%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM759^1 : 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 : n025.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 09:24:36 AM UTC 2026
% Result : Theorem 1.61s 1.31s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 50 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 270 ( 25 ~; 20 |; 0 &; 216 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% 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,
eq: frac > frac > $o ).
thf(func_def_5,type,
pf: frac > frac > frac ).
thf(f63,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f60,f26]) ).
thf(f26,plain,
( ( eq @ x @ y )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( eq @ x @ y )
!= $true ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( eq @ x @ y )
!= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( eq @ x @ y ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( eq @ x @ y ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
eq @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',satz63e) ).
thf(f60,plain,
( ( eq @ x @ y )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( eq @ x @ y )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f28,f49]) ).
thf(f49,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true != $true )
| ( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ) ),
inference(superposition,[status(thm)],[f33,f41]) ).
thf(f41,plain,
( ( eq @ ( pf @ x @ z ) @ ( pf @ z @ y ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true != $true )
| ( ( eq @ ( pf @ x @ z ) @ ( pf @ z @ y ) )
= $true ) ),
inference(superposition,[status(thm)],[f32,f25]) ).
thf(f25,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X0 @ X1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X0 @ X1 ) )
= $true ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: frac,X0: frac] :
( ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: frac,X1: frac] : ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: frac,X1: frac] : ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',satz58) ).
thf(f32,plain,
! [X0: frac] :
( ( ( eq @ X0 @ ( pf @ z @ x ) )
!= $true )
| ( ( eq @ X0 @ ( pf @ z @ y ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: frac] :
( ( $true != $true )
| ( ( eq @ X0 @ ( pf @ z @ x ) )
!= $true )
| ( ( eq @ X0 @ ( pf @ z @ y ) )
= $true ) ),
inference(superposition,[status(thm)],[f29,f27]) ).
thf(f27,plain,
( ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
eq @ ( pf @ z @ x ) @ ( pf @ z @ y ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
eq @ ( pf @ z @ x ) @ ( pf @ z @ y ),
file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',e) ).
thf(f29,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X2 @ X0 )
!= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X2 @ X0 )
!= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( ( eq @ X2 @ X1 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
| ( ( eq @ X2 @ X1 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
=> ( ( ( eq @ X2 @ X1 )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X2 )
=> ( ( eq @ X2 @ X1 )
=> ( eq @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: frac,X2: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',satz39) ).
thf(f33,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X2 @ ( pf @ X0 @ X1 ) )
!= $true )
| ( ( eq @ X2 @ ( pf @ X1 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( ( eq @ X2 @ ( pf @ X1 @ X0 ) )
= $true )
| ( ( eq @ X2 @ ( pf @ X0 @ X1 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f29,f25]) ).
thf(f28,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( ( eq @ X0 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( ( eq @ X0 @ X2 )
= $true ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: frac,X1: frac,X0: frac] :
( ( ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
=> ( eq @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
=> ( eq @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',satz63b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM759^1 : 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 : n025.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 11:13:12 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
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : NUM759^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.47 % Domain : Number Theory
% 0.27/0.47 % Problem : Landau theorem 63e
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English : eq x y
% 0.27/0.47
% 0.27/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.27/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.27/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : satz63e [Lan30]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % : Without extensionality : Theorem
% 0.27/0.47 % 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, 0.00 v5.3.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.27/0.47 % Syntax : Number of formulae : 11 ( 3 unt; 6 typ; 0 def)
% 0.27/0.47 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 3 ( 1 avg)
% 0.27/0.47 % Number of connectives : 31 ( 0 ~; 0 |; 0 &; 28 @)
% 0.27/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 9 ( 6 avg)
% 0.27/0.47 % Number of types : 2 ( 1 usr)
% 0.27/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.27/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.27/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.47
% 0.27/0.47 % Comments :
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(frac_type,type,
% 0.27/0.47 frac: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(x,type,
% 0.27/0.47 x: frac ).
% 0.27/0.47
% 0.27/0.47 thf(y,type,
% 0.27/0.47 y: frac ).
% 0.27/0.47
% 0.27/0.47 thf(z,type,
% 0.27/0.47 z: frac ).
% 0.27/0.47
% 0.27/0.47 thf(eq,type,
% 0.27/0.47 eq: frac > frac > $o ).
% 0.27/0.47
% 0.27/0.47 thf(pf,type,
% 0.27/0.47 pf: frac > frac > frac ).
% 0.27/0.47
% 0.27/0.47 thf(e,axiom,
% 0.27/0.47 eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) ).
% 0.27/0.47
% 0.27/0.47 thf(satz63b,axiom,
% 0.27/0.47 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.27/0.47 ( ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) )
% 0.27/0.47 => ( eq @ Xx @ Xy ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(satz39,axiom,
% 0.27/0.47 ! [Xx: frac,Xy: frac,Xz: frac] :
% 0.27/0.47 ( ( eq @ Xx @ Xy )
% 0.27/0.47 => ( ( eq @ Xy @ Xz )
% 0.27/0.47 => ( eq @ Xx @ Xz ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(satz58,axiom,
% 0.27/0.47 ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(satz63e,conjecture,
% 0.27/0.47 eq @ x @ y ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.45/1.27 ---- Embedded in THF ---
% 1.45/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.27 %%% Generated on Tue Feb 24 11:13:13 EST 2026
% 1.45/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.27 %%% Logic specification used:
% 1.45/1.27 %%% thf(spec, logic, $$dhol).
% 1.45/1.27
% 1.45/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2DTF22209.p
% See solution above
% 1.45/1.27 ------------------------
% 1.45/1.28 ---- Cleaned THF ---
% 1.45/1.28 thf(frac_type,type,
% 1.45/1.28 frac: $tType ).
% 1.45/1.28
% 1.45/1.28 thf(x,type,
% 1.45/1.28 x: frac ).
% 1.45/1.28
% 1.45/1.28 thf(y,type,
% 1.45/1.28 y: frac ).
% 1.45/1.28
% 1.45/1.28 thf(z,type,
% 1.45/1.28 z: frac ).
% 1.45/1.28
% 1.45/1.28 thf(eq,type,
% 1.45/1.28 eq: frac > frac > $o ).
% 1.45/1.28
% 1.45/1.28 thf(pf,type,
% 1.45/1.28 pf: frac > frac > frac ).
% 1.45/1.28
% 1.45/1.28 thf(e,axiom,
% 1.45/1.28 eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) ).
% 1.45/1.28
% 1.45/1.28 thf(satz63b,axiom,
% 1.45/1.28 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.45/1.28 ( ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xz ) )
% 1.45/1.28 => ( eq @ Xx @ Xy ) ) ).
% 1.45/1.28
% 1.45/1.28 thf(satz39,axiom,
% 1.45/1.28 ! [Xx: frac,Xy: frac,Xz: frac] :
% 1.45/1.28 ( ( eq @ Xx @ Xy )
% 1.45/1.28 => ( ( eq @ Xy @ Xz )
% 1.45/1.28 => ( eq @ Xx @ Xz ) ) ) ).
% 1.45/1.28
% 1.45/1.28 thf(satz58,axiom,
% 1.45/1.28 ! [Xx: frac,Xy: frac] : ( eq @ ( pf @ Xx @ Xy ) @ ( pf @ Xy @ Xx ) ) ).
% 1.45/1.28
% 1.45/1.28 thf(satz63e,conjecture,
% 1.45/1.28 eq @ x @ y ).
% 1.45/1.28 ------------------------
% 1.45/1.30 % (22487)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22209 for (2999ds/2Mi)
% 1.45/1.30 % (22487)Instruction limit reached!
% 1.45/1.30 % (22487)------------------------------
% 1.45/1.30 % (22487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.30 % (22487)Termination reason: Unknown
% 1.45/1.30 % (22487)Termination phase: Saturation
% 1.45/1.30
% 1.45/1.30 % (22487)Memory used [KB]: 5373
% 1.45/1.30 % (22487)Time elapsed: 0.002 s
% 1.45/1.30 % (22487)Instructions burned: 2 (million)
% 1.45/1.30 % (22487)------------------------------
% 1.45/1.30 % (22487)------------------------------
% 1.61/1.30 % (22485)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_22209 for (2999ds/4Mi)
% 1.61/1.30 % (22484)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22209 for (2999ds/183Mi)
% 1.61/1.30 % (22486)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_22209 for (2999ds/27Mi)
% 1.61/1.30 % (22488)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_22209 for (2999ds/2Mi)
% 1.61/1.30 % (22490)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22209 for (2999ds/18Mi)
% 1.61/1.30 % (22489)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_22209 for (2999ds/275Mi)
% 1.61/1.30 % (22488)Instruction limit reached!
% 1.61/1.30 % (22488)------------------------------
% 1.61/1.30 % (22488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (22488)Termination reason: Unknown
% 1.61/1.30 % (22488)Termination phase: Property scanning
% 1.61/1.30
% 1.61/1.30 % (22488)Memory used [KB]: 895
% 1.61/1.30 % (22488)Time elapsed: 0.003 s
% 1.61/1.30 % (22488)Instructions burned: 2 (million)
% 1.61/1.30 % (22488)------------------------------
% 1.61/1.30 % (22488)------------------------------
% 1.61/1.31 % (22491)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22209 for (2999ds/3Mi)
% 1.61/1.31 % (22485)Instruction limit reached!
% 1.61/1.31 % (22485)------------------------------
% 1.61/1.31 % (22485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (22485)Termination reason: Unknown
% 1.61/1.31 % (22485)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (22485)Memory used [KB]: 5500
% 1.61/1.31 % (22485)Time elapsed: 0.005 s
% 1.61/1.31 % (22485)Instructions burned: 4 (million)
% 1.61/1.31 % (22485)------------------------------
% 1.61/1.31 % (22485)------------------------------
% 1.61/1.31 % (22491)Instruction limit reached!
% 1.61/1.31 % (22491)------------------------------
% 1.61/1.31 % (22491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (22491)Termination reason: Unknown
% 1.61/1.31 % (22491)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (22491)Memory used [KB]: 5500
% 1.61/1.31 % (22491)Time elapsed: 0.002 s
% 1.61/1.31 % (22491)Instructions burned: 3 (million)
% 1.61/1.31 % (22491)------------------------------
% 1.61/1.31 % (22491)------------------------------
% 1.61/1.31 % (22490)First to succeed.
% 1.61/1.31 % (22486)Also succeeded, but the first one will report.
% 1.61/1.31 % (22490)Refutation found. Thanks to Tanya!
% 1.61/1.31 % SZS status Theorem for DTF2THF_22209
% 1.61/1.31 % SZS output start Proof for DTF2THF_22209
% 1.61/1.31 thf(type_def_5, type, frac: $tType).
% 1.61/1.31 thf(func_def_0, type, frac: $tType).
% 1.61/1.31 thf(func_def_1, type, x: frac).
% 1.61/1.31 thf(func_def_2, type, y: frac).
% 1.61/1.31 thf(func_def_3, type, z: frac).
% 1.61/1.31 thf(func_def_4, type, eq: frac > frac > $o).
% 1.61/1.31 thf(func_def_5, type, pf: frac > frac > frac).
% 1.61/1.31 thf(f63,plain,(
% 1.61/1.31 $false),
% 1.61/1.31 inference(subsumption_resolution,[status(thm)],[f60,f26])).
% 1.61/1.31 thf(f26,plain,(
% 1.61/1.31 ((eq @ x @ y) != $true)),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f18])).
% 1.61/1.31 thf(f18,plain,(
% 1.61/1.31 ((eq @ x @ y) != $true)),
% 1.61/1.31 inference(flattening,[status(thm)],[f9])).
% 1.61/1.31 thf(f9,plain,(
% 1.61/1.31 ~((eq @ x @ y) = $true)),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.61/1.31 thf(f8,plain,(
% 1.61/1.31 ~(eq @ x @ y)),
% 1.61/1.31 inference(rectify,[status(thm)],[f6])).
% 1.61/1.31 thf(f6,negated_conjecture,(
% 1.61/1.31 ~(eq @ x @ y)),
% 1.61/1.31 inference(negated_conjecture,[status(cth)],[f5])).
% 1.61/1.31 thf(f5,conjecture,(
% 1.61/1.31 (eq @ x @ y)),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',satz63e)).
% 1.61/1.31 thf(f60,plain,(
% 1.61/1.31 ((eq @ x @ y) = $true)),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.61/1.31 thf(f57,plain,(
% 1.61/1.31 ((eq @ x @ y) = $true) | ($true != $true)),
% 1.61/1.31 inference(superposition,[status(thm)],[f28,f49])).
% 1.61/1.31 thf(f49,plain,(
% 1.61/1.31 ((eq @ (pf @ x @ z) @ (pf @ y @ z)) = $true)),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.61/1.31 thf(f47,plain,(
% 1.61/1.31 ($true != $true) | ((eq @ (pf @ x @ z) @ (pf @ y @ z)) = $true)),
% 1.61/1.31 inference(superposition,[status(thm)],[f33,f41])).
% 1.61/1.31 thf(f41,plain,(
% 1.61/1.31 ((eq @ (pf @ x @ z) @ (pf @ z @ y)) = $true)),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.61/1.31 thf(f39,plain,(
% 1.61/1.31 ($true != $true) | ((eq @ (pf @ x @ z) @ (pf @ z @ y)) = $true)),
% 1.61/1.31 inference(superposition,[status(thm)],[f32,f25])).
% 1.61/1.31 thf(f25,plain,(
% 1.61/1.31 ( ! [X0 : frac,X1 : frac] : (((eq @ (pf @ X1 @ X0) @ (pf @ X0 @ X1)) = $true)) )),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f22])).
% 1.61/1.31 thf(f22,plain,(
% 1.61/1.31 ! [X0 : frac,X1 : frac] : ((eq @ (pf @ X1 @ X0) @ (pf @ X0 @ X1)) = $true)),
% 1.61/1.31 inference(rectify,[status(thm)],[f15])).
% 1.61/1.31 thf(f15,plain,(
% 1.61/1.31 ! [X1 : frac,X0 : frac] : ((eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0)) = $true)),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f14])).
% 1.61/1.31 thf(f14,plain,(
% 1.61/1.31 ! [X0 : frac,X1 : frac] : (eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))),
% 1.61/1.31 inference(rectify,[status(thm)],[f4])).
% 1.61/1.31 thf(f4,axiom,(
% 1.61/1.31 ! [X0 : frac,X1 : frac] : (eq @ (pf @ X0 @ X1) @ (pf @ X1 @ X0))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',satz58)).
% 1.61/1.31 thf(f32,plain,(
% 1.61/1.31 ( ! [X0 : frac] : (((eq @ X0 @ (pf @ z @ x)) != $true) | ((eq @ X0 @ (pf @ z @ y)) = $true)) )),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.61/1.31 thf(f31,plain,(
% 1.61/1.31 ( ! [X0 : frac] : (($true != $true) | ((eq @ X0 @ (pf @ z @ x)) != $true) | ((eq @ X0 @ (pf @ z @ y)) = $true)) )),
% 1.61/1.31 inference(superposition,[status(thm)],[f29,f27])).
% 1.61/1.31 thf(f27,plain,(
% 1.61/1.31 ((eq @ (pf @ z @ x) @ (pf @ z @ y)) = $true)),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f13])).
% 1.61/1.31 thf(f13,plain,(
% 1.61/1.31 ((eq @ (pf @ z @ x) @ (pf @ z @ y)) = $true)),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f12])).
% 1.61/1.31 thf(f12,plain,(
% 1.61/1.31 (eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 1.61/1.31 inference(rectify,[status(thm)],[f1])).
% 1.61/1.31 thf(f1,axiom,(
% 1.61/1.31 (eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',e)).
% 1.61/1.31 thf(f29,plain,(
% 1.61/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X2 @ X0) != $true) | ((eq @ X1 @ X2) != $true) | ((eq @ X1 @ X0) = $true)) )),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f24])).
% 1.61/1.31 thf(f24,plain,(
% 1.61/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : (((eq @ X2 @ X0) != $true) | ((eq @ X1 @ X2) != $true) | ((eq @ X1 @ X0) = $true))),
% 1.61/1.31 inference(rectify,[status(thm)],[f20])).
% 1.61/1.31 thf(f20,plain,(
% 1.61/1.31 ! [X1 : frac,X0 : frac,X2 : frac] : (((eq @ X2 @ X1) != $true) | ((eq @ X0 @ X2) != $true) | ((eq @ X0 @ X1) = $true))),
% 1.61/1.31 inference(flattening,[status(thm)],[f19])).
% 1.61/1.31 thf(f19,plain,(
% 1.61/1.31 ! [X2 : frac,X0 : frac,X1 : frac] : ((((eq @ X0 @ X1) = $true) | ((eq @ X2 @ X1) != $true)) | ((eq @ X0 @ X2) != $true))),
% 1.61/1.31 inference(ennf_transformation,[status(thm)],[f17])).
% 1.61/1.31 thf(f17,plain,(
% 1.61/1.31 ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X0 @ X2) = $true) => (((eq @ X2 @ X1) = $true) => ((eq @ X0 @ X1) = $true)))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f16])).
% 1.61/1.31 thf(f16,plain,(
% 1.61/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X2) => ((eq @ X2 @ X1) => (eq @ X0 @ X1)))),
% 1.61/1.31 inference(rectify,[status(thm)],[f3])).
% 1.61/1.31 thf(f3,axiom,(
% 1.61/1.31 ! [X0 : frac,X2 : frac,X1 : frac] : ((eq @ X0 @ X1) => ((eq @ X1 @ X2) => (eq @ X0 @ X2)))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',satz39)).
% 1.61/1.31 thf(f33,plain,(
% 1.61/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (((eq @ X2 @ (pf @ X0 @ X1)) != $true) | ((eq @ X2 @ (pf @ X1 @ X0)) = $true)) )),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.61/1.31 thf(f30,plain,(
% 1.61/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ((eq @ X2 @ (pf @ X1 @ X0)) = $true) | ((eq @ X2 @ (pf @ X0 @ X1)) != $true)) )),
% 1.61/1.31 inference(superposition,[status(thm)],[f29,f25])).
% 1.61/1.31 thf(f28,plain,(
% 1.61/1.31 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != (eq @ (pf @ X0 @ X1) @ (pf @ X2 @ X1))) | ((eq @ X0 @ X2) = $true)) )),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.61/1.31 thf(f23,plain,(
% 1.61/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : (($true != (eq @ (pf @ X0 @ X1) @ (pf @ X2 @ X1))) | ((eq @ X0 @ X2) = $true))),
% 1.61/1.31 inference(rectify,[status(thm)],[f21])).
% 1.61/1.31 thf(f21,plain,(
% 1.61/1.31 ! [X0 : frac,X2 : frac,X1 : frac] : (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)) != $true) | ((eq @ X0 @ X1) = $true))),
% 1.61/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.61/1.31 thf(f11,plain,(
% 1.61/1.31 ! [X2 : frac,X1 : frac,X0 : frac] : (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)) = $true) => ((eq @ X0 @ X1) = $true))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.61/1.31 thf(f10,plain,(
% 1.61/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)) => (eq @ X0 @ X1))),
% 1.61/1.31 inference(rectify,[status(thm)],[f2])).
% 1.61/1.31 thf(f2,axiom,(
% 1.61/1.31 ! [X0 : frac,X1 : frac,X2 : frac] : ((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)) => (eq @ X0 @ X1))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.f7mXuFoFCU/DTF2THF_22209.p',satz63b)).
% 1.61/1.31 % SZS output end Proof for DTF2THF_22209
% 1.61/1.31 % (22490)------------------------------
% 1.61/1.31 % (22490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (22490)Termination reason: Refutation
% 1.61/1.31
% 1.61/1.31 % (22490)Memory used [KB]: 5500
% 1.61/1.31 % (22490)Time elapsed: 0.009 s
% 1.61/1.31 % (22490)Instructions burned: 9 (million)
% 1.61/1.31 % (22490)------------------------------
% 1.61/1.31 % (22490)------------------------------
% 1.61/1.31 % (22483)Success in time 0.024 s
%------------------------------------------------------------------------------