%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM767^1 : 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 : n003.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 09:24:39 AM UTC 2026
% Result : Theorem 1.65s 1.40s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 190 ( 56 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 258 ( 27 ~; 21 |; 0 &; 198 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 0 ^; 53 !; 0 ?; 53 :)
% 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,
v: frac ).
thf(func_def_4,type,
w: frac ).
thf(func_def_5,type,
eq: frac > frac > $o ).
thf(func_def_6,type,
pf: frac > frac > frac ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f94,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
$true != $true,
inference(superposition,[status(thm)],[f33,f88]) ).
thf(f88,plain,
( ( eq @ v @ w )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( eq @ v @ w )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f30,f84]) ).
thf(f84,plain,
( $true
= ( eq @ w @ v ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true != $true )
| ( $true
= ( eq @ w @ v ) ) ),
inference(superposition,[status(thm)],[f29,f62]) ).
thf(f62,plain,
( $true
= ( eq @ ( pf @ y @ w ) @ ( pf @ y @ v ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( $true
= ( eq @ ( pf @ y @ w ) @ ( pf @ y @ v ) ) ) ),
inference(superposition,[status(thm)],[f49,f32]) ).
thf(f32,plain,
( ( eq @ ( pf @ y @ w ) @ x )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( eq @ ( pf @ y @ w ) @ x )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
eq @ ( pf @ y @ w ) @ x,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
eq @ ( pf @ y @ w ) @ x,
file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',f) ).
thf(f49,plain,
! [X0: frac] :
( ( ( eq @ X0 @ x )
!= $true )
| ( $true
= ( eq @ X0 @ ( pf @ y @ v ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true
= ( eq @ X0 @ ( pf @ y @ v ) ) )
| ( ( eq @ X0 @ x )
!= $true ) ),
inference(superposition,[status(thm)],[f34,f38]) ).
thf(f38,plain,
( $true
= ( eq @ x @ ( pf @ y @ v ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true != $true )
| ( $true
= ( eq @ x @ ( pf @ y @ v ) ) ) ),
inference(superposition,[status(thm)],[f30,f31]) ).
thf(f31,plain,
( ( eq @ ( pf @ y @ v ) @ x )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( eq @ ( pf @ y @ v ) @ x )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
eq @ ( pf @ y @ v ) @ x,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
eq @ ( pf @ y @ v ) @ x,
file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',e) ).
thf(f34,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X2 @ X1 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X2 @ X1 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true )
| ( ( eq @ X0 @ X2 )
!= $true ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( ( eq @ X1 @ X2 )
= $true )
=> ( ( eq @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',satz39) ).
thf(f29,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) )
| ( ( eq @ X0 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( $true
!= ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: frac,X1: frac,X0: frac] :
( ( $true
= ( eq @ X2 @ X0 ) )
| ( ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X1 @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X1 @ X0 ) )
= $true )
=> ( $true
= ( eq @ X2 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X1 @ X0 ) )
=> ( eq @ X2 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: frac,X2: frac,X0: frac] :
( ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X2 @ X1 ) )
=> ( eq @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',satz63e) ).
thf(f30,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( eq @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',satz38) ).
thf(f33,plain,
( ( eq @ v @ w )
!= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( eq @ v @ w )
!= $true ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( eq @ v @ w )
!= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( eq @ v @ w ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( eq @ v @ w ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
eq @ v @ w,
file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',satz67b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM767^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n003.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 11:13:25 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : NUM767^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.40 % Domain : Number Theory
% 0.17/0.40 % Problem : Landau theorem 67b
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English : eq v w
% 0.17/0.40
% 0.17/0.40 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.17/0.40 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.17/0.40 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Bro09]
% 0.17/0.40 % Names : satz67b [Lan30]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % : Without extensionality : Theorem
% 0.17/0.40 % Rating : 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 v4.0.0, 0.00 v3.7.0
% 0.17/0.40 % Syntax : Number of formulae : 13 ( 3 unt; 7 typ; 0 def)
% 0.17/0.40 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 3 ( 1 avg)
% 0.17/0.40 % Number of connectives : 32 ( 0 ~; 0 |; 0 &; 28 @)
% 0.17/0.40 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 9 ( 6 avg)
% 0.17/0.40 % Number of types : 2 ( 1 usr)
% 0.17/0.40 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 6 ( 6 usr; 4 con; 0-2 aty)
% 0.17/0.40 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.17/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.40
% 0.17/0.40 % Comments :
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(frac_type,type,
% 0.17/0.40 frac: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(x,type,
% 0.17/0.40 x: frac ).
% 0.17/0.40
% 0.17/0.40 thf(y,type,
% 0.17/0.40 y: frac ).
% 0.17/0.40
% 0.17/0.40 thf(v,type,
% 0.17/0.40 v: frac ).
% 0.17/0.40
% 0.17/0.40 thf(w,type,
% 0.17/0.40 w: frac ).
% 0.17/0.40
% 0.17/0.40 thf(eq,type,
% 0.17/0.40 eq: frac > frac > $o ).
% 0.17/0.40
% 0.17/0.40 thf(pf,type,
% 0.17/0.40 pf: frac > frac > frac ).
% 0.17/0.40
% 0.17/0.40 thf(e,axiom,
% 0.17/0.40 eq @ ( pf @ y @ v ) @ x ).
% 0.17/0.40
% 0.17/0.40 thf(f,axiom,
% 0.17/0.40 eq @ ( pf @ y @ w ) @ x ).
% 0.17/0.40
% 0.17/0.40 thf(satz63e,axiom,
% 0.17/0.40 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.17/0.40 ( ( eq @ ( pf @ Xz @ Xx ) @ ( pf @ Xz @ Xy ) )
% 0.17/0.40 => ( eq @ Xx @ Xy ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(satz39,axiom,
% 0.17/0.40 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.17/0.40 ( ( eq @ Xx @ Xy )
% 0.17/0.40 => ( ( eq @ Xy @ Xz )
% 0.17/0.40 => ( eq @ Xx @ Xz ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(satz38,axiom,
% 0.17/0.40 ! [Xx: frac,Xy: frac] :
% 0.17/0.40 ( ( eq @ Xx @ Xy )
% 0.17/0.40 => ( eq @ Xy @ Xx ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(satz67b,conjecture,
% 0.17/0.40 eq @ v @ w ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.52/1.36 ---- Embedded in THF ---
% 1.52/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.36 %%% Generated on Tue Feb 24 11:13:26 EST 2026
% 1.52/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.36 %%% Logic specification used:
% 1.52/1.36 %%% thf(spec, logic, $$dhol).
% 1.52/1.36
% 1.52/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2DTF20047.p
% See solution above
% 1.52/1.36 ------------------------
% 1.52/1.37 ---- Cleaned THF ---
% 1.52/1.37 thf(frac_type,type,
% 1.52/1.37 frac: $tType ).
% 1.52/1.37
% 1.52/1.37 thf(x,type,
% 1.52/1.37 x: frac ).
% 1.52/1.37
% 1.52/1.37 thf(y,type,
% 1.52/1.37 y: frac ).
% 1.52/1.37
% 1.52/1.37 thf(v,type,
% 1.52/1.37 v: frac ).
% 1.52/1.37
% 1.52/1.37 thf(w,type,
% 1.52/1.37 w: frac ).
% 1.52/1.37
% 1.52/1.37 thf(eq,type,
% 1.52/1.37 eq: frac > frac > $o ).
% 1.52/1.37
% 1.52/1.37 thf(pf,type,
% 1.52/1.37 pf: frac > frac > frac ).
% 1.52/1.37
% 1.52/1.37 thf(e,axiom,
% 1.52/1.37 eq @ ( pf @ y @ v ) @ x ).
% 1.52/1.37
% 1.52/1.37 thf(f,axiom,
% 1.52/1.37 eq @ ( pf @ y @ w ) @ x ).
% 1.52/1.37
% 1.52/1.37 thf(satz63e,axiom,
% 1.52/1.37 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.52/1.37 ( ( eq @ ( pf @ Xz @ Xx ) @ ( pf @ Xz @ Xy ) )
% 1.52/1.37 => ( eq @ Xx @ Xy ) ) ).
% 1.52/1.37
% 1.52/1.37 thf(satz39,axiom,
% 1.52/1.37 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.52/1.37 ( ( eq @ Xx @ Xy )
% 1.52/1.37 => ( ( eq @ Xy @ Xz )
% 1.52/1.37 => ( eq @ Xx @ Xz ) ) ) ).
% 1.52/1.37
% 1.52/1.37 thf(satz38,axiom,
% 1.52/1.37 ! [Xx: frac,Xy: frac] :
% 1.52/1.37 ( ( eq @ Xx @ Xy )
% 1.52/1.37 => ( eq @ Xy @ Xx ) ) ).
% 1.52/1.37
% 1.52/1.37 thf(satz67b,conjecture,
% 1.52/1.37 eq @ v @ w ).
% 1.52/1.37 ------------------------
% 1.52/1.39 % (20150)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_20047 for (2999ds/275Mi)
% 1.52/1.39 % (20147)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_20047 for (2999ds/27Mi)
% 1.52/1.39 % (20145)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20047 for (2999ds/183Mi)
% 1.52/1.39 % (20149)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_20047 for (2999ds/2Mi)
% 1.52/1.39 % (20151)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20047 for (2999ds/18Mi)
% 1.52/1.39 % (20148)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20047 for (2999ds/2Mi)
% 1.52/1.39 % (20146)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_20047 for (2999ds/4Mi)
% 1.52/1.39 % (20148)Instruction limit reached!
% 1.52/1.39 % (20148)------------------------------
% 1.52/1.39 % (20148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.39 % (20148)Termination reason: Unknown
% 1.52/1.39 % (20148)Termination phase: Saturation
% 1.52/1.39 % (20149)Instruction limit reached!
% 1.52/1.39 % (20149)------------------------------
% 1.52/1.39 % (20149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.39
% 1.52/1.39 % (20148)Memory used [KB]: 5373
% 1.52/1.39 % (20148)Time elapsed: 0.003 s
% 1.52/1.39 % (20148)Instructions burned: 2 (million)
% 1.52/1.39 % (20148)------------------------------
% 1.52/1.39 % (20148)------------------------------
% 1.52/1.39 % (20149)Termination reason: Unknown
% 1.52/1.39 % (20149)Termination phase: Saturation
% 1.52/1.39
% 1.52/1.39 % (20149)Memory used [KB]: 1023
% 1.52/1.39 % (20149)Time elapsed: 0.003 s
% 1.52/1.39 % (20149)Instructions burned: 2 (million)
% 1.52/1.39 % (20149)------------------------------
% 1.52/1.39 % (20149)------------------------------
% 1.52/1.39 % (20146)Instruction limit reached!
% 1.52/1.39 % (20146)------------------------------
% 1.52/1.39 % (20146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.39 % (20146)Termination reason: Unknown
% 1.52/1.39 % (20146)Termination phase: Saturation
% 1.52/1.39
% 1.52/1.39 % (20146)Memory used [KB]: 5500
% 1.52/1.39 % (20146)Time elapsed: 0.004 s
% 1.52/1.39 % (20146)Instructions burned: 5 (million)
% 1.52/1.39 % (20146)------------------------------
% 1.52/1.39 % (20146)------------------------------
% 1.52/1.39 % (20147)First to succeed.
% 1.52/1.40 % (20151)Also succeeded, but the first one will report.
% 1.65/1.40 % (20147)Refutation found. Thanks to Tanya!
% 1.65/1.40 % SZS status Theorem for DTF2THF_20047
% 1.65/1.40 % SZS output start Proof for DTF2THF_20047
% 1.65/1.40 thf(type_def_5, type, frac: $tType).
% 1.65/1.40 thf(func_def_0, type, frac: $tType).
% 1.65/1.40 thf(func_def_1, type, x: frac).
% 1.65/1.40 thf(func_def_2, type, y: frac).
% 1.65/1.40 thf(func_def_3, type, v: frac).
% 1.65/1.40 thf(func_def_4, type, w: frac).
% 1.65/1.40 thf(func_def_5, type, eq: frac > frac > $o).
% 1.65/1.40 thf(func_def_6, type, pf: frac > frac > frac).
% 1.65/1.40 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.65/1.40 thf(f94,plain,(
% 1.65/1.40 $false),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.65/1.40 thf(f89,plain,(
% 1.65/1.40 ($true != $true)),
% 1.65/1.40 inference(superposition,[status(thm)],[f33,f88])).
% 1.65/1.40 thf(f88,plain,(
% 1.65/1.40 ((eq @ v @ w) = $true)),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.65/1.40 thf(f86,plain,(
% 1.65/1.40 ((eq @ v @ w) = $true) | ($true != $true)),
% 1.65/1.40 inference(superposition,[status(thm)],[f30,f84])).
% 1.65/1.40 thf(f84,plain,(
% 1.65/1.40 ($true = (eq @ w @ v))),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.65/1.40 thf(f77,plain,(
% 1.65/1.40 ($true != $true) | ($true = (eq @ w @ v))),
% 1.65/1.40 inference(superposition,[status(thm)],[f29,f62])).
% 1.65/1.40 thf(f62,plain,(
% 1.65/1.40 ($true = (eq @ (pf @ y @ w) @ (pf @ y @ v)))),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.65/1.40 thf(f58,plain,(
% 1.65/1.40 ($true != $true) | ($true = (eq @ (pf @ y @ w) @ (pf @ y @ v)))),
% 1.65/1.40 inference(superposition,[status(thm)],[f49,f32])).
% 1.65/1.40 thf(f32,plain,(
% 1.65/1.40 ((eq @ (pf @ y @ w) @ x) = $true)),
% 1.65/1.40 inference(cnf_transformation,[status(thm)],[f14])).
% 1.65/1.40 thf(f14,plain,(
% 1.65/1.40 ((eq @ (pf @ y @ w) @ x) = $true)),
% 1.65/1.40 inference(fool_elimination,[status(thm)],[f13])).
% 1.65/1.40 thf(f13,plain,(
% 1.65/1.40 (eq @ (pf @ y @ w) @ x)),
% 1.65/1.40 inference(rectify,[status(thm)],[f2])).
% 1.65/1.40 thf(f2,axiom,(
% 1.65/1.40 (eq @ (pf @ y @ w) @ x)),
% 1.65/1.40 file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',f)).
% 1.65/1.40 thf(f49,plain,(
% 1.65/1.40 ( ! [X0 : frac] : (((eq @ X0 @ x) != $true) | ($true = (eq @ X0 @ (pf @ y @ v)))) )),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.65/1.40 thf(f46,plain,(
% 1.65/1.40 ( ! [X0 : frac] : (($true != $true) | ($true = (eq @ X0 @ (pf @ y @ v))) | ((eq @ X0 @ x) != $true)) )),
% 1.65/1.40 inference(superposition,[status(thm)],[f34,f38])).
% 1.65/1.40 thf(f38,plain,(
% 1.65/1.40 ($true = (eq @ x @ (pf @ y @ v)))),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.65/1.40 thf(f35,plain,(
% 1.65/1.40 ($true != $true) | ($true = (eq @ x @ (pf @ y @ v)))),
% 1.65/1.40 inference(superposition,[status(thm)],[f30,f31])).
% 1.65/1.40 thf(f31,plain,(
% 1.65/1.40 ((eq @ (pf @ y @ v) @ x) = $true)),
% 1.65/1.40 inference(cnf_transformation,[status(thm)],[f10])).
% 1.65/1.40 thf(f10,plain,(
% 1.65/1.40 ((eq @ (pf @ y @ v) @ x) = $true)),
% 1.65/1.40 inference(fool_elimination,[status(thm)],[f9])).
% 1.65/1.40 thf(f9,plain,(
% 1.65/1.40 (eq @ (pf @ y @ v) @ x)),
% 1.65/1.40 inference(rectify,[status(thm)],[f1])).
% 1.65/1.40 thf(f1,axiom,(
% 1.65/1.40 (eq @ (pf @ y @ v) @ x)),
% 1.65/1.40 file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',e)).
% 1.65/1.40 thf(f34,plain,(
% 1.65/1.40 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X2 @ X1) != $true) | ((eq @ X0 @ X2) != $true) | ((eq @ X0 @ X1) = $true)) )),
% 1.65/1.40 inference(cnf_transformation,[status(thm)],[f28])).
% 1.65/1.40 thf(f28,plain,(
% 1.65/1.40 ! [X0 : frac,X1 : frac,X2 : frac] : (((eq @ X2 @ X1) != $true) | ((eq @ X0 @ X1) = $true) | ((eq @ X0 @ X2) != $true))),
% 1.65/1.40 inference(rectify,[status(thm)],[f23])).
% 1.65/1.40 thf(f23,plain,(
% 1.65/1.40 ! [X0 : frac,X2 : frac,X1 : frac] : (((eq @ X1 @ X2) != $true) | ((eq @ X0 @ X2) = $true) | ((eq @ X0 @ X1) != $true))),
% 1.65/1.40 inference(flattening,[status(thm)],[f22])).
% 1.65/1.40 thf(f22,plain,(
% 1.65/1.40 ! [X0 : frac,X1 : frac,X2 : frac] : ((((eq @ X0 @ X2) = $true) | ((eq @ X1 @ X2) != $true)) | ((eq @ X0 @ X1) != $true))),
% 1.65/1.40 inference(ennf_transformation,[status(thm)],[f18])).
% 1.65/1.40 thf(f18,plain,(
% 1.65/1.40 ! [X0 : frac,X1 : frac,X2 : frac] : (((eq @ X0 @ X1) = $true) => (((eq @ X1 @ X2) = $true) => ((eq @ X0 @ X2) = $true)))),
% 1.65/1.40 inference(fool_elimination,[status(thm)],[f17])).
% 1.65/1.40 thf(f17,plain,(
% 1.65/1.40 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X1) => ((eq @ X1 @ X2) => (eq @ X0 @ X2)))),
% 1.65/1.40 inference(rectify,[status(thm)],[f4])).
% 1.65/1.40 thf(f4,axiom,(
% 1.65/1.40 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X1) => ((eq @ X1 @ X2) => (eq @ X0 @ X2)))),
% 1.65/1.40 file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',satz39)).
% 1.65/1.40 thf(f29,plain,(
% 1.65/1.40 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (eq @ (pf @ X1 @ X0) @ (pf @ X1 @ X2))) | ((eq @ X0 @ X2) = $true)) )),
% 1.65/1.40 inference(cnf_transformation,[status(thm)],[f26])).
% 1.65/1.40 thf(f26,plain,(
% 1.65/1.40 ! [X0 : frac,X1 : frac,X2 : frac] : (((eq @ X0 @ X2) = $true) | ($true != (eq @ (pf @ X1 @ X0) @ (pf @ X1 @ X2))))),
% 1.65/1.40 inference(rectify,[status(thm)],[f25])).
% 1.65/1.40 thf(f25,plain,(
% 1.65/1.40 ! [X2 : frac,X1 : frac,X0 : frac] : (($true = (eq @ X2 @ X0)) | ((eq @ (pf @ X1 @ X2) @ (pf @ X1 @ X0)) != $true))),
% 1.65/1.40 inference(ennf_transformation,[status(thm)],[f16])).
% 1.65/1.40 thf(f16,plain,(
% 1.65/1.40 ! [X1 : frac,X0 : frac,X2 : frac] : (((eq @ (pf @ X1 @ X2) @ (pf @ X1 @ X0)) = $true) => ($true = (eq @ X2 @ X0)))),
% 1.65/1.40 inference(fool_elimination,[status(thm)],[f15])).
% 1.65/1.40 thf(f15,plain,(
% 1.65/1.40 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ (pf @ X1 @ X2) @ (pf @ X1 @ X0)) => (eq @ X2 @ X0))),
% 1.65/1.40 inference(rectify,[status(thm)],[f3])).
% 1.65/1.40 thf(f3,axiom,(
% 1.65/1.40 ! [X1 : frac,X2 : frac,X0 : frac] : ((eq @ (pf @ X2 @ X0) @ (pf @ X2 @ X1)) => (eq @ X0 @ X1))),
% 1.65/1.40 file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',satz63e)).
% 1.65/1.40 thf(f30,plain,(
% 1.65/1.40 ( ! [X0 : frac,X1 : frac] : (((eq @ X1 @ X0) != $true) | ((eq @ X0 @ X1) = $true)) )),
% 1.65/1.40 inference(cnf_transformation,[status(thm)],[f27])).
% 1.65/1.40 thf(f27,plain,(
% 1.65/1.40 ! [X0 : frac,X1 : frac] : (((eq @ X1 @ X0) != $true) | ((eq @ X0 @ X1) = $true))),
% 1.65/1.40 inference(rectify,[status(thm)],[f24])).
% 1.65/1.40 thf(f24,plain,(
% 1.65/1.40 ! [X1 : frac,X0 : frac] : (((eq @ X0 @ X1) != $true) | ((eq @ X1 @ X0) = $true))),
% 1.65/1.40 inference(ennf_transformation,[status(thm)],[f20])).
% 1.65/1.40 thf(f20,plain,(
% 1.65/1.40 ! [X1 : frac,X0 : frac] : (((eq @ X0 @ X1) = $true) => ((eq @ X1 @ X0) = $true))),
% 1.65/1.40 inference(fool_elimination,[status(thm)],[f19])).
% 1.65/1.40 thf(f19,plain,(
% 1.65/1.40 ! [X0 : frac,X1 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 1.65/1.40 inference(rectify,[status(thm)],[f5])).
% 1.65/1.40 thf(f5,axiom,(
% 1.65/1.40 ! [X0 : frac,X1 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 1.65/1.40 file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',satz38)).
% 1.65/1.40 thf(f33,plain,(
% 1.65/1.40 ((eq @ v @ w) != $true)),
% 1.65/1.40 inference(cnf_transformation,[status(thm)],[f21])).
% 1.65/1.40 thf(f21,plain,(
% 1.65/1.40 ((eq @ v @ w) != $true)),
% 1.65/1.40 inference(flattening,[status(thm)],[f12])).
% 1.65/1.40 thf(f12,plain,(
% 1.65/1.40 ~((eq @ v @ w) = $true)),
% 1.65/1.40 inference(fool_elimination,[status(thm)],[f11])).
% 1.65/1.40 thf(f11,plain,(
% 1.65/1.40 ~(eq @ v @ w)),
% 1.65/1.40 inference(rectify,[status(thm)],[f7])).
% 1.65/1.40 thf(f7,negated_conjecture,(
% 1.65/1.40 ~(eq @ v @ w)),
% 1.65/1.40 inference(negated_conjecture,[status(cth)],[f6])).
% 1.65/1.40 thf(f6,conjecture,(
% 1.65/1.40 (eq @ v @ w)),
% 1.65/1.40 file('/export/starexec/sandbox/tmp/tmp.FKgIzL9lbl/DTF2THF_20047.p',satz67b)).
% 1.65/1.40 % SZS output end Proof for DTF2THF_20047
% 1.65/1.40 % (20147)------------------------------
% 1.65/1.40 % (20147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (20147)Termination reason: Refutation
% 1.65/1.40
% 1.65/1.40 % (20147)Memory used [KB]: 5500
% 1.65/1.40 % (20147)Time elapsed: 0.009 s
% 1.65/1.40 % (20147)Instructions burned: 9 (million)
% 1.65/1.40 % (20147)------------------------------
% 1.65/1.40 % (20147)------------------------------
% 1.65/1.40 % (20144)Success in time 0.024 s
%------------------------------------------------------------------------------