true)),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f28])).
% 1.71/1.35 thf(f28,plain,(
% 1.71/1.35 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.71/1.35 inference(rectify,[status(thm)],[f6])).
% 1.71/1.35 thf(f6,axiom,(
% 1.71/1.35 ! [X1 : frac] : (eq @ X1 @ X1)),
% 1.71/1.35 file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz37)).
% 1.71/1.35 thf(f138,plain,(
% 1.71/1.35 ((eq @ y @ y) != $true) | ~spl0_3),
% 1.71/1.35 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.71/1.35 thf(f135,plain,(
% 1.71/1.35 ($true != $true) | ((eq @ y @ y) != $true) | ~spl0_3),
% 1.71/1.35 inference(superposition,[status(thm)],[f108,f54])).
% 1.71/1.35 thf(f54,plain,(
% 1.71/1.35 ((moref @ x @ y) = $true)),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f17])).
% 1.71/1.35 thf(f17,plain,(
% 1.71/1.35 ((moref @ x @ y) = $true)),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f16])).
% 1.71/1.35 thf(f16,plain,(
% 1.71/1.35 (moref @ x @ y)),
% 1.71/1.35 inference(rectify,[status(thm)],[f1])).
% 1.71/1.35 thf(f1,axiom,(
% 1.71/1.35 (moref @ x @ y)),
% 1.71/1.35 file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',m)).
% 1.71/1.35 thf(f108,plain,(
% 1.71/1.35 ( ! [X0 : frac] : (($true != (moref @ x @ X0)) | ((eq @ X0 @ y) != $true)) ) | ~spl0_3),
% 1.71/1.35 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.71/1.35 thf(f107,definition,(
% 1.71/1.35 spl0_3 <=> ! [X0 : frac] : (($true != (moref @ x @ X0)) | ((eq @ X0 @ y) != $true))),
% 1.71/1.35 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.71/1.35 thf(f124,plain,(
% 1.71/1.35 spl0_4),
% 1.71/1.35 inference(avatar_contradiction_clause,[status(thm)],[f123])).
% 1.71/1.35 thf(f123,plain,(
% 1.71/1.35 $false | spl0_4),
% 1.71/1.35 inference(subsumption_resolution,[status(thm)],[f122,f60])).
% 1.71/1.35 thf(f60,plain,(
% 1.71/1.35 ((moref @ z @ u) != $true)),
% 1.71/1.35 inference(subsumption_resolution,[status(thm)],[f58,f54])).
% 1.71/1.35 thf(f58,plain,(
% 1.71/1.35 ((moref @ x @ y) != $true) | ((moref @ z @ u) != $true)),
% 1.71/1.35 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.71/1.35 thf(f56,plain,(
% 1.71/1.35 ((moref @ z @ u) != $true) | ($true != $true) | ((moref @ x @ y) != $true)),
% 1.71/1.35 inference(superposition,[status(thm)],[f47,f51])).
% 1.71/1.35 thf(f51,plain,(
% 1.71/1.35 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((moref @ (pf @ X3 @ X1) @ (pf @ X0 @ X2)) = $true) | ((moref @ X1 @ X2) != $true) | ((moref @ X3 @ X0) != $true)) )),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f44])).
% 1.71/1.35 thf(f44,plain,(
% 1.71/1.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((moref @ X3 @ X0) != $true) | ((moref @ X1 @ X2) != $true) | ((moref @ (pf @ X3 @ X1) @ (pf @ X0 @ X2)) = $true))),
% 1.71/1.35 inference(rectify,[status(thm)],[f39])).
% 1.71/1.35 thf(f39,plain,(
% 1.71/1.35 ! [X1 : frac,X3 : frac,X2 : frac,X0 : frac] : (((moref @ X0 @ X1) != $true) | ((moref @ X3 @ X2) != $true) | ((moref @ (pf @ X0 @ X3) @ (pf @ X1 @ X2)) = $true))),
% 1.71/1.35 inference(flattening,[status(thm)],[f38])).
% 1.71/1.35 thf(f38,plain,(
% 1.71/1.35 ! [X2 : frac,X0 : frac,X3 : frac,X1 : frac] : ((((moref @ (pf @ X0 @ X3) @ (pf @ X1 @ X2)) = $true) | ((moref @ X3 @ X2) != $true)) | ((moref @ X0 @ X1) != $true))),
% 1.71/1.35 inference(ennf_transformation,[status(thm)],[f13])).
% 1.71/1.35 thf(f13,plain,(
% 1.71/1.35 ! [X2 : frac,X0 : frac,X3 : frac,X1 : frac] : (((moref @ X0 @ X1) = $true) => (((moref @ X3 @ X2) = $true) => ((moref @ (pf @ X0 @ X3) @ (pf @ X1 @ X2)) = $true)))),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f12])).
% 1.71/1.35 thf(f12,plain,(
% 1.71/1.35 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((moref @ X3 @ X2) => (moref @ (pf @ X0 @ X3) @ (pf @ X1 @ X2))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f8])).
% 1.71/1.36 thf(f8,axiom,(
% 1.71/1.36 ! [X1 : frac,X2 : frac,X4 : frac,X3 : frac] : ((moref @ X1 @ X2) => ((moref @ X3 @ X4) => (moref @ (pf @ X1 @ X3) @ (pf @ X2 @ X4))))),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz64)).
% 1.71/1.36 thf(f47,plain,(
% 1.71/1.36 ((moref @ (pf @ x @ z) @ (pf @ y @ u)) != $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f30])).
% 1.71/1.36 thf(f30,plain,(
% 1.71/1.36 ((moref @ (pf @ x @ z) @ (pf @ y @ u)) != $true)),
% 1.71/1.36 inference(flattening,[status(thm)],[f15])).
% 1.71/1.36 thf(f15,plain,(
% 1.71/1.36 ~((moref @ (pf @ x @ z) @ (pf @ y @ u)) = $true)),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f14])).
% 1.71/1.36 thf(f14,plain,(
% 1.71/1.36 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 1.71/1.36 inference(rectify,[status(thm)],[f10])).
% 1.71/1.36 thf(f10,negated_conjecture,(
% 1.71/1.36 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 1.71/1.36 inference(negated_conjecture,[status(cth)],[f9])).
% 1.71/1.36 thf(f9,conjecture,(
% 1.71/1.36 (moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz65b)).
% 1.71/1.36 thf(f122,plain,(
% 1.71/1.36 ((moref @ z @ u) = $true) | spl0_4),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.71/1.36 thf(f121,plain,(
% 1.71/1.36 ($true != $true) | ((moref @ z @ u) = $true) | spl0_4),
% 1.71/1.36 inference(superposition,[status(thm)],[f112,f48])).
% 1.71/1.36 thf(f48,plain,(
% 1.71/1.36 ((eq @ z @ u) = $true) | ((moref @ z @ u) = $true)),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f41])).
% 1.71/1.36 thf(f41,plain,(
% 1.71/1.36 ((moref @ z @ u) = $true) | ((eq @ z @ u) = $true)),
% 1.71/1.36 inference(ennf_transformation,[status(thm)],[f32])).
% 1.71/1.36 thf(f32,plain,(
% 1.71/1.36 ((moref @ z @ u) != $true) => ((eq @ z @ u) = $true)),
% 1.71/1.36 inference(flattening,[status(thm)],[f21])).
% 1.71/1.36 thf(f21,plain,(
% 1.71/1.36 ~((moref @ z @ u) = $true) => ((eq @ z @ u) = $true)),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f20])).
% 1.71/1.36 thf(f20,plain,(
% 1.71/1.36 ~(moref @ z @ u) => (eq @ z @ u)),
% 1.71/1.36 inference(rectify,[status(thm)],[f2])).
% 1.71/1.36 thf(f2,axiom,(
% 1.71/1.36 ~(moref @ z @ u) => (eq @ z @ u)),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',n)).
% 1.71/1.36 thf(f112,plain,(
% 1.71/1.36 ((eq @ z @ u) != $true) | spl0_4),
% 1.71/1.36 inference(avatar_component_clause,[status(thm)],[f110])).
% 1.71/1.36 thf(f110,definition,(
% 1.71/1.36 spl0_4 <=> ((eq @ z @ u) = $true)),
% 1.71/1.36 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.71/1.36 thf(f113,plain,(
% 1.71/1.36 spl0_3 | ~spl0_4),
% 1.71/1.36 inference(avatar_split_clause,[status(thm)],[f105,f110,f107])).
% 1.71/1.36 thf(f105,plain,(
% 1.71/1.36 ( ! [X0 : frac] : (($true != (moref @ x @ X0)) | ((eq @ z @ u) != $true) | ((eq @ X0 @ y) != $true)) )),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f103])).
% 1.71/1.36 thf(f103,plain,(
% 1.71/1.36 ( ! [X0 : frac] : (((eq @ X0 @ y) != $true) | ((eq @ z @ u) != $true) | ($true != $true) | ($true != (moref @ x @ X0))) )),
% 1.71/1.36 inference(superposition,[status(thm)],[f85,f49])).
% 1.71/1.36 thf(f85,plain,(
% 1.71/1.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ (pf @ X0 @ X1) @ (pf @ x @ z)) != $true) | ((eq @ X1 @ u) != $true) | ((moref @ X0 @ X2) != $true) | ((eq @ X2 @ y) != $true)) )),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.71/1.36 thf(f81,plain,(
% 1.71/1.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ (pf @ X0 @ X1) @ (pf @ x @ z)) != $true) | ($true != $true) | ((eq @ X1 @ u) != $true) | ((moref @ X0 @ X2) != $true) | ((eq @ X2 @ y) != $true)) )),
% 1.71/1.36 inference(superposition,[status(thm)],[f70,f50])).
% 1.71/1.36 thf(f50,plain,(
% 1.71/1.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((moref @ (pf @ X1 @ X0) @ (pf @ X2 @ X0)) = $true) | ((moref @ X1 @ X2) != $true)) )),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f43])).
% 1.71/1.36 thf(f43,plain,(
% 1.71/1.36 ! [X0 : frac,X1 : frac,X2 : frac] : (((moref @ X1 @ X2) != $true) | ((moref @ (pf @ X1 @ X0) @ (pf @ X2 @ X0)) = $true))),
% 1.71/1.36 inference(rectify,[status(thm)],[f33])).
% 1.71/1.36 thf(f33,plain,(
% 1.71/1.36 ! [X1 : frac,X2 : frac,X0 : frac] : (($true != (moref @ X2 @ X0)) | ($true = (moref @ (pf @ X2 @ X1) @ (pf @ X0 @ X1))))),
% 1.71/1.36 inference(ennf_transformation,[status(thm)],[f27])).
% 1.71/1.36 thf(f27,plain,(
% 1.71/1.36 ! [X0 : frac,X2 : frac,X1 : frac] : (($true = (moref @ X2 @ X0)) => ($true = (moref @ (pf @ X2 @ X1) @ (pf @ X0 @ X1))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f26])).
% 1.71/1.36 thf(f26,plain,(
% 1.71/1.36 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X2 @ X0) => (moref @ (pf @ X2 @ X1) @ (pf @ X0 @ X1)))),
% 1.71/1.36 inference(rectify,[status(thm)],[f5])).
% 1.71/1.36 thf(f5,axiom,(
% 1.71/1.36 ! [X2 : frac,X3 : frac,X1 : frac] : ((moref @ X1 @ X2) => (moref @ (pf @ X1 @ X3) @ (pf @ X2 @ X3)))),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz61)).
% 1.71/1.36 thf(f70,plain,(
% 1.71/1.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (moref @ X2 @ (pf @ X0 @ X1))) | ((eq @ X2 @ (pf @ x @ z)) != $true) | ((eq @ X1 @ u) != $true) | ((eq @ X0 @ y) != $true)) )),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.71/1.36 thf(f68,plain,(
% 1.71/1.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X2 @ (pf @ x @ z)) != $true) | ((eq @ X1 @ u) != $true) | ($true != (moref @ X2 @ (pf @ X0 @ X1))) | ($true != $true) | ((eq @ X0 @ y) != $true)) )),
% 1.71/1.36 inference(superposition,[status(thm)],[f59,f46])).
% 1.71/1.36 thf(f46,plain,(
% 1.71/1.36 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((eq @ (pf @ X3 @ X2) @ (pf @ X1 @ X0)) = $true) | ($true != (eq @ X2 @ X0)) | ((eq @ X3 @ X1) != $true)) )),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f42])).
% 1.71/1.36 thf(f42,plain,(
% 1.71/1.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true != (eq @ X2 @ X0)) | ((eq @ (pf @ X3 @ X2) @ (pf @ X1 @ X0)) = $true) | ((eq @ X3 @ X1) != $true))),
% 1.71/1.36 inference(rectify,[status(thm)],[f35])).
% 1.71/1.36 thf(f35,plain,(
% 1.71/1.36 ! [X1 : frac,X2 : frac,X3 : frac,X0 : frac] : (((eq @ X3 @ X1) != $true) | ((eq @ (pf @ X0 @ X3) @ (pf @ X2 @ X1)) = $true) | ($true != (eq @ X0 @ X2)))),
% 1.71/1.36 inference(flattening,[status(thm)],[f34])).
% 1.71/1.36 thf(f34,plain,(
% 1.71/1.36 ! [X3 : frac,X1 : frac,X2 : frac,X0 : frac] : ((((eq @ (pf @ X0 @ X3) @ (pf @ X2 @ X1)) = $true) | ((eq @ X3 @ X1) != $true)) | ($true != (eq @ X0 @ X2)))),
% 1.71/1.36 inference(ennf_transformation,[status(thm)],[f23])).
% 1.71/1.36 thf(f23,plain,(
% 1.71/1.36 ! [X3 : frac,X1 : frac,X2 : frac,X0 : frac] : (($true = (eq @ X0 @ X2)) => (((eq @ X3 @ X1) = $true) => ((eq @ (pf @ X0 @ X3) @ (pf @ X2 @ X1)) = $true)))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f22])).
% 1.71/1.36 thf(f22,plain,(
% 1.71/1.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X2) => ((eq @ X3 @ X1) => (eq @ (pf @ X0 @ X3) @ (pf @ X2 @ X1))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f7])).
% 1.71/1.36 thf(f7,axiom,(
% 1.71/1.36 ! [X1 : frac,X4 : frac,X2 : frac,X3 : frac] : ((eq @ X1 @ X2) => ((eq @ X3 @ X4) => (eq @ (pf @ X1 @ X3) @ (pf @ X2 @ X4))))),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz56)).
% 1.71/1.36 thf(f59,plain,(
% 1.71/1.36 ( ! [X0 : frac,X1 : frac] : (((eq @ X1 @ (pf @ y @ u)) != $true) | ((moref @ X0 @ X1) != $true) | ((eq @ X0 @ (pf @ x @ z)) != $true)) )),
% 1.71/1.36 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.71/1.36 thf(f57,plain,(
% 1.71/1.36 ( ! [X0 : frac,X1 : frac] : (((eq @ X0 @ (pf @ x @ z)) != $true) | ((eq @ X1 @ (pf @ y @ u)) != $true) | ((moref @ X0 @ X1) != $true) | ($true != $true)) )),
% 1.71/1.36 inference(superposition,[status(thm)],[f47,f52])).
% 1.71/1.36 thf(f52,plain,(
% 1.71/1.36 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((moref @ X2 @ X3) = $true) | ((moref @ X1 @ X0) != $true) | ((eq @ X1 @ X2) != $true) | ((eq @ X0 @ X3) != $true)) )),
% 1.71/1.36 inference(cnf_transformation,[status(thm)],[f45])).
% 1.71/1.36 thf(f45,plain,(
% 1.71/1.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((eq @ X0 @ X3) != $true) | ((eq @ X1 @ X2) != $true) | ((moref @ X2 @ X3) = $true) | ((moref @ X1 @ X0) != $true))),
% 1.71/1.36 inference(rectify,[status(thm)],[f37])).
% 1.71/1.36 thf(f37,plain,(
% 1.71/1.36 ! [X1 : frac,X3 : frac,X2 : frac,X0 : frac] : (((eq @ X1 @ X0) != $true) | ((eq @ X3 @ X2) != $true) | ($true = (moref @ X2 @ X0)) | ((moref @ X3 @ X1) != $true))),
% 1.71/1.36 inference(flattening,[status(thm)],[f36])).
% 1.71/1.36 thf(f36,plain,(
% 1.71/1.36 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((($true = (moref @ X2 @ X0)) | ((eq @ X1 @ X0) != $true)) | ((eq @ X3 @ X2) != $true)) | ((moref @ X3 @ X1) != $true))),
% 1.71/1.36 inference(ennf_transformation,[status(thm)],[f19])).
% 1.71/1.36 thf(f19,plain,(
% 1.71/1.36 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((moref @ X3 @ X1) = $true) => (((eq @ X3 @ X2) = $true) => (((eq @ X1 @ X0) = $true) => ($true = (moref @ X2 @ X0)))))),
% 1.71/1.36 inference(fool_elimination,[status(thm)],[f18])).
% 1.71/1.36 thf(f18,plain,(
% 1.71/1.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X3 @ X1) => ((eq @ X3 @ X2) => ((eq @ X1 @ X0) => (moref @ X2 @ X0))))),
% 1.71/1.36 inference(rectify,[status(thm)],[f4])).
% 1.71/1.36 thf(f4,axiom,(
% 1.71/1.36 ! [X4 : frac,X2 : frac,X3 : frac,X1 : frac] : ((moref @ X1 @ X2) => ((eq @ X1 @ X3) => ((eq @ X2 @ X4) => (moref @ X3 @ X4))))),
% 1.71/1.36 file('/export/starexec/sandbox/tmp/tmp.kdjnnQlqPn/DTF2THF_22314.p',satz44)).
% 1.71/1.36 % SZS output end Proof for DTF2THF_22314
% 1.71/1.36 % (22509)------------------------------
% 1.71/1.36 % (22509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.36 % (22509)Termination reason: Refutation
% 1.71/1.36
% 1.71/1.36 % (22509)Memory used [KB]: 5628
% 1.71/1.36 % (22509)Time elapsed: 0.015 s
% 1.71/1.36 % (22509)Instructions burned: 19 (million)
% 1.71/1.36 % (22509)------------------------------
% 1.71/1.36 % (22509)------------------------------
% 1.71/1.36 % (22503)Success in time 0.028 s
%------------------------------------------------------------------------------