%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM729^1 : 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 : n009.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 09:24:27 AM UTC 2026
% Result : Theorem 1.66s 1.32s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 172 ( 11 ~; 4 |; 0 &; 154 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 0 ^; 27 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
frac: $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
x1: nat ).
thf(func_def_2,type,
x2: nat ).
thf(func_def_3,type,
n: nat ).
thf(func_def_4,type,
frac: $tType ).
thf(func_def_5,type,
eq: frac > frac > $o ).
thf(func_def_6,type,
fr: nat > nat > frac ).
thf(func_def_7,type,
ts: nat > nat > nat ).
thf(f21,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f20,f16]) ).
thf(f16,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( eq @ ( fr @ X2 @ X0 ) @ ( fr @ ( ts @ X2 @ X1 ) @ ( ts @ X0 @ X1 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( eq @ ( fr @ X2 @ X0 ) @ ( fr @ ( ts @ X2 @ X1 ) @ ( ts @ X0 @ X1 ) ) )
= $true ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( eq @ ( fr @ X1 @ X2 ) @ ( fr @ ( ts @ X1 @ X0 ) @ ( ts @ X2 @ X0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: nat,X1: nat,X2: nat] : ( eq @ ( fr @ X1 @ X2 ) @ ( fr @ ( ts @ X1 @ X0 ) @ ( ts @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X4: nat,X2: nat,X3: nat] : ( eq @ ( fr @ X2 @ X3 ) @ ( fr @ ( ts @ X2 @ X4 ) @ ( ts @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bIh1Wxilwh/DTF2THF_18242.p',satz40b) ).
thf(f20,plain,
( $true
!= ( eq @ ( fr @ x1 @ x2 ) @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $true != $true )
| ( $true
!= ( eq @ ( fr @ x1 @ x2 ) @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) ) ) ),
inference(superposition,[status(thm)],[f17,f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: frac,X1: frac] :
( ( eq @ X1 @ X0 )
=> ( eq @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: frac,X0: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.bIh1Wxilwh/DTF2THF_18242.p',satz38) ).
thf(f17,plain,
( ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) )
!= $true ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ),
file('/export/starexec/sandbox/tmp/tmp.bIh1Wxilwh/DTF2THF_18242.p',satz40c) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM729^1 : 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
% 0.18/0.34 % Computer : n009.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 11:15:40 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : NUM729^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Number Theory
% 0.28/0.46 % Problem : Landau theorem 40c
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : eq (fr (ts x1 n) (ts x2 n)) (fr x1 x2)
% 0.28/0.46
% 0.28/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.28/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.28/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : satz40c [Lan30]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % : Without extensionality : Theorem
% 0.28/0.46 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 11 ( 2 unt; 8 typ; 0 def)
% 0.28/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.28/0.46 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 24 @)
% 0.28/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 9 ( 7 avg)
% 0.28/0.46 % Number of types : 3 ( 2 usr)
% 0.28/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments :
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(nat_type,type,
% 0.28/0.46 nat: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(x1,type,
% 0.28/0.46 x1: nat ).
% 0.28/0.46
% 0.28/0.46 thf(x2,type,
% 0.28/0.46 x2: nat ).
% 0.28/0.46
% 0.28/0.46 thf(n,type,
% 0.28/0.46 n: nat ).
% 0.28/0.46
% 0.28/0.46 thf(frac_type,type,
% 0.28/0.46 frac: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(eq,type,
% 0.28/0.46 eq: frac > frac > $o ).
% 0.28/0.46
% 0.28/0.46 thf(fr,type,
% 0.28/0.46 fr: nat > nat > frac ).
% 0.28/0.46
% 0.28/0.46 thf(ts,type,
% 0.28/0.46 ts: nat > nat > nat ).
% 0.28/0.46
% 0.28/0.46 thf(satz38,axiom,
% 0.28/0.46 ! [Xx: frac,Xy: frac] :
% 0.28/0.46 ( ( eq @ Xx @ Xy )
% 0.28/0.46 => ( eq @ Xy @ Xx ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz40b,axiom,
% 0.28/0.46 ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( fr @ Xx1 @ Xx2 ) @ ( fr @ ( ts @ Xx1 @ Xn ) @ ( ts @ Xx2 @ Xn ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(satz40c,conjecture,
% 0.28/0.46 eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.46/1.28 ---- 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 11:15:41 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/sandbox/tmp/tmp.bIh1Wxilwh/DTF2DTF18242.p
% See solution above
% 1.46/1.29 ------------------------
% 1.66/1.30 ---- Cleaned THF ---
% 1.66/1.30 thf(nat_type,type,
% 1.66/1.30 nat: $tType ).
% 1.66/1.30
% 1.66/1.30 thf(x1,type,
% 1.66/1.30 x1: nat ).
% 1.66/1.30
% 1.66/1.30 thf(x2,type,
% 1.66/1.30 x2: nat ).
% 1.66/1.30
% 1.66/1.30 thf(n,type,
% 1.66/1.30 n: nat ).
% 1.66/1.30
% 1.66/1.30 thf(frac_type,type,
% 1.66/1.30 frac: $tType ).
% 1.66/1.30
% 1.66/1.30 thf(eq,type,
% 1.66/1.30 eq: frac > frac > $o ).
% 1.66/1.30
% 1.66/1.30 thf(fr,type,
% 1.66/1.30 fr: nat > nat > frac ).
% 1.66/1.30
% 1.66/1.30 thf(ts,type,
% 1.66/1.30 ts: nat > nat > nat ).
% 1.66/1.30
% 1.66/1.30 thf(satz38,axiom,
% 1.66/1.30 ! [Xx: frac,Xy: frac] :
% 1.66/1.30 ( ( eq @ Xx @ Xy )
% 1.66/1.30 => ( eq @ Xy @ Xx ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(satz40b,axiom,
% 1.66/1.30 ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( fr @ Xx1 @ Xx2 ) @ ( fr @ ( ts @ Xx1 @ Xn ) @ ( ts @ Xx2 @ Xn ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(satz40c,conjecture,
% 1.66/1.30 eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) ).
% 1.66/1.30 ------------------------
% 1.66/1.31 % (18354)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_18242 for (2999ds/2Mi)
% 1.66/1.31 % (18354)Instruction limit reached!
% 1.66/1.31 % (18354)------------------------------
% 1.66/1.31 % (18354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (18354)Termination reason: Unknown
% 1.66/1.31 % (18354)Termination phase: Saturation
% 1.66/1.31
% 1.66/1.31 % (18354)Memory used [KB]: 895
% 1.66/1.31 % (18354)Time elapsed: 0.002 s
% 1.66/1.31 % (18354)Instructions burned: 2 (million)
% 1.66/1.31 % (18354)------------------------------
% 1.66/1.31 % (18354)------------------------------
% 1.66/1.32 % (18350)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18242 for (2999ds/183Mi)
% 1.66/1.32 % (18351)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_18242 for (2999ds/4Mi)
% 1.66/1.32 % (18353)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18242 for (2999ds/2Mi)
% 1.66/1.32 % (18352)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_18242 for (2999ds/27Mi)
% 1.66/1.32 % (18355)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_18242 for (2999ds/275Mi)
% 1.66/1.32 % (18356)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18242 for (2999ds/18Mi)
% 1.66/1.32 % (18353)Instruction limit reached!
% 1.66/1.32 % (18353)------------------------------
% 1.66/1.32 % (18353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (18353)Termination reason: Unknown
% 1.66/1.32 % (18353)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (18353)Memory used [KB]: 5373
% 1.66/1.32 % (18353)Time elapsed: 0.003 s
% 1.66/1.32 % (18353)Instructions burned: 2 (million)
% 1.66/1.32 % (18353)------------------------------
% 1.66/1.32 % (18353)------------------------------
% 1.66/1.32 % (18350)First to succeed.
% 1.66/1.32 % (18357)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18242 for (2999ds/3Mi)
% 1.66/1.32 % (18355)Also succeeded, but the first one will report.
% 1.66/1.32 % (18351)Instruction limit reached!
% 1.66/1.32 % (18351)------------------------------
% 1.66/1.32 % (18351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (18351)Termination reason: Unknown
% 1.66/1.32 % (18351)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (18351)Memory used [KB]: 5500
% 1.66/1.32 % (18351)Time elapsed: 0.005 s
% 1.66/1.32 % (18351)Instructions burned: 4 (million)
% 1.66/1.32 % (18351)------------------------------
% 1.66/1.32 % (18351)------------------------------
% 1.66/1.32 % (18357)Instruction limit reached!
% 1.66/1.32 % (18357)------------------------------
% 1.66/1.32 % (18357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (18357)Termination reason: Unknown
% 1.66/1.32 % (18357)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (18357)Memory used [KB]: 5500
% 1.66/1.32 % (18357)Time elapsed: 0.002 s
% 1.66/1.32 % (18357)Instructions burned: 3 (million)
% 1.66/1.32 % (18357)------------------------------
% 1.66/1.32 % (18357)------------------------------
% 1.66/1.32 % (18352)Also succeeded, but the first one will report.
% 1.66/1.32 % (18350)Refutation found. Thanks to Tanya!
% 1.66/1.32 % SZS status Theorem for DTF2THF_18242
% 1.66/1.32 % SZS output start Proof for DTF2THF_18242
% 1.66/1.32 thf(type_def_5, type, nat: $tType).
% 1.66/1.32 thf(type_def_6, type, frac: $tType).
% 1.66/1.32 thf(func_def_0, type, nat: $tType).
% 1.66/1.32 thf(func_def_1, type, x1: nat).
% 1.66/1.32 thf(func_def_2, type, x2: nat).
% 1.66/1.32 thf(func_def_3, type, n: nat).
% 1.66/1.32 thf(func_def_4, type, frac: $tType).
% 1.66/1.32 thf(func_def_5, type, eq: frac > frac > $o).
% 1.66/1.32 thf(func_def_6, type, fr: nat > nat > frac).
% 1.66/1.32 thf(func_def_7, type, ts: nat > nat > nat).
% 1.66/1.32 thf(f21,plain,(
% 1.66/1.32 $false),
% 1.66/1.32 inference(subsumption_resolution,[status(thm)],[f20,f16])).
% 1.66/1.32 thf(f16,plain,(
% 1.66/1.32 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((eq @ (fr @ X2 @ X0) @ (fr @ (ts @ X2 @ X1) @ (ts @ X0 @ X1))) = $true)) )),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.32 thf(f14,plain,(
% 1.66/1.32 ! [X0 : nat,X1 : nat,X2 : nat] : ((eq @ (fr @ X2 @ X0) @ (fr @ (ts @ X2 @ X1) @ (ts @ X0 @ X1))) = $true)),
% 1.66/1.32 inference(rectify,[status(thm)],[f7])).
% 1.66/1.32 thf(f7,plain,(
% 1.66/1.32 ! [X2 : nat,X0 : nat,X1 : nat] : ((eq @ (fr @ X1 @ X2) @ (fr @ (ts @ X1 @ X0) @ (ts @ X2 @ X0))) = $true)),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f6])).
% 1.66/1.32 thf(f6,plain,(
% 1.66/1.32 ! [X0 : nat,X1 : nat,X2 : nat] : (eq @ (fr @ X1 @ X2) @ (fr @ (ts @ X1 @ X0) @ (ts @ X2 @ X0)))),
% 1.66/1.32 inference(rectify,[status(thm)],[f2])).
% 1.66/1.32 thf(f2,axiom,(
% 1.66/1.32 ! [X4 : nat,X2 : nat,X3 : nat] : (eq @ (fr @ X2 @ X3) @ (fr @ (ts @ X2 @ X4) @ (ts @ X3 @ X4)))),
% 1.66/1.32 file('/export/starexec/sandbox/tmp/tmp.bIh1Wxilwh/DTF2THF_18242.p',satz40b)).
% 1.66/1.32 thf(f20,plain,(
% 1.66/1.32 ($true != (eq @ (fr @ x1 @ x2) @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n))))),
% 1.66/1.32 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.66/1.32 thf(f19,plain,(
% 1.66/1.32 ($true != $true) | ($true != (eq @ (fr @ x1 @ x2) @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n))))),
% 1.66/1.32 inference(superposition,[status(thm)],[f17,f18])).
% 1.66/1.32 thf(f18,plain,(
% 1.66/1.32 ( ! [X0 : frac,X1 : frac] : (((eq @ X1 @ X0) = $true) | ((eq @ X0 @ X1) != $true)) )),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.32 thf(f15,plain,(
% 1.66/1.32 ! [X0 : frac,X1 : frac] : (((eq @ X0 @ X1) != $true) | ((eq @ X1 @ X0) = $true))),
% 1.66/1.32 inference(rectify,[status(thm)],[f13])).
% 1.66/1.32 thf(f13,plain,(
% 1.66/1.32 ! [X1 : frac,X0 : frac] : (((eq @ X1 @ X0) != $true) | ((eq @ X0 @ X1) = $true))),
% 1.66/1.32 inference(ennf_transformation,[status(thm)],[f11])).
% 1.66/1.32 thf(f11,plain,(
% 1.66/1.32 ! [X1 : frac,X0 : frac] : (((eq @ X1 @ X0) = $true) => ((eq @ X0 @ X1) = $true))),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.32 thf(f10,plain,(
% 1.66/1.32 ! [X0 : frac,X1 : frac] : ((eq @ X1 @ X0) => (eq @ X0 @ X1))),
% 1.66/1.32 inference(rectify,[status(thm)],[f1])).
% 1.66/1.32 thf(f1,axiom,(
% 1.66/1.32 ! [X1 : frac,X0 : frac] : ((eq @ X0 @ X1) => (eq @ X1 @ X0))),
% 1.66/1.32 file('/export/starexec/sandbox/tmp/tmp.bIh1Wxilwh/DTF2THF_18242.p',satz38)).
% 1.66/1.32 thf(f17,plain,(
% 1.66/1.32 ((eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2)) != $true)),
% 1.66/1.32 inference(cnf_transformation,[status(thm)],[f12])).
% 1.66/1.32 thf(f12,plain,(
% 1.66/1.32 ((eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2)) != $true)),
% 1.66/1.32 inference(flattening,[status(thm)],[f9])).
% 1.66/1.32 thf(f9,plain,(
% 1.66/1.32 ~((eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2)) = $true)),
% 1.66/1.32 inference(fool_elimination,[status(thm)],[f8])).
% 1.66/1.32 thf(f8,plain,(
% 1.66/1.32 ~(eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))),
% 1.66/1.32 inference(rectify,[status(thm)],[f4])).
% 1.66/1.32 thf(f4,negated_conjecture,(
% 1.66/1.32 ~(eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))),
% 1.66/1.32 inference(negated_conjecture,[status(cth)],[f3])).
% 1.66/1.32 thf(f3,conjecture,(
% 1.66/1.32 (eq @ (fr @ (ts @ x1 @ n) @ (ts @ x2 @ n)) @ (fr @ x1 @ x2))),
% 1.66/1.32 file('/export/starexec/sandbox/tmp/tmp.bIh1Wxilwh/DTF2THF_18242.p',satz40c)).
% 1.66/1.32 % SZS output end Proof for DTF2THF_18242
% 1.66/1.32 % (18350)------------------------------
% 1.66/1.32 % (18350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (18350)Termination reason: Refutation
% 1.66/1.32
% 1.66/1.32 % (18350)Memory used [KB]: 5500
% 1.66/1.32 % (18350)Time elapsed: 0.004 s
% 1.66/1.32 % (18350)Instructions burned: 2 (million)
% 1.66/1.32 % (18350)------------------------------
% 1.66/1.32 % (18350)------------------------------
% 1.66/1.32 % (18349)Success in time 0.011 s
%------------------------------------------------------------------------------