%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM748^1 : 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 : n015.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 09:24:32 AM UTC 2026
% Result : Theorem 1.72s 1.42s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 13 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 311 ( 7 ~; 0 |; 0 &; 304 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_7,type,
nat: $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,
eq: frac > frac > $o ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
fr: nat > nat > frac ).
thf(func_def_6,type,
pl: nat > nat > nat ).
thf(func_def_7,type,
ts: nat > nat > nat ).
thf(func_def_8,type,
num: frac > nat ).
thf(func_def_9,type,
den: frac > nat ).
thf(f20,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f19,f16]) ).
thf(f16,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: frac] : ( eq @ X0 @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.JefQUiK3Iu/DTF2THF_7339.p',satz37) ).
thf(f19,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f18,f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.JefQUiK3Iu/DTF2THF_7339.p',satz29) ).
thf(f18,plain,
( $true
!= ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f17,f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.JefQUiK3Iu/DTF2THF_7339.p',satz6) ).
thf(f17,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JefQUiK3Iu/DTF2THF_7339.p',satz58) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM748^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n015.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:13:01 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : NUM748^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.47 % Domain : Number Theory
% 0.20/0.47 % Problem : Landau theorem 58
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : eq (fr (pl (ts (num x) (den y)) (ts (num y) (den x))) (ts (den x)
% 0.20/0.47 % (den y))) (fr (pl (ts (num y) (den x)) (ts (num x) (den y)))
% 0.20/0.47 % (ts (den y) (den x)))
% 0.20/0.47
% 0.20/0.47 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.47 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : satz58 [Lan30]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % : Without extensionality : Theorem
% 0.20/0.47 % Rating : 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.20/0.47 % Syntax : Number of formulae : 14 ( 4 unt; 10 typ; 0 def)
% 0.20/0.47 % Number of atoms : 4 ( 2 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.47 % Number of connectives : 44 ( 0 ~; 0 |; 0 &; 44 @)
% 0.20/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 10 ( 5 avg)
% 0.20/0.47 % Number of types : 3 ( 2 usr)
% 0.20/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 9 ( 8 usr; 2 con; 0-2 aty)
% 0.20/0.47 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments :
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(frac_type,type,
% 0.20/0.47 frac: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(x,type,
% 0.20/0.47 x: frac ).
% 0.20/0.47
% 0.20/0.47 thf(y,type,
% 0.20/0.47 y: frac ).
% 0.20/0.47
% 0.20/0.47 thf(eq,type,
% 0.20/0.47 eq: frac > frac > $o ).
% 0.20/0.47
% 0.20/0.47 thf(nat_type,type,
% 0.20/0.47 nat: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(fr,type,
% 0.20/0.47 fr: nat > nat > frac ).
% 0.20/0.47
% 0.20/0.47 thf(pl,type,
% 0.20/0.47 pl: nat > nat > nat ).
% 0.20/0.47
% 0.20/0.47 thf(ts,type,
% 0.20/0.47 ts: nat > nat > nat ).
% 0.20/0.47
% 0.20/0.47 thf(num,type,
% 0.20/0.47 num: frac > nat ).
% 0.20/0.47
% 0.20/0.47 thf(den,type,
% 0.20/0.47 den: frac > nat ).
% 0.20/0.47
% 0.20/0.47 thf(satz37,axiom,
% 0.20/0.47 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz29,axiom,
% 0.20/0.47 ! [Xx: nat,Xy: nat] :
% 0.20/0.47 ( ( ts @ Xx @ Xy )
% 0.20/0.47 = ( ts @ Xy @ Xx ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz6,axiom,
% 0.20/0.47 ! [Xx: nat,Xy: nat] :
% 0.20/0.47 ( ( pl @ Xx @ Xy )
% 0.20/0.47 = ( pl @ Xy @ Xx ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(satz58,conjecture,
% 0.20/0.47 eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.52/1.38 ---- Embedded in THF ---
% 1.52/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.38 %%% Generated on Tue Feb 24 11:13:02 EST 2026
% 1.52/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.38 %%% Logic specification used:
% 1.52/1.38 %%% thf(spec, logic, $$dhol).
% 1.52/1.38
% 1.52/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JefQUiK3Iu/DTF2DTF7339.p
% See solution above
% 1.52/1.38 ------------------------
% 1.52/1.39 ---- Cleaned THF ---
% 1.52/1.39 thf(frac_type,type,
% 1.52/1.39 frac: $tType ).
% 1.52/1.39
% 1.52/1.39 thf(x,type,
% 1.52/1.39 x: frac ).
% 1.52/1.39
% 1.52/1.39 thf(y,type,
% 1.52/1.39 y: frac ).
% 1.52/1.39
% 1.52/1.39 thf(eq,type,
% 1.52/1.39 eq: frac > frac > $o ).
% 1.52/1.39
% 1.52/1.39 thf(nat_type,type,
% 1.52/1.39 nat: $tType ).
% 1.52/1.39
% 1.52/1.39 thf(fr,type,
% 1.52/1.39 fr: nat > nat > frac ).
% 1.52/1.39
% 1.52/1.39 thf(pl,type,
% 1.52/1.39 pl: nat > nat > nat ).
% 1.52/1.39
% 1.52/1.39 thf(ts,type,
% 1.52/1.39 ts: nat > nat > nat ).
% 1.52/1.39
% 1.52/1.39 thf(num,type,
% 1.52/1.39 num: frac > nat ).
% 1.52/1.39
% 1.52/1.39 thf(den,type,
% 1.52/1.39 den: frac > nat ).
% 1.52/1.39
% 1.52/1.39 thf(satz37,axiom,
% 1.52/1.39 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 1.52/1.39
% 1.52/1.39 thf(satz29,axiom,
% 1.52/1.39 ! [Xx: nat,Xy: nat] :
% 1.52/1.39 ( ( ts @ Xx @ Xy )
% 1.52/1.39 = ( ts @ Xy @ Xx ) ) ).
% 1.52/1.39
% 1.52/1.39 thf(satz6,axiom,
% 1.52/1.39 ! [Xx: nat,Xy: nat] :
% 1.52/1.39 ( ( pl @ Xx @ Xy )
% 1.52/1.39 = ( pl @ Xy @ Xx ) ) ).
% 1.52/1.39
% 1.52/1.39 thf(satz58,conjecture,
% 1.52/1.39 eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ).
% 1.52/1.39 ------------------------
% 1.72/1.41 % (7441)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_7339 for (2999ds/2Mi)
% 1.72/1.41 % (7440)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7339 for (2999ds/2Mi)
% 1.72/1.41 % (7439)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_7339 for (2999ds/27Mi)
% 1.72/1.41 % (7443)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7339 for (2999ds/18Mi)
% 1.72/1.41 % (7437)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7339 for (2999ds/183Mi)
% 1.72/1.41 % (7438)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_7339 for (2999ds/4Mi)
% 1.72/1.41 % (7442)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_7339 for (2999ds/275Mi)
% 1.72/1.41 % (7440)Instruction limit reached!
% 1.72/1.41 % (7440)------------------------------
% 1.72/1.41 % (7440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (7440)Termination reason: Unknown
% 1.72/1.42 % (7441)Instruction limit reached!
% 1.72/1.42 % (7441)------------------------------
% 1.72/1.42 % (7441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (7441)Termination reason: Unknown
% 1.72/1.42 % (7441)Termination phase: Saturation
% 1.72/1.42
% 1.72/1.42 % (7441)Memory used [KB]: 1023
% 1.72/1.42 % (7441)Time elapsed: 0.003 s
% 1.72/1.42 % (7441)Instructions burned: 2 (million)
% 1.72/1.42 % (7441)------------------------------
% 1.72/1.42 % (7441)------------------------------
% 1.72/1.42 % (7440)Termination phase: Saturation
% 1.72/1.42
% 1.72/1.42 % (7440)Memory used [KB]: 5373
% 1.72/1.42 % (7440)Time elapsed: 0.003 s
% 1.72/1.42 % (7440)Instructions burned: 2 (million)
% 1.72/1.42 % (7440)------------------------------
% 1.72/1.42 % (7440)------------------------------
% 1.72/1.42 % (7442)First to succeed.
% 1.72/1.42 % (7438)Instruction limit reached!
% 1.72/1.42 % (7438)------------------------------
% 1.72/1.42 % (7438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (7438)Termination reason: Unknown
% 1.72/1.42 % (7438)Termination phase: Saturation
% 1.72/1.42
% 1.72/1.42 % (7438)Memory used [KB]: 5500
% 1.72/1.42 % (7438)Time elapsed: 0.004 s
% 1.72/1.42 % (7438)Instructions burned: 4 (million)
% 1.72/1.42 % (7438)------------------------------
% 1.72/1.42 % (7438)------------------------------
% 1.72/1.42 % (7442)Refutation found. Thanks to Tanya!
% 1.72/1.42 % SZS status Theorem for DTF2THF_7339
% 1.72/1.42 % SZS output start Proof for DTF2THF_7339
% 1.72/1.42 thf(type_def_5, type, frac: $tType).
% 1.72/1.42 thf(type_def_7, type, nat: $tType).
% 1.72/1.42 thf(func_def_0, type, frac: $tType).
% 1.72/1.42 thf(func_def_1, type, x: frac).
% 1.72/1.42 thf(func_def_2, type, y: frac).
% 1.72/1.42 thf(func_def_3, type, eq: frac > frac > $o).
% 1.72/1.42 thf(func_def_4, type, nat: $tType).
% 1.72/1.42 thf(func_def_5, type, fr: nat > nat > frac).
% 1.72/1.42 thf(func_def_6, type, pl: nat > nat > nat).
% 1.72/1.42 thf(func_def_7, type, ts: nat > nat > nat).
% 1.72/1.42 thf(func_def_8, type, num: frac > nat).
% 1.72/1.42 thf(func_def_9, type, den: frac > nat).
% 1.72/1.42 thf(f20,plain,(
% 1.72/1.42 $false),
% 1.72/1.42 inference(subsumption_resolution,[status(thm)],[f19,f16])).
% 1.72/1.42 thf(f16,plain,(
% 1.72/1.42 ( ! [X0 : frac] : (((eq @ X0 @ X0) = $true)) )),
% 1.72/1.42 inference(cnf_transformation,[status(thm)],[f10])).
% 1.72/1.42 thf(f10,plain,(
% 1.72/1.42 ! [X0 : frac] : ((eq @ X0 @ X0) = $true)),
% 1.72/1.42 inference(fool_elimination,[status(thm)],[f9])).
% 1.72/1.42 thf(f9,plain,(
% 1.72/1.42 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.72/1.42 inference(rectify,[status(thm)],[f1])).
% 1.72/1.42 thf(f1,axiom,(
% 1.72/1.42 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.72/1.42 file('/export/starexec/sandbox/tmp/tmp.JefQUiK3Iu/DTF2THF_7339.p',satz37)).
% 1.72/1.42 thf(f19,plain,(
% 1.72/1.42 ((eq @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ x) @ (den @ y)))) != $true)),
% 1.72/1.42 inference(forward_demodulation,[status(thm)],[f18,f14])).
% 1.72/1.42 thf(f14,plain,(
% 1.72/1.42 ( ! [X0 : nat,X1 : nat] : (((ts @ X0 @ X1) = (ts @ X1 @ X0))) )),
% 1.72/1.42 inference(cnf_transformation,[status(thm)],[f13])).
% 1.72/1.42 thf(f13,plain,(
% 1.72/1.42 ! [X0 : nat,X1 : nat] : ((ts @ X0 @ X1) = (ts @ X1 @ X0))),
% 1.72/1.42 inference(rectify,[status(thm)],[f2])).
% 1.72/1.42 thf(f2,axiom,(
% 1.72/1.42 ! [X1 : nat,X0 : nat] : ((ts @ X0 @ X1) = (ts @ X1 @ X0))),
% 1.72/1.42 file('/export/starexec/sandbox/tmp/tmp.JefQUiK3Iu/DTF2THF_7339.p',satz29)).
% 1.72/1.42 thf(f18,plain,(
% 1.72/1.42 ($true != (eq @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ y) @ (den @ x)))))),
% 1.72/1.42 inference(forward_demodulation,[status(thm)],[f17,f15])).
% 1.72/1.42 thf(f15,plain,(
% 1.72/1.42 ( ! [X0 : nat,X1 : nat] : (((pl @ X0 @ X1) = (pl @ X1 @ X0))) )),
% 1.72/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.72/1.42 thf(f12,plain,(
% 1.72/1.42 ! [X0 : nat,X1 : nat] : ((pl @ X0 @ X1) = (pl @ X1 @ X0))),
% 1.72/1.42 inference(rectify,[status(thm)],[f3])).
% 1.72/1.42 thf(f3,axiom,(
% 1.72/1.42 ! [X1 : nat,X0 : nat] : ((pl @ X0 @ X1) = (pl @ X1 @ X0))),
% 1.72/1.42 file('/export/starexec/sandbox/tmp/tmp.JefQUiK3Iu/DTF2THF_7339.p',satz6)).
% 1.72/1.42 thf(f17,plain,(
% 1.72/1.42 ((eq @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (pl @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) @ (ts @ (den @ y) @ (den @ x)))) != $true)),
% 1.72/1.42 inference(cnf_transformation,[status(thm)],[f11])).
% 1.72/1.42 thf(f11,plain,(
% 1.72/1.42 ((eq @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (pl @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) @ (ts @ (den @ y) @ (den @ x)))) != $true)),
% 1.72/1.42 inference(flattening,[status(thm)],[f8])).
% 1.72/1.42 thf(f8,plain,(
% 1.72/1.42 ~((eq @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (pl @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) @ (ts @ (den @ y) @ (den @ x)))) = $true)),
% 1.72/1.42 inference(fool_elimination,[status(thm)],[f7])).
% 1.72/1.42 thf(f7,plain,(
% 1.72/1.42 ~(eq @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (pl @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) @ (ts @ (den @ y) @ (den @ x))))),
% 1.72/1.42 inference(rectify,[status(thm)],[f5])).
% 1.72/1.42 thf(f5,negated_conjecture,(
% 1.72/1.42 ~(eq @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (pl @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) @ (ts @ (den @ y) @ (den @ x))))),
% 1.72/1.42 inference(negated_conjecture,[status(cth)],[f4])).
% 1.72/1.42 thf(f4,conjecture,(
% 1.72/1.42 (eq @ (fr @ (pl @ (ts @ (num @ x) @ (den @ y)) @ (ts @ (num @ y) @ (den @ x))) @ (ts @ (den @ x) @ (den @ y))) @ (fr @ (pl @ (ts @ (num @ y) @ (den @ x)) @ (ts @ (num @ x) @ (den @ y))) @ (ts @ (den @ y) @ (den @ x))))),
% 1.72/1.42 file('/export/starexec/sandbox/tmp/tmp.JefQUiK3Iu/DTF2THF_7339.p',satz58)).
% 1.72/1.42 % SZS output end Proof for DTF2THF_7339
% 1.72/1.42 % (7442)------------------------------
% 1.72/1.42 % (7442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (7442)Termination reason: Refutation
% 1.72/1.42
% 1.72/1.42 % (7442)Memory used [KB]: 5500
% 1.72/1.42 % (7442)Time elapsed: 0.004 s
% 1.72/1.42 % (7442)Instructions burned: 2 (million)
% 1.72/1.42 % (7442)------------------------------
% 1.72/1.42 % (7442)------------------------------
% 1.72/1.42 % (7436)Success in time 0.019 s
%------------------------------------------------------------------------------