%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM751^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.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 09:24:33 AM UTC 2026
% Result : Theorem 1.68s 1.33s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 55 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 307 ( 40 ~; 27 |; 0 &; 228 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% 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,
moref: frac > frac > $o ).
thf(func_def_6,type,
pf: frac > frac > frac ).
thf(func_def_7,type,
eq: frac > frac > $o ).
thf(f39,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f38,f27]) ).
thf(f27,plain,
( ( moref @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( moref @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
moref @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
moref @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',m) ).
thf(f38,plain,
( ( moref @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true != $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f36,f28]) ).
thf(f28,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X0 @ X1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X0 @ X1 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: frac,X1: frac] : ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: frac,X0: frac] : ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',satz58) ).
thf(f36,plain,
! [X0: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ z ) @ ( pf @ z @ x ) ) )
| ( ( moref @ X0 @ y )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ z ) @ ( pf @ z @ x ) ) )
| ( ( moref @ X0 @ y )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f32,f25]) ).
thf(f25,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: frac,X1: frac,X0: frac] :
( ( $true
= ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) )
| ( $true
!= ( moref @ X2 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ X2 @ X1 ) )
=> ( $true
= ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X2 @ X1 )
=> ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: frac,X1: frac,X0: frac] :
( ( moref @ X0 @ X1 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',satz62a) ).
thf(f32,plain,
! [X0: frac] :
( ( $true
!= ( moref @ X0 @ ( pf @ y @ z ) ) )
| ( ( eq @ X0 @ ( pf @ z @ x ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true
!= ( moref @ X0 @ ( pf @ y @ z ) ) )
| ( ( eq @ X0 @ ( pf @ z @ x ) )
!= $true ) ),
inference(superposition,[status(thm)],[f30,f28]) ).
thf(f30,plain,
! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X1 @ ( pf @ z @ y ) ) )
| ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X0 @ ( pf @ z @ x ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: frac,X1: frac] :
( ( $true != $true )
| ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X0 @ ( pf @ z @ x ) )
!= $true )
| ( $true
!= ( eq @ X1 @ ( pf @ z @ y ) ) ) ),
inference(superposition,[status(thm)],[f26,f24]) ).
thf(f24,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ X2 @ X1 ) )
| ( ( moref @ X3 @ X0 )
!= $true )
| ( ( eq @ X3 @ X2 )
!= $true )
| ( $true
!= ( eq @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
!= ( eq @ X0 @ X1 ) )
| ( $true
= ( moref @ X2 @ X1 ) )
| ( ( eq @ X3 @ X2 )
!= $true )
| ( ( moref @ X3 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: frac,X0: frac,X3: frac,X2: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( moref @ X3 @ X0 )
= $true )
| ( $true
!= ( eq @ X2 @ X3 ) )
| ( $true
!= ( moref @ X2 @ X1 ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ X3 @ X0 )
= $true )
| ( ( eq @ X1 @ X0 )
!= $true )
| ( $true
!= ( eq @ X2 @ X3 ) )
| ( $true
!= ( moref @ X2 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ X2 @ X1 ) )
=> ( ( $true
= ( eq @ X2 @ X3 ) )
=> ( ( ( eq @ X1 @ X0 )
= $true )
=> ( ( moref @ X3 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X2 @ X1 )
=> ( ( eq @ X2 @ X3 )
=> ( ( eq @ X1 @ X0 )
=> ( moref @ X3 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X3: frac,X1: frac,X0: frac,X2: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',satz44) ).
thf(f26,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= $true ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
moref @ ( pf @ z @ x ) @ ( pf @ z @ y ),
file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',satz62d) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM751^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 11:12:59 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : NUM751^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Number Theory
% 0.29/0.46 % Problem : Landau theorem 62d
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : moref (pf z x) (pf z y)
% 0.29/0.46
% 0.29/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.29/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : satz62d [Lan30]
% 0.29/0.46 % : satz72d [Lan30]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % : Without extensionality : Theorem
% 0.29/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.5.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v4.1.0, 0.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 12 ( 3 unt; 7 typ; 0 def)
% 0.29/0.46 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.29/0.46 % Number of connectives : 34 ( 0 ~; 0 |; 0 &; 30 @)
% 0.29/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 10 ( 7 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(frac_type,type,
% 0.29/0.46 frac: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(x,type,
% 0.29/0.46 x: frac ).
% 0.29/0.46
% 0.29/0.46 thf(y,type,
% 0.29/0.46 y: frac ).
% 0.29/0.46
% 0.29/0.46 thf(z,type,
% 0.29/0.46 z: frac ).
% 0.29/0.46
% 0.29/0.46 thf(moref,type,
% 0.29/0.46 moref: frac > frac > $o ).
% 0.29/0.46
% 0.29/0.46 thf(m,axiom,
% 0.29/0.46 moref @ x @ y ).
% 0.29/0.46
% 0.29/0.46 thf(pf,type,
% 0.29/0.46 pf: frac > frac > frac ).
% 0.29/0.46
% 0.29/0.46 thf(eq,type,
% 0.29/0.46 eq: frac > frac > $o ).
% 0.29/0.46
% 0.29/0.46 thf(satz44,axiom,
% 0.29/0.46 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.29/0.46 ( ( moref @ Xx @ Xy )
% 0.29/0.46 => ( ( eq @ Xx @ Xz )
% 0.29/0.46 => ( ( eq @ Xy @ Xu )
% 0.29/0.46 => ( moref @ Xz @ Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz62a,axiom,
% 0.29/0.46 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.29/0.46 ( ( moref @ Xx @ Xy )
% 0.29/0.46 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz58,axiom,
% 0.29/0.46 ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(satz62d,conjecture,
% 0.29/0.46 moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.46/1.29 ---- Embedded in THF ---
% 1.46/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.29 %%% Generated on Tue Feb 24 11:13:00 EST 2026
% 1.46/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.29 %%% Logic specification used:
% 1.46/1.29 %%% thf(spec, logic, $$dhol).
% 1.46/1.29
% 1.46/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2DTF9297.p
% See solution above
% 1.46/1.29 ------------------------
% 1.46/1.30 ---- Cleaned THF ---
% 1.68/1.30 thf(frac_type,type,
% 1.68/1.30 frac: $tType ).
% 1.68/1.30
% 1.68/1.30 thf(x,type,
% 1.68/1.30 x: frac ).
% 1.68/1.30
% 1.68/1.30 thf(y,type,
% 1.68/1.30 y: frac ).
% 1.68/1.30
% 1.68/1.30 thf(z,type,
% 1.68/1.30 z: frac ).
% 1.68/1.30
% 1.68/1.30 thf(moref,type,
% 1.68/1.30 moref: frac > frac > $o ).
% 1.68/1.30
% 1.68/1.30 thf(m,axiom,
% 1.68/1.30 moref @ x @ y ).
% 1.68/1.30
% 1.68/1.30 thf(pf,type,
% 1.68/1.30 pf: frac > frac > frac ).
% 1.68/1.30
% 1.68/1.30 thf(eq,type,
% 1.68/1.30 eq: frac > frac > $o ).
% 1.68/1.30
% 1.68/1.30 thf(satz44,axiom,
% 1.68/1.30 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.68/1.30 ( ( moref @ Xx @ Xy )
% 1.68/1.30 => ( ( eq @ Xx @ Xz )
% 1.68/1.30 => ( ( eq @ Xy @ Xu )
% 1.68/1.30 => ( moref @ Xz @ Xu ) ) ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(satz62a,axiom,
% 1.68/1.30 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.68/1.30 ( ( moref @ Xx @ Xy )
% 1.68/1.30 => ( moref @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(satz58,axiom,
% 1.68/1.30 ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(satz62d,conjecture,
% 1.68/1.30 moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) ).
% 1.68/1.30 ------------------------
% 1.68/1.32 % (9458)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9297 for (2999ds/18Mi)
% 1.68/1.32 % (9457)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_9297 for (2999ds/275Mi)
% 1.68/1.32 % (9452)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9297 for (2999ds/183Mi)
% 1.68/1.32 % (9457)Refutation not found, incomplete strategy
% 1.68/1.32 % (9457)------------------------------
% 1.68/1.32 % (9457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (9457)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.32
% 1.68/1.32
% 1.68/1.32 % (9457)Memory used [KB]: 5500
% 1.68/1.32 % (9457)Time elapsed: 0.003 s
% 1.68/1.32 % (9457)Instructions burned: 2 (million)
% 1.68/1.32 % (9457)------------------------------
% 1.68/1.32 % (9457)------------------------------
% 1.68/1.33 % (9456)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_9297 for (2999ds/2Mi)
% 1.68/1.33 % (9455)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9297 for (2999ds/2Mi)
% 1.68/1.33 % (9456)Instruction limit reached!
% 1.68/1.33 % (9456)------------------------------
% 1.68/1.33 % (9456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (9456)Termination reason: Unknown
% 1.68/1.33 % (9456)Termination phase: Naming
% 1.68/1.33
% 1.68/1.33 % (9455)Instruction limit reached!
% 1.68/1.33 % (9455)------------------------------
% 1.68/1.33 % (9455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (9456)Memory used [KB]: 895
% 1.68/1.33 % (9456)Time elapsed: 0.003 s
% 1.68/1.33 % (9456)Instructions burned: 2 (million)
% 1.68/1.33 % (9456)------------------------------
% 1.68/1.33 % (9456)------------------------------
% 1.68/1.33 % (9455)Termination reason: Unknown
% 1.68/1.33 % (9455)Termination phase: Saturation
% 1.68/1.33
% 1.68/1.33 % (9455)Memory used [KB]: 895
% 1.68/1.33 % (9455)Time elapsed: 0.002 s
% 1.68/1.33 % (9455)Instructions burned: 2 (million)
% 1.68/1.33 % (9455)------------------------------
% 1.68/1.33 % (9455)------------------------------
% 1.68/1.33 % (9453)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_9297 for (2999ds/4Mi)
% 1.68/1.33 % (9452)First to succeed.
% 1.68/1.33 % (9458)Also succeeded, but the first one will report.
% 1.68/1.33 % (9453)Instruction limit reached!
% 1.68/1.33 % (9453)------------------------------
% 1.68/1.33 % (9453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (9453)Termination reason: Unknown
% 1.68/1.33 % (9453)Termination phase: Saturation
% 1.68/1.33
% 1.68/1.33 % (9453)Memory used [KB]: 5500
% 1.68/1.33 % (9453)Time elapsed: 0.003 s
% 1.68/1.33 % (9453)Instructions burned: 4 (million)
% 1.68/1.33 % (9453)------------------------------
% 1.68/1.33 % (9453)------------------------------
% 1.68/1.33 % (9452)Refutation found. Thanks to Tanya!
% 1.68/1.33 % SZS status Theorem for DTF2THF_9297
% 1.68/1.33 % SZS output start Proof for DTF2THF_9297
% 1.68/1.33 thf(type_def_5, type, frac: $tType).
% 1.68/1.33 thf(func_def_0, type, frac: $tType).
% 1.68/1.33 thf(func_def_1, type, x: frac).
% 1.68/1.33 thf(func_def_2, type, y: frac).
% 1.68/1.33 thf(func_def_3, type, z: frac).
% 1.68/1.33 thf(func_def_4, type, moref: frac > frac > $o).
% 1.68/1.33 thf(func_def_6, type, pf: frac > frac > frac).
% 1.68/1.33 thf(func_def_7, type, eq: frac > frac > $o).
% 1.68/1.33 thf(f39,plain,(
% 1.68/1.33 $false),
% 1.68/1.33 inference(subsumption_resolution,[status(thm)],[f38,f27])).
% 1.68/1.33 thf(f27,plain,(
% 1.68/1.33 ((moref @ x @ y) = $true)),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f15])).
% 1.68/1.33 thf(f15,plain,(
% 1.68/1.33 ((moref @ x @ y) = $true)),
% 1.68/1.33 inference(fool_elimination,[status(thm)],[f14])).
% 1.68/1.33 thf(f14,plain,(
% 1.68/1.33 (moref @ x @ y)),
% 1.68/1.33 inference(rectify,[status(thm)],[f1])).
% 1.68/1.33 thf(f1,axiom,(
% 1.68/1.33 (moref @ x @ y)),
% 1.68/1.33 file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',m)).
% 1.68/1.33 thf(f38,plain,(
% 1.68/1.33 ((moref @ x @ y) != $true)),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.68/1.33 thf(f37,plain,(
% 1.68/1.33 ($true != $true) | ((moref @ x @ y) != $true)),
% 1.68/1.33 inference(superposition,[status(thm)],[f36,f28])).
% 1.68/1.33 thf(f28,plain,(
% 1.68/1.33 ( ! [X0 : frac,X1 : frac] : (((eq @ (pf @ X1 @ X0) @ (pf @ X0 @ X1)) = $true)) )),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.33 thf(f11,plain,(
% 1.68/1.33 ! [X0 : frac,X1 : frac] : ((eq @ (pf @ X1 @ X0) @ (pf @ X0 @ X1)) = $true)),
% 1.68/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.68/1.33 thf(f10,plain,(
% 1.68/1.33 ! [X0 : frac,X1 : frac] : (eq @ (pf @ X1 @ X0) @ (pf @ X0 @ X1))),
% 1.68/1.33 inference(rectify,[status(thm)],[f4])).
% 1.68/1.33 thf(f4,axiom,(
% 1.68/1.33 ! [X1 : frac,X0 : frac] : (eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))),
% 1.68/1.33 file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',satz58)).
% 1.68/1.33 thf(f36,plain,(
% 1.68/1.33 ( ! [X0 : frac] : (($true != (eq @ (pf @ X0 @ z) @ (pf @ z @ x))) | ((moref @ X0 @ y) != $true)) )),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.68/1.33 thf(f33,plain,(
% 1.68/1.33 ( ! [X0 : frac] : (($true != (eq @ (pf @ X0 @ z) @ (pf @ z @ x))) | ((moref @ X0 @ y) != $true) | ($true != $true)) )),
% 1.68/1.33 inference(superposition,[status(thm)],[f32,f25])).
% 1.68/1.33 thf(f25,plain,(
% 1.68/1.33 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)) = $true) | ((moref @ X0 @ X1) != $true)) )),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f23])).
% 1.68/1.33 thf(f23,plain,(
% 1.68/1.33 ! [X0 : frac,X1 : frac,X2 : frac] : (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)) = $true) | ((moref @ X0 @ X1) != $true))),
% 1.68/1.33 inference(rectify,[status(thm)],[f21])).
% 1.68/1.33 thf(f21,plain,(
% 1.68/1.33 ! [X2 : frac,X1 : frac,X0 : frac] : (($true = (moref @ (pf @ X2 @ X0) @ (pf @ X1 @ X0))) | ($true != (moref @ X2 @ X1)))),
% 1.68/1.33 inference(ennf_transformation,[status(thm)],[f13])).
% 1.68/1.33 thf(f13,plain,(
% 1.68/1.33 ! [X2 : frac,X0 : frac,X1 : frac] : (($true = (moref @ X2 @ X1)) => ($true = (moref @ (pf @ X2 @ X0) @ (pf @ X1 @ X0))))),
% 1.68/1.33 inference(fool_elimination,[status(thm)],[f12])).
% 1.68/1.33 thf(f12,plain,(
% 1.68/1.33 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X2 @ X1) => (moref @ (pf @ X2 @ X0) @ (pf @ X1 @ X0)))),
% 1.68/1.33 inference(rectify,[status(thm)],[f3])).
% 1.68/1.33 thf(f3,axiom,(
% 1.68/1.33 ! [X2 : frac,X1 : frac,X0 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 1.68/1.33 file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',satz62a)).
% 1.68/1.33 thf(f32,plain,(
% 1.68/1.33 ( ! [X0 : frac] : (($true != (moref @ X0 @ (pf @ y @ z))) | ((eq @ X0 @ (pf @ z @ x)) != $true)) )),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.68/1.33 thf(f31,plain,(
% 1.68/1.33 ( ! [X0 : frac] : (($true != $true) | ($true != (moref @ X0 @ (pf @ y @ z))) | ((eq @ X0 @ (pf @ z @ x)) != $true)) )),
% 1.68/1.33 inference(superposition,[status(thm)],[f30,f28])).
% 1.68/1.33 thf(f30,plain,(
% 1.68/1.33 ( ! [X0 : frac,X1 : frac] : (($true != (eq @ X1 @ (pf @ z @ y))) | ((moref @ X0 @ X1) != $true) | ((eq @ X0 @ (pf @ z @ x)) != $true)) )),
% 1.68/1.33 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.68/1.33 thf(f29,plain,(
% 1.68/1.33 ( ! [X0 : frac,X1 : frac] : (($true != $true) | ((moref @ X0 @ X1) != $true) | ((eq @ X0 @ (pf @ z @ x)) != $true) | ($true != (eq @ X1 @ (pf @ z @ y)))) )),
% 1.68/1.33 inference(superposition,[status(thm)],[f26,f24])).
% 1.68/1.33 thf(f24,plain,(
% 1.68/1.33 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true = (moref @ X2 @ X1)) | ((moref @ X3 @ X0) != $true) | ((eq @ X3 @ X2) != $true) | ($true != (eq @ X0 @ X1))) )),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f22])).
% 1.68/1.33 thf(f22,plain,(
% 1.68/1.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (($true != (eq @ X0 @ X1)) | ($true = (moref @ X2 @ X1)) | ((eq @ X3 @ X2) != $true) | ((moref @ X3 @ X0) != $true))),
% 1.68/1.33 inference(rectify,[status(thm)],[f20])).
% 1.68/1.33 thf(f20,plain,(
% 1.68/1.33 ! [X1 : frac,X0 : frac,X3 : frac,X2 : frac] : (((eq @ X1 @ X0) != $true) | ((moref @ X3 @ X0) = $true) | ($true != (eq @ X2 @ X3)) | ($true != (moref @ X2 @ X1)))),
% 1.68/1.33 inference(flattening,[status(thm)],[f19])).
% 1.68/1.33 thf(f19,plain,(
% 1.68/1.33 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (((((moref @ X3 @ X0) = $true) | ((eq @ X1 @ X0) != $true)) | ($true != (eq @ X2 @ X3))) | ($true != (moref @ X2 @ X1)))),
% 1.68/1.33 inference(ennf_transformation,[status(thm)],[f17])).
% 1.68/1.33 thf(f17,plain,(
% 1.68/1.33 ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true = (moref @ X2 @ X1)) => (($true = (eq @ X2 @ X3)) => (((eq @ X1 @ X0) = $true) => ((moref @ X3 @ X0) = $true))))),
% 1.68/1.33 inference(fool_elimination,[status(thm)],[f16])).
% 1.68/1.33 thf(f16,plain,(
% 1.68/1.33 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X2 @ X1) => ((eq @ X2 @ X3) => ((eq @ X1 @ X0) => (moref @ X3 @ X0))))),
% 1.68/1.33 inference(rectify,[status(thm)],[f2])).
% 1.68/1.33 thf(f2,axiom,(
% 1.68/1.33 ! [X3 : frac,X1 : frac,X0 : frac,X2 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 1.68/1.33 file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',satz44)).
% 1.68/1.33 thf(f26,plain,(
% 1.68/1.33 ((moref @ (pf @ z @ x) @ (pf @ z @ y)) != $true)),
% 1.68/1.33 inference(cnf_transformation,[status(thm)],[f18])).
% 1.68/1.33 thf(f18,plain,(
% 1.68/1.33 ((moref @ (pf @ z @ x) @ (pf @ z @ y)) != $true)),
% 1.68/1.33 inference(flattening,[status(thm)],[f9])).
% 1.68/1.33 thf(f9,plain,(
% 1.68/1.33 ~((moref @ (pf @ z @ x) @ (pf @ z @ y)) = $true)),
% 1.68/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.68/1.33 thf(f8,plain,(
% 1.68/1.33 ~(moref @ (pf @ z @ x) @ (pf @ z @ y))),
% 1.68/1.33 inference(rectify,[status(thm)],[f6])).
% 1.68/1.33 thf(f6,negated_conjecture,(
% 1.68/1.33 ~(moref @ (pf @ z @ x) @ (pf @ z @ y))),
% 1.68/1.33 inference(negated_conjecture,[status(cth)],[f5])).
% 1.68/1.33 thf(f5,conjecture,(
% 1.68/1.33 (moref @ (pf @ z @ x) @ (pf @ z @ y))),
% 1.68/1.33 file('/export/starexec/sandbox2/tmp/tmp.GQ0f0wHitb/DTF2THF_9297.p',satz62d)).
% 1.68/1.33 % SZS output end Proof for DTF2THF_9297
% 1.68/1.33 % (9452)------------------------------
% 1.68/1.33 % (9452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (9452)Termination reason: Refutation
% 1.68/1.33
% 1.68/1.33 % (9452)Memory used [KB]: 5500
% 1.68/1.33 % (9452)Time elapsed: 0.007 s
% 1.68/1.33 % (9452)Instructions burned: 5 (million)
% 1.68/1.33 % (9452)------------------------------
% 1.68/1.33 % (9452)------------------------------
% 1.68/1.33 % (9451)Success in time 0.023 s
%------------------------------------------------------------------------------